Elliptic Curve Digital Signature Algorithm - Bitcoin

ECDSA In Bitcoin

Digital signatures are considered the foundation of online sovereignty. The advent of public-key cryptography in 1976 paved the way for the creation of a global communications tool – the Internet, and a completely new form of money – Bitcoin. Although the fundamental properties of public-key cryptography have not changed much since then, dozens of different open-source digital signature schemes are now available to cryptographers.

How ECDSA was incorporated into Bitcoin

When Satoshi Nakamoto, a mystical founder of the first crypto, started working on Bitcoin, one of the key points was to select the signature schemes for an open and public financial system. The requirements were clear. An algorithm should have been widely used, understandable, safe enough, easy, and, what is more important, open-sourced.
Of all the options available at that time, he chose the one that met these criteria: Elliptic Curve Digital Signature Algorithm, or ECDSA.
At that time, native support for ECDSA was provided in OpenSSL, an open set of encryption tools developed by experienced cipher banks in order to increase the confidentiality of online communications. Compared to other popular schemes, ECDSA had such advantages as:
These are extremely useful features for digital money. At the same time, it provides a proportional level of security: for example, a 256-bit ECDSA key has the same level of security as a 3072-bit RSA key (Rivest, Shamir и Adleman) with a significantly smaller key size.

Basic principles of ECDSA

ECDSA is a process that uses elliptic curves and finite fields to “sign” data in such a way that third parties can easily verify the authenticity of the signature, but the signer himself reserves the exclusive opportunity to create signatures. In the case of Bitcoin, the “data” that is signed is a transaction that transfers ownership of bitcoins.
ECDSA has two separate procedures for signing and verifying. Each procedure is an algorithm consisting of several arithmetic operations. The signature algorithm uses the private key, and the verification algorithm uses only the public key.
To use ECDSA, such protocol as Bitcoin must fix a set of parameters for the elliptic curve and its finite field, so that all users of the protocol know and apply these parameters. Otherwise, everyone will solve their own equations, which will not converge with each other, and they will never agree on anything.
For all these parameters, Bitcoin uses very, very large (well, awesomely incredibly huge) numbers. It is important. In fact, all practical applications of ECDSA use huge numbers. After all, the security of this algorithm relies on the fact that these values are too large to pick up a key with a simple brute force. The 384-bit ECDSA key is considered safe enough for the NSA's most secretive government service (USA).

Replacement of ECDSA

Thanks to the hard work done by Peter Wuille (a famous cryptography specialist) and his colleagues on an improved elliptical curve called secp256k1, Bitcoin's ECDSA has become even faster and more efficient. However, ECDSA still has some shortcomings, which can serve as a sufficient basis for its complete replacement. After several years of research and experimentation, a new signature scheme was established to increase the confidentiality and efficiency of Bitcoin transactions: Schnorr's digital signature scheme.
Schnorr's signature takes the process of using “keys” to a new level. It takes only 64 bytes when it gets into the block, which reduces the space occupied by transactions by 4%. Since transactions with the Schnorr signature are the same size, this makes it possible to pre-calculate the total size of the part of the block that contains such signatures. A preliminary calculation of the block size is the key to its safe increase in the future.
Keep up with the news of the crypto world at CoinJoy.io Follow us on Twitter and Medium. Subscribe to our YouTube channel. Join our Telegram channel. For any inquiries mail us at [[email protected]](mailto:[email protected]).
submitted by CoinjoyAssistant to btc [link] [comments]

ECDSA In Bitcoin

Digital signatures are considered the foundation of online sovereignty. The advent of public-key cryptography in 1976 paved the way for the creation of a global communications tool – the Internet, and a completely new form of money – Bitcoin. Although the fundamental properties of public-key cryptography have not changed much since then, dozens of different open-source digital signature schemes are now available to cryptographers.

How ECDSA was incorporated into Bitcoin

When Satoshi Nakamoto, a mystical founder of the first crypto, started working on Bitcoin, one of the key points was to select the signature schemes for an open and public financial system. The requirements were clear. An algorithm should have been widely used, understandable, safe enough, easy, and, what is more important, open-sourced.
Of all the options available at that time, he chose the one that met these criteria: Elliptic Curve Digital Signature Algorithm, or ECDSA.
At that time, native support for ECDSA was provided in OpenSSL, an open set of encryption tools developed by experienced cipher banks in order to increase the confidentiality of online communications. Compared to other popular schemes, ECDSA had such advantages as:
These are extremely useful features for digital money. At the same time, it provides a proportional level of security: for example, a 256-bit ECDSA key has the same level of security as a 3072-bit RSA key (Rivest, Shamir и Adleman) with a significantly smaller key size.

Basic principles of ECDSA

ECDSA is a process that uses elliptic curves and finite fields to “sign” data in such a way that third parties can easily verify the authenticity of the signature, but the signer himself reserves the exclusive opportunity to create signatures. In the case of Bitcoin, the “data” that is signed is a transaction that transfers ownership of bitcoins.
ECDSA has two separate procedures for signing and verifying. Each procedure is an algorithm consisting of several arithmetic operations. The signature algorithm uses the private key, and the verification algorithm uses only the public key.
To use ECDSA, such protocol as Bitcoin must fix a set of parameters for the elliptic curve and its finite field, so that all users of the protocol know and apply these parameters. Otherwise, everyone will solve their own equations, which will not converge with each other, and they will never agree on anything.
For all these parameters, Bitcoin uses very, very large (well, awesomely incredibly huge) numbers. It is important. In fact, all practical applications of ECDSA use huge numbers. After all, the security of this algorithm relies on the fact that these values are too large to pick up a key with a simple brute force. The 384-bit ECDSA key is considered safe enough for the NSA's most secretive government service (USA).

Replacement of ECDSA

Thanks to the hard work done by Peter Wuille (a famous cryptography specialist) and his colleagues on an improved elliptical curve called secp256k1, Bitcoin's ECDSA has become even faster and more efficient. However, ECDSA still has some shortcomings, which can serve as a sufficient basis for its complete replacement. After several years of research and experimentation, a new signature scheme was established to increase the confidentiality and efficiency of Bitcoin transactions: Schnorr's digital signature scheme.
Schnorr's signature takes the process of using “keys” to a new level. It takes only 64 bytes when it gets into the block, which reduces the space occupied by transactions by 4%. Since transactions with the Schnorr signature are the same size, this makes it possible to pre-calculate the total size of the part of the block that contains such signatures. A preliminary calculation of the block size is the key to its safe increase in the future.
Keep up with the news of the crypto world at CoinJoy.io Follow us on Twitter and Medium. Subscribe to our YouTube channel. Join our Telegram channel. For any inquiries mail us at [[email protected]](mailto:[email protected]).
submitted by CoinjoyAssistant to Bitcoin [link] [comments]

Bitcoin (BTC)A Peer-to-Peer Electronic Cash System.

Bitcoin (BTC)A Peer-to-Peer Electronic Cash System.
  • Bitcoin (BTC) is a peer-to-peer cryptocurrency that aims to function as a means of exchange that is independent of any central authority. BTC can be transferred electronically in a secure, verifiable, and immutable way.
  • Launched in 2009, BTC is the first virtual currency to solve the double-spending issue by timestamping transactions before broadcasting them to all of the nodes in the Bitcoin network. The Bitcoin Protocol offered a solution to the Byzantine Generals’ Problem with a blockchain network structure, a notion first created by Stuart Haber and W. Scott Stornetta in 1991.
  • Bitcoin’s whitepaper was published pseudonymously in 2008 by an individual, or a group, with the pseudonym “Satoshi Nakamoto”, whose underlying identity has still not been verified.
  • The Bitcoin protocol uses an SHA-256d-based Proof-of-Work (PoW) algorithm to reach network consensus. Its network has a target block time of 10 minutes and a maximum supply of 21 million tokens, with a decaying token emission rate. To prevent fluctuation of the block time, the network’s block difficulty is re-adjusted through an algorithm based on the past 2016 block times.
  • With a block size limit capped at 1 megabyte, the Bitcoin Protocol has supported both the Lightning Network, a second-layer infrastructure for payment channels, and Segregated Witness, a soft-fork to increase the number of transactions on a block, as solutions to network scalability.


1. What is Bitcoin (BTC)?

  • Bitcoin is a peer-to-peer cryptocurrency that aims to function as a means of exchange and is independent of any central authority. Bitcoins are transferred electronically in a secure, verifiable, and immutable way.
  • Network validators, whom are often referred to as miners, participate in the SHA-256d-based Proof-of-Work consensus mechanism to determine the next global state of the blockchain.
  • The Bitcoin protocol has a target block time of 10 minutes, and a maximum supply of 21 million tokens. The only way new bitcoins can be produced is when a block producer generates a new valid block.
  • The protocol has a token emission rate that halves every 210,000 blocks, or approximately every 4 years.
  • Unlike public blockchain infrastructures supporting the development of decentralized applications (Ethereum), the Bitcoin protocol is primarily used only for payments, and has only very limited support for smart contract-like functionalities (Bitcoin “Script” is mostly used to create certain conditions before bitcoins are used to be spent).

2. Bitcoin’s core features

For a more beginner’s introduction to Bitcoin, please visit Binance Academy’s guide to Bitcoin.

Unspent Transaction Output (UTXO) model

A UTXO transaction works like cash payment between two parties: Alice gives money to Bob and receives change (i.e., unspent amount). In comparison, blockchains like Ethereum rely on the account model.

Nakamoto consensus

In the Bitcoin network, anyone can join the network and become a bookkeeping service provider i.e., a validator. All validators are allowed in the race to become the block producer for the next block, yet only the first to complete a computationally heavy task will win. This feature is called Proof of Work (PoW).
The probability of any single validator to finish the task first is equal to the percentage of the total network computation power, or hash power, the validator has. For instance, a validator with 5% of the total network computation power will have a 5% chance of completing the task first, and therefore becoming the next block producer.
Since anyone can join the race, competition is prone to increase. In the early days, Bitcoin mining was mostly done by personal computer CPUs.
As of today, Bitcoin validators, or miners, have opted for dedicated and more powerful devices such as machines based on Application-Specific Integrated Circuit (“ASIC”).
Proof of Work secures the network as block producers must have spent resources external to the network (i.e., money to pay electricity), and can provide proof to other participants that they did so.
With various miners competing for block rewards, it becomes difficult for one single malicious party to gain network majority (defined as more than 51% of the network’s hash power in the Nakamoto consensus mechanism). The ability to rearrange transactions via 51% attacks indicates another feature of the Nakamoto consensus: the finality of transactions is only probabilistic.
Once a block is produced, it is then propagated by the block producer to all other validators to check on the validity of all transactions in that block. The block producer will receive rewards in the network’s native currency (i.e., bitcoin) as all validators approve the block and update their ledgers.

The blockchain

Block production

The Bitcoin protocol utilizes the Merkle tree data structure in order to organize hashes of numerous individual transactions into each block. This concept is named after Ralph Merkle, who patented it in 1979.
With the use of a Merkle tree, though each block might contain thousands of transactions, it will have the ability to combine all of their hashes and condense them into one, allowing efficient and secure verification of this group of transactions. This single hash called is a Merkle root, which is stored in the Block Header of a block. The Block Header also stores other meta information of a block, such as a hash of the previous Block Header, which enables blocks to be associated in a chain-like structure (hence the name “blockchain”).
An illustration of block production in the Bitcoin Protocol is demonstrated below.


Block time and mining difficulty

Block time is the period required to create the next block in a network. As mentioned above, the node who solves the computationally intensive task will be allowed to produce the next block. Therefore, block time is directly correlated to the amount of time it takes for a node to find a solution to the task. The Bitcoin protocol sets a target block time of 10 minutes, and attempts to achieve this by introducing a variable named mining difficulty.
Mining difficulty refers to how difficult it is for the node to solve the computationally intensive task. If the network sets a high difficulty for the task, while miners have low computational power, which is often referred to as “hashrate”, it would statistically take longer for the nodes to get an answer for the task. If the difficulty is low, but miners have rather strong computational power, statistically, some nodes will be able to solve the task quickly.
Therefore, the 10 minute target block time is achieved by constantly and automatically adjusting the mining difficulty according to how much computational power there is amongst the nodes. The average block time of the network is evaluated after a certain number of blocks, and if it is greater than the expected block time, the difficulty level will decrease; if it is less than the expected block time, the difficulty level will increase.

What are orphan blocks?

In a PoW blockchain network, if the block time is too low, it would increase the likelihood of nodes producingorphan blocks, for which they would receive no reward. Orphan blocks are produced by nodes who solved the task but did not broadcast their results to the whole network the quickest due to network latency.
It takes time for a message to travel through a network, and it is entirely possible for 2 nodes to complete the task and start to broadcast their results to the network at roughly the same time, while one’s messages are received by all other nodes earlier as the node has low latency.
Imagine there is a network latency of 1 minute and a target block time of 2 minutes. A node could solve the task in around 1 minute but his message would take 1 minute to reach the rest of the nodes that are still working on the solution. While his message travels through the network, all the work done by all other nodes during that 1 minute, even if these nodes also complete the task, would go to waste. In this case, 50% of the computational power contributed to the network is wasted.
The percentage of wasted computational power would proportionally decrease if the mining difficulty were higher, as it would statistically take longer for miners to complete the task. In other words, if the mining difficulty, and therefore targeted block time is low, miners with powerful and often centralized mining facilities would get a higher chance of becoming the block producer, while the participation of weaker miners would become in vain. This introduces possible centralization and weakens the overall security of the network.
However, given a limited amount of transactions that can be stored in a block, making the block time too longwould decrease the number of transactions the network can process per second, negatively affecting network scalability.

3. Bitcoin’s additional features

Segregated Witness (SegWit)

Segregated Witness, often abbreviated as SegWit, is a protocol upgrade proposal that went live in August 2017.
SegWit separates witness signatures from transaction-related data. Witness signatures in legacy Bitcoin blocks often take more than 50% of the block size. By removing witness signatures from the transaction block, this protocol upgrade effectively increases the number of transactions that can be stored in a single block, enabling the network to handle more transactions per second. As a result, SegWit increases the scalability of Nakamoto consensus-based blockchain networks like Bitcoin and Litecoin.
SegWit also makes transactions cheaper. Since transaction fees are derived from how much data is being processed by the block producer, the more transactions that can be stored in a 1MB block, the cheaper individual transactions become.
The legacy Bitcoin block has a block size limit of 1 megabyte, and any change on the block size would require a network hard-fork. On August 1st 2017, the first hard-fork occurred, leading to the creation of Bitcoin Cash (“BCH”), which introduced an 8 megabyte block size limit.
Conversely, Segregated Witness was a soft-fork: it never changed the transaction block size limit of the network. Instead, it added an extended block with an upper limit of 3 megabytes, which contains solely witness signatures, to the 1 megabyte block that contains only transaction data. This new block type can be processed even by nodes that have not completed the SegWit protocol upgrade.
Furthermore, the separation of witness signatures from transaction data solves the malleability issue with the original Bitcoin protocol. Without Segregated Witness, these signatures could be altered before the block is validated by miners. Indeed, alterations can be done in such a way that if the system does a mathematical check, the signature would still be valid. However, since the values in the signature are changed, the two signatures would create vastly different hash values.
For instance, if a witness signature states “6,” it has a mathematical value of 6, and would create a hash value of 12345. However, if the witness signature were changed to “06”, it would maintain a mathematical value of 6 while creating a (faulty) hash value of 67890.
Since the mathematical values are the same, the altered signature remains a valid signature. This would create a bookkeeping issue, as transactions in Nakamoto consensus-based blockchain networks are documented with these hash values, or transaction IDs. Effectively, one can alter a transaction ID to a new one, and the new ID can still be valid.
This can create many issues, as illustrated in the below example:
  1. Alice sends Bob 1 BTC, and Bob sends Merchant Carol this 1 BTC for some goods.
  2. Bob sends Carols this 1 BTC, while the transaction from Alice to Bob is not yet validated. Carol sees this incoming transaction of 1 BTC to him, and immediately ships goods to B.
  3. At the moment, the transaction from Alice to Bob is still not confirmed by the network, and Bob can change the witness signature, therefore changing this transaction ID from 12345 to 67890.
  4. Now Carol will not receive his 1 BTC, as the network looks for transaction 12345 to ensure that Bob’s wallet balance is valid.
  5. As this particular transaction ID changed from 12345 to 67890, the transaction from Bob to Carol will fail, and Bob will get his goods while still holding his BTC.
With the Segregated Witness upgrade, such instances can not happen again. This is because the witness signatures are moved outside of the transaction block into an extended block, and altering the witness signature won’t affect the transaction ID.
Since the transaction malleability issue is fixed, Segregated Witness also enables the proper functioning of second-layer scalability solutions on the Bitcoin protocol, such as the Lightning Network.

Lightning Network

Lightning Network is a second-layer micropayment solution for scalability.
Specifically, Lightning Network aims to enable near-instant and low-cost payments between merchants and customers that wish to use bitcoins.
Lightning Network was conceptualized in a whitepaper by Joseph Poon and Thaddeus Dryja in 2015. Since then, it has been implemented by multiple companies. The most prominent of them include Blockstream, Lightning Labs, and ACINQ.
A list of curated resources relevant to Lightning Network can be found here.
In the Lightning Network, if a customer wishes to transact with a merchant, both of them need to open a payment channel, which operates off the Bitcoin blockchain (i.e., off-chain vs. on-chain). None of the transaction details from this payment channel are recorded on the blockchain, and only when the channel is closed will the end result of both party’s wallet balances be updated to the blockchain. The blockchain only serves as a settlement layer for Lightning transactions.
Since all transactions done via the payment channel are conducted independently of the Nakamoto consensus, both parties involved in transactions do not need to wait for network confirmation on transactions. Instead, transacting parties would pay transaction fees to Bitcoin miners only when they decide to close the channel.
One limitation to the Lightning Network is that it requires a person to be online to receive transactions attributing towards him. Another limitation in user experience could be that one needs to lock up some funds every time he wishes to open a payment channel, and is only able to use that fund within the channel.
However, this does not mean he needs to create new channels every time he wishes to transact with a different person on the Lightning Network. If Alice wants to send money to Carol, but they do not have a payment channel open, they can ask Bob, who has payment channels open to both Alice and Carol, to help make that transaction. Alice will be able to send funds to Bob, and Bob to Carol. Hence, the number of “payment hubs” (i.e., Bob in the previous example) correlates with both the convenience and the usability of the Lightning Network for real-world applications.

Schnorr Signature upgrade proposal

Elliptic Curve Digital Signature Algorithm (“ECDSA”) signatures are used to sign transactions on the Bitcoin blockchain.
However, many developers now advocate for replacing ECDSA with Schnorr Signature. Once Schnorr Signatures are implemented, multiple parties can collaborate in producing a signature that is valid for the sum of their public keys.
This would primarily be beneficial for network scalability. When multiple addresses were to conduct transactions to a single address, each transaction would require their own signature. With Schnorr Signature, all these signatures would be combined into one. As a result, the network would be able to store more transactions in a single block.
The reduced size in signatures implies a reduced cost on transaction fees. The group of senders can split the transaction fees for that one group signature, instead of paying for one personal signature individually.
Schnorr Signature also improves network privacy and token fungibility. A third-party observer will not be able to detect if a user is sending a multi-signature transaction, since the signature will be in the same format as a single-signature transaction.

4. Economics and supply distribution

The Bitcoin protocol utilizes the Nakamoto consensus, and nodes validate blocks via Proof-of-Work mining. The bitcoin token was not pre-mined, and has a maximum supply of 21 million. The initial reward for a block was 50 BTC per block. Block mining rewards halve every 210,000 blocks. Since the average time for block production on the blockchain is 10 minutes, it implies that the block reward halving events will approximately take place every 4 years.
As of May 12th 2020, the block mining rewards are 6.25 BTC per block. Transaction fees also represent a minor revenue stream for miners.
submitted by D-platform to u/D-platform [link] [comments]

Google and NASA have reached quantum supremacy in a year collaboration. What does it mean for future blockchain security?

As can be read in this article. Although quantum supremacy simply means that at least 1 specific problem has been proven to be solved by a quantum computer that can't be solved (in a realistic timeframe) by any existing classical computer, it is a very important milestone. Many have been skeptical on crossing this milestone at all.
Supremacy does not mean that current cryptography is at risk tomorrow. It does however prove quantum computing is real, and has advantage over classical computers in certain tasks as has always been thought. For blockchain this means that in the future, Shor's algorithm could be used to break ECDSA, the signature scheme that is used in most blockchain. This signature scheme can be upgraded to a quantum resistant signature scheme. It does come with specific challenges though. As opposed to banks, websites, government systems, email services etc, blockchain is decentralized. That makes the following challenges exclusive blockchain challenges:
Consider the full analysis on this subject here
Blockchains that implement quantum resistance from the very beginning, from genesis block, will not face these challenges. See for example QRL which has launched over a year ago.
submitted by QRCollector to CryptoCurrency [link] [comments]

Best General RenVM Questions of February 2020

Best General RenVM Questions of January 2020

\These questions are sourced directly from Telegram*
Q: Are all the projects listed in the Ren Alliance, the final set of members?
A: No, please do keep in mind this just our first round of partners, some larger orgs require a bit more DD (i.e our audit). We’ll release the final set of members when Mainnet goes live.

Q: How do projects join the Ren Alliance?
A: It’s simple, just fill out this application. It takes about five minutes, and all you need is your company’s logo files and your preferred area(s) of involvement. Joining the Alliance requires no binding commitments, only a desire to help bring cross-chain assets to DeFi.

Q: For example let's say there is a crypto index which contains 1 BTC and 1 ZEC. I have 1 BTC and 1 ZEC and I would like to “mint” this index token with RenVM. Will something like this possible in the future?
A: This is already possible today. RenVM allows you to mint renBTC and renZEC (and renBCH) on Ethereum. This result is an ERC20 like any other with the addition that when you burn it, you get real BTC and ZEC back.
Another nice feature is that you can directly call smart contracts when minting. This is not possible in any other system, and results in a very clean and simple user experience. People can make a BTC transaction followed by a ZEC transaction and with no other blockchain actions end up with their BTC and ZEC in your example system (your example system would have functions for accepting BTC and ZEC and when receiving both, it would output some kind of index token; exactly how it functions is up to how you want to implement your contract!)

Q: What blockchains does RenVM support?
A: RenVM can support any ECDSA based blockchain but we'll be starting with BTC, ZEC, and BCH. More info here: https://github.com/renproject/ren/wiki/Supported-Blockchains

Q: Another concern is chain rollback. In the case of MakerDAO getting hacked (unlikely, but not impossible), the Ethereum network could rollback just like with the DAO. (Unlikely, but not impossible). But what if the attacker already has deposited the hacked funds into RenVM and gotten a private coin?
A: A roll-back would still revert that state. Privacy on-chain != no state tracking something (just in a way that doesn’t reveal information). So reverts don’t really matter in that sense. They do matter in a broader sense: you have renBTC and you burn it for BTC, then Ethereum rolls back to when you had renBTC still. This is something the Ethereum community has to consider very carefully these days if they were to ever do such a revert. This is an ultimately unavoidable truth RE interoperability; you are compounding risks of the chains you are using. In general, this is why it’s always safer to keep your BTC on Bitcoin unless there is a specific reason you need it on Ethereum at any given point in time.

Q: If BTC can be transferred with zero confirmation how many transactions RenVM can handle?
A: RenVMs throughput isn’t affected by conf-less transactions. This is a service provided by L2 technology (like the 0Conf team, who are building exactly this!). This doesn’t affect RenVM directly, but it does have the pleasant impact that users won’t notice network congestion if it happens.

Q: Can you explain the over-collateralization security dynamic between tBTC and RenVM? Does this play into Maker using RenVM vs. tBTC to collaetize their CDP’s
A1: It’s not the over collateralization that’s the problem. It’s that to get $X BTC they need 1.5x $X ETH locked up in their protocol. What about other places that give better ETH returns? What about the fact that ETH doesn’t go up in price just because tBTC is used?
With REN, we are actually over collateralized (so they’re wrong that they are more secure in this regard). The big difference: BTC flowing through REN increases the value of the REN collateral, increasing the security, increasing the capacity of BTC that can flow through the system. It’s a positive feedback loop for capacity and security that simply doesn’t exist if you don’t use an isolated token.
A2: Maker wants to use BTC to collateralise Dai, because it diversifies risk and expands the possible Dai supply (by expanding possible collateral). If you use tBTC, then tBTC is collateralised by ETH so you actually become less efficient at minting Dai, and you don’t diversify risk because tBTC gets liquidated by ETH price movements.
You don’t want your network secured by collateral that has speculative value that is not correlated with the usage of the network. That makes things unstable.
If RenVM is being used, the value of REN increases, and the more RenVM can be used (and Darknodes get the positive upside of their bond increasing in value). This means by pumping lots of BTC into RenVM, you gain more capacity to pump more BTC into RenVM. This creates a positive feedback loop for the returns earned by Darknodes, the value of their bond, and overall/capacity security of the network.
Compare to tBTC: you are waiting for ETH to go up in value. It’s value, which does not correlate with the amount of BTC in the system, limits the AUM that the system can hold. You’re hoping it will go up independently of the usage of your network and if it doesn’t you’re out of luck. Network growth does not drive the ability for the network to grow. Your are also competing with the returns on ETH that other ecosystems allow you to get (why bond ETH in tBTC if you can get better returns on that ETH in other places; lending it or staking it in Eth2.0). (Btw: we’re doing research to get our collateralisation of REN to 150%. It’s already possible, and could be done today, but we are just seeing if we can make it safelivelier than the current best-in-class algorithms.)

Q: How do we define the value of L and R if we don't use oracle price feed?
A: It will be decided by the Darknodes. The best mechanism of doing this is still being decided upon. However, it won’t simply be taken from the current market price / third-party oracles as those are vulnerable to manipulation. Ultimately, the only valuation that matters is the Darknodes (because they’re the ones being potentially bribed).

Q: In my opinion, RenVM (and tBTC adoption bottleneck: 300% collateral ratio» this ratio is important for security and decentralization» to sustain this ratio we need significant fees to be imposed on Renbtc holders» example: if there was 100m$ Renbtc total supply then we need 300m$ ren locked in darknodes» if 3-5% fees paid for those 300m$ then we need to extract 9-15 million fees from the 100m renbtc» that equal 9-15% annual fees» of course it will be lower with the minting and burning fees but I don't think it will cover half of the total needed fees» the result with the current design there are still too much economic friction IMO.
A: The key thing to keep in mind is velocity. Not just TVL. Let’s take Kyber as an example: they have $4.9M AUM. But, they did $3.7M in trades in the last 24 hours. Over the year, that’s 275x their AUM.
So, if RenVM is holding $100M AUM, and achieves a volume multiplier of 200x then it gets $1M p/a in holding fees but $40M in minting/burning fees. This is all assuming the minimum fee as well (it rises as TVL approaches the limit). So RenVM would need a $300M market cap on $41M in revenue. That’s 13% p/a, assuming we don’t make the move to only 150% collateral. If we do move to that, then it’s almost 33% p/a.
RenVM is by far and away the best UX for instantly swapping BTC on DEXs (with no gas, and no confirmations). All of the interfaces we’re building and the tools we’re providing give people that native experience. This is precisely because high TVL is not what yields good returns and increases cap for the protocol.
Even systems like MakerDAO/Compound have people moving BTC in/out. Their AUM is by no means static. People are constantly opening/closing/liquidating positions and all of this is would create velocity through RenVM.

Q: How was ETHDenver?
A: ETHDenver was great, and very productive, confirmed a lot of our thoughts on what needs to be done but also gave us a good amount of exposure, so overall it was a positive for the team and RenVM.
submitted by RENProtocol to RenProject [link] [comments]

Best General RenVM Questions of January 2020

Best General RenVM Questions of January 2020

‌*These questions are sourced directly from Telegram
Q: When you say RenVM is Trustless, Permissionless, and Decentralized, what does that actually mean?
A: Trustless = RenVM is a virtual machine (a network of nodes, that do computations), this means if you ask RenVM to trade an asset via smart contract logic, it will. No trusted intermediary that holds assets or that you need to rely on. Because RenVM is a decentralized network and computes verified information in a secure environment, no single party can prevent users from sending funds in, withdrawing deposited funds, or computing information needed for updating outside ledgers. RenVM is an agnostic and autonomous virtual broker that holds your digital assets as they move between blockchains.
Permissionless = RenVM is an open protocol; meaning anyone can use RenVM and any project can build with RenVM. You don't need anyone's permission, just plug RenVM into your dApp and you have interoperability.
Decentralized = The nodes that power RenVM ( Darknodes) are scattered throughout the world. RenVM has a peak capacity of up to 10,000 Darknodes (due to REN’s token economics). Realistically, there will probably be 100 - 500 Darknodes run in the initial Mainnet phases, ample decentralized nonetheless.

Q: Okay, so how can you prove this?
A: The publication of our audit results will help prove the trustlessness piece; permissionless and decentralized can be proven today.
Permissionless = https://github.com/renproject/ren-js
Decentralized = https://chaosnet.renproject.io/

Q: How does Ren sMPC work? Sharmir's secret sharing? TSS?
A: There is some confusion here that keeps arising so I will do my best to clarify.TL;DR: *SSS is just data. It’s what you do with the data that matters. RenVM uses sMPC on SSS to create TSS for ECDSA keys.*SSS and TSS aren’t fundamental different things. It’s kind of like asking: do you use numbers, or equations? Equations often (but not always) use numbers or at some point involve numbers.
SSS by itself is just a way of representing secret data (like numbers). sMPC is how to generate and work with that data (like equations). One of the things you can do with that work is produce a form of TSS (this is what RenVM does).
However, TSS is slightly different because it can also be done *without* SSS and sMPC. For example, BLS signatures don’t use SSS or sMPC but they are still a form of TSS.
So, we say that RenVM uses SSS+sMPC because this is more specific than just saying TSS (and you can also do more with SSS+sMPC than just TSS). Specifically, all viable forms of turning ECDSA (a scheme that isn’t naturally threshold based) into a TSS needs SSS+sMPC.
People often get confused about RenVM and claim “SSS can’t be used to sign transactions without making the private key whole again”. That’s a strange statement and shows a fundamental misunderstanding about what SSS is.
To come back to our analogy, it’s like saying “numbers can’t be used to write a book”. That’s kind of true in a direct sense, but there are plenty of ways to encode a book as numbers and then it’s up to how you interpret (how you *use*) those numbers. This is exactly how this text I’m writing is appearing on your screen right now.
SSS is just secret data. It doesn’t make sense to say that SSS *functions*. RenVM is what does the functioning. RenVM *uses* the SSSs to represent private keys. But these are generated and used and destroyed as part of sMPC. The keys are never whole at any point.

Q: Thanks for the explanation. Based on my understanding of SSS, a trusted dealer does need to briefly put the key together. Is this not the case?
A: Remember, SSS is just the representation of a secret. How you get from the secret to its representation is something else. There are many ways to do it. The simplest way is to have a “dealer” that knows the secret and gives out the shares. But, there are other ways. For example: we all act as dealers, and all give each other shares of our individual secret. If there are N of us, we now each have N shares (one from every person). Then we all individually add up the shares that we have. We now each have a share of a “global” secret that no one actually knows. We know this global secret is the sum of everyone’s individual secrets, but unless you know every individual’s secret you cannot know the global secret (even though you have all just collectively generates shares for it). This is an example of an sMPC generation of a random number with collusion resistance against all-but-one adversaries.

Q: If you borrow Ren, you can profit from the opposite Ren gain. That means you could profit from breaking the network and from falling Ren price (because breaking the network, would cause Ren price to drop) (lower amount to be repaid, when the bond gets slashed)
A: Yes, this is why it’s important there has a large number of Darknodes before moving to full decentralisation (large borrowing becomes harder). We’re exploring a few other options too, that should help prevent these kinds of issues.

Q: What are RenVM’s Security and Liveliness parameters?
A: These are discussed in detail in our Wiki, please check it out here: https://github.com/renproject/ren/wiki/Safety-and-Liveliness#analysis

Q: What are the next blockchain under consideration for RenVM?
A: These can be found here: https://github.com/renproject/ren/wiki/Supported-Blockchains

Q: I've just read that Aztec is going to be live this month and currently tests txs with third parties. Are you going to participate in early access or you just more focused on bringing Ren to Subzero stage?
A: At this stage, our entire focus is on Mainnet SubZero. But, we will definitely be following up on integrating with AZTEC once everything is out and stable.

Q: So how does RenVM compare to tBTC, Thorchain, WBTC, etc..?
A: An easy way to think about it is..RenVM’s functionality is a combination of tBTC (+ WBTC by extension), and Thorchain’s (proposed) capabilities... All wrapped into one. Just depends on what the end-user application wants to do with it.

Q1: What are the core technical/security differences between RenVM and tBTC?A1: The algorithm used by tBTC faults if even one node goes offline at the wrong moment (and the whole “keep” of nodes can be penalised for this). RenVM can survive 1/3rd going offline at any point at any time. Advantage for tBTC is that collusion is harder, disadvantage is obviously availability and permissionlessness is lower.
tBTC an only mint/burn lots of 1 BTC and requires an on-Ethereum SPV relay for Bitcoin headers (and for any other chain it adds). No real advantage trade-off IMO.
tBTC has a liquidation mechanism that means nodes can have their bond liquidated because of ETH/BTC price ratio. Advantage means users can get 1 BTC worth of ETH. Disadvantage is it means tBTC is kind of a synthetic: needs a price feed, needs liquid markets for liquidation, users must accept exposure to ETH even if they only hold tBTC, nodes must stay collateralized or lose lots of ETH. RenVM doesn’t have this, and instead uses fees to prevent becoming under-collateralized. This requires a mature market, and assumed Darknodes will value their REN bonds fairly (based on revenue, not necessarily what they can sell it for at current —potentially manipulated—market value). That can be an advantage or disadvantage depending on how you feel.
tBTC focuses more on the idea of a tokenized version of BTC that feels like an ERC20 to the user (and is). RenVM focuses more on letting the user interact with DeFi and use real BTC and real Bitcoin transactions to do so (still an ERC20 under the hood, but the UX is more fluid and integrated). Advantage of tBTC is that it’s probably easier to understand and that might mean better overall experience, disadvantage really comes back to that 1 BTC limit and the need for a more clunky minting/burning experience that might mean worse overall experience. Too early to tell, different projects taking different bets.
tBTC supports BTC (I think they have ZEC these days too). RenVM supports BTC, BCH, and ZEC (docs discuss Matic, XRP, and LTC).
Q2: This are my assumed differences between tBTC and RenVM, are they correct? Some key comparisons:
-Both are vulnerable to oracle attacks
-REN federation failure results in loss or theft of all funds
-tBTC failures tend to result in frothy markets, but holders of tBTC are made whole
-REN quorum rotation is new crypto, and relies on honest deletion of old key shares
-tBTC rotates micro-quorums regularly without relying on honest deletion
-tBTC relies on an SPV relay
-REN relies on federation honesty to fill the relay's purpose
-Both are brittle to deep reorgs, so expanding to weaker chains like ZEC is not clearly a good idea
-REN may see total system failure as the result of a deep reorg, as it changes federation incentives significantly
-tBTC may accidentally punish some honest micro-federations as the result of a deep reorg
-REN generally has much more interaction between incentive models, as everything is mixed into the same pot.
-tBTC is a large collection of small incentive models, while REN is a single complex incentive model
A2: To correct some points:
The oracle situation is different with RenVM, because the fee model is what determines the value of REN with respect to the cross-chain asset. This is the asset is what is used to pay the fee, so no external pricing is needed for it (because you only care about the ratio between REN and the cross-chain asset).
RenVM does rotate quorums regularly, in fact more regularly than in tBTC (although there are micro-quorums, each deposit doesn’t get rotated as far as I know and sticks around for up to 6 months). This rotation involves rotations of the keys too, so it does not rely on honest deletion of key shares.
Federated views of blockchains are easier to expand to support deep re-orgs (just get the nodes to wait for more blocks for that chain). SPV requires longer proofs which begins to scale more poorly.
Not sure what you mean by “one big pot”, but there are multiple quorums so the failure of one is isolated from the failures of others. For example, if there are 10 shards supporting BTC and one of them fails, then this is equivalent to a sudden 10% fee being applied. Harsh, yes, but not total failure of the whole system (and doesn’t affect other assets).
Would be interesting what RenVM would look like with lots more shards that are smaller. Failure becomes much more isolated and affects the overall network less.
Further, the amount of tBTC you can mint is dependent on people who are long ETH and prefer locking it up in Keep for earning a smallish fee instead of putting it in Compound or leveraging with dydx. tBTC is competing for liquidity while RenVM isn't.

Q: I understand correctly RenVM (sMPC) can get up to a 50% security threshold, can you tell me more?
A: The best you can theoretically do with sMPC is 50-67% of the total value of REN used to bond Darknodes (RenVM will eventually work up to 50% and won’t go for 67% because we care about liveliness just as much as safety). As an example, if there’s $1M of REN currently locked up in bonded Darknodes you could have up to $500K of tokens shifted through RenVM at any one specific moment. You could do more than that in daily volume, but at any one moment this is the limit.Beyond this limit, you can still remain secure but you cannot assume that players are going to be acting to maximize their profit. Under this limit, a colluding group of adversaries has no incentive to subvert safety/liveliness properties because the cost to attack roughly outweighs the gain. Beyond this limit, you need to assume that players are behaving out of commitment to the network (not necessarily a bad assumption, but definitely weaker than the maximizing profits assumption).

Q: Why is using ETH as collateral for RenVM a bad idea?
A: Using ETH as collateral in this kind of system (like having to deposit say 20 ETH for a bond) would not make any sense because the collateral value would then fluctuate independently of what kind of value RenVM is providing. The REN token on the other hand directly correlates with the usage of RenVM which makes bonding with REN much more appropriate. DAI as a bond would not work as well because then you can't limit attackers with enough funds to launch as many darknodes as they want until they can attack the network. REN is limited in supply and therefore makes it harder to get enough of it without the price shooting up (making it much more expensive to attack as they would lose their bonds as well).
A major advantage of Ren's specific usage of sMPC is that security can be regulated economically. All value (that's being interopped at least) passing through RenVM has explicit value. The network can self-regulate to ensure an attack is never worth it.

Q: Given the fee model proposal/ceiling, might be a liquidity issue with renBTC. More demand than possible supply?A: I don’t think so. As renBTC is minted, the fees being earned by Darknodes go up, and therefore the value of REN goes up. Imagine that the demand is so great that the amount of renBTC is pushing close to 100% of the limit. This is a very loud and clear message to the Darknodes that they’re going to be earning good fees and that demand is high. Almost by definition, this means REN is worth more.
Profits of the Darknodes, and therefore security of the network, is based solely on the use of the network (this is what you want because your network does not make or break on things outside the systems control). In a system like tBTC there are liquidity issues because you need to convince ETH holders to bond ETH and this is an external problem. Maybe ETH is pumping irrespective of tBTC use and people begin leaving tBTC to sell their ETH. Or, that ETH is dumping, and so tBTC nodes are either liquidated or all their profits are eaten by the fact that they have to be long on ETH (and tBTC holders cannot get their BTC back in this case). Feels real bad man.

Q: I’m still wondering which asset people will choose: tbtc or renBTC? I’m assuming the fact that all tbtc is backed by eth + btc might make some people more comfortable with it.
A: Maybe :) personally I’d rather know that my renBTC can always be turned back into BTC, and that my transactions will always go through. I also think there are many BTC holders that would rather not have to “believe in ETH” as an externality just to maximize use of their BTC.

Q: How does the liquidation mechanism work? Can any party, including non-nodes act as liquidators? There needs to be a price feed for liquidation and to determine the minting fee - where does this price feed come from?
A: RenVM does not have a liquidation mechanism.
Q: I don’t understand how the price feeds for minting fees make sense. You are saying that the inputs for the fee curve depend on the amount of fees derived by the system. This is circular in a sense?
A: By evaluating the REN based on the income you can get from bonding it and working. The only thing that drives REN value is the fact that REN can be bonded to allow work to be done to earn revenue. So any price feed (however you define it) is eventually rooted in the fees earned.

Q: Who’s doing RenVM’s Security Audit?
A: ChainSecurity | https://chainsecurity.com/

Q: Can you explain RenVM’s proposed fee model?
A: The proposed fee model can be found here: https://github.com/renproject/ren/wiki/Safety-and-Liveliness#fees

Q: Can you explain in more detail the difference between "execution" and "powering P2P Network". I think that these functions are somehow overlapping? Can you define in more detail what is "execution" and "powering P2P Network"? You also said that at later stages semi-core might still exist "as a secondary signature on everything (this can mathematically only increase security, because the fully decentralised signature is still needed)". What power will this secondary signature have?
A: By execution we specifically mean signing things with the secret ECDSA keys. The P2P network is how every node communicates with every other node. The semi-core doesn’t have any “special powers”. If it stays, it would literally just be a second signature required (as opposed to the one signature required right now).
This cannot affect safety, because the first signature is still required. Any attack you wanted to do would still have to succeed against the “normal” part of the network. This can affect liveliness, because the semi-core could decide not to sign. However, the semi-core follows the same rules as normal shards. The signature is tolerant to 1/3rd for both safety/liveliness. So, 1/3rd+ would have to decide to not sign.
Members of the semi-core would be there under governance from the rest of our ecosystem. The idea is that members would be chosen for their external value. We’ve discussed in-depth the idea of L<3. But, if RenVM is used in MakerDAO, Compound, dYdX, Kyber, etc. it would be desirable to capture the value of these ecosystems too, not just the value of REN bonded. The semi-core as a second signature is a way to do this.
Imagine if the members for those projects, because those projects want to help secure renBTC, because it’s used in their ecosystems. There is a very strong incentive for them to behave honestly. To attack RenVM you first have to attack the Darknodes “as per usual” (the current design), and then somehow convince 1/3rd of these projects to act dishonestly and collapse their own ecosystems and their own reputations. This is a very difficult thing to do.
Worth reminding: the draft for this proposal isn’t finished. It would be great for everyone to give us their thoughts on GitHub when it is proposed, so we can keep a persistent record.

Q: Which method or equation is used to calculate REN value based on fees? I'm interested in how REN value is calculated as well, to maintain the L < 3 ratio?
A: We haven’t finalized this yet. But, at this stage, the plan is to have a smart contract that is controlled by the Darknodes. We want to wait to see how SubZero and Zero go before committing to a specific formulation, as this will give us a chance to bootstrap the network and field inputs from the Darknodes owners after the earnings they can make have become more apparent.
submitted by RENProtocol to RenProject [link] [comments]

You can call you a Bitcoiner if you know/can explain these terms...

10 Minutes
10,000 BTC Pizza
2016 Blocks
21 Million
210,000 Blocks
51% Attack
Asic Boost
Bitcoin Cash
Bitcoin Improvement Proposal (BIP)
Bitcoin SV
Block height
Block reward
Bloom Filter
Brain Wallet
Change Address
Child pays for parent (CPFP)
Coinbase (not the exchange)
Coinmarketcap (CMC)
Colored Coin
Custodial Wallet
Craig Wright
David Kleinman
Difficulty adjustment
Difficulty Target
Dorian Nakamoto
Double spend
Elliptic Curve Digital Signature Algorithm (ECDSA)
Full Node
Gavin Andresen
Genesis Block
Getting goxed
Hard Fork
Hardware Wallet
Hierarchical Deterministic (HD) Wallet
Hot Wallet
Initial Coin Offering (ICO)
Initial Exchange Offering (IEO)
Light Node
Master Private Key
Master Public Key
Master Seed
Merkle Tree
Mining Farm
Mining Pool
Not your keys,...
Orphan block
Paper Wallet
Pieter Wuille
Private key
Proof of Stake (PoS)
Proof of Work (PoW)
Public key
Replace by Fee (RBF)
Roger Ver
Satoshi Nakamoto
Schnorr Signatures
Segregated Witness (Segwit)
Simplified Payment Verification (SPV)
Smart Contract
Soft Fork
Transaction Fees
TransactionId (Txid)
User Activated Soft Fork (UASF)
Wallet Import Format (WIF)
Watch-Only Address
List obviously not complete. Suggestions appreciated.
https://bitcoin.org/en/developer-glossary https://en.bitcoin.it/wiki/Main_Page https://www.youtube.com/channel/UCgo7FCCPuylVk4luP3JAgVw https://www.youtube.com/useaantonop
submitted by PolaT1x to Bitcoin [link] [comments]

Bitcoin’s Security and Hash Rate Explained

Bitcoin’s Security and Hash Rate Explained
As the Bitcoin hash rate reaches new all-time highs, there’s never been a better time to discuss blockchain security and its relation to the hashing power and the Proof of Work (PoW) that feed the network. The Bitcoin system is based on a form of decentralized trust, heavily relying on cryptography. This makes its blockchain highly secure and able to be used for financial transactions and other operations requiring a trustless ledger.
Far from popular belief, cryptography dates back to thousands of years ago. The same root of the word encryption — crypt — comes from the Greek word ‘kryptos’, meaning hidden or secret. Indeed, humans have always wanted to keep some information private. The Assyrians, the Chinese, the Romans, and the Greeks, they all tried over the centuries to conceal some information like trade deals or manufacturing secrets by using symbols or ciphers carved in stone or leather. In 1900 BC, Egyptians used hieroglyphics and experts often refer to them as the first example of cryptography.
Back to our days, Bitcoin uses cryptographic technologies such as:
  1. Cryptographic hash functions (i.e. SHA-256 and RIPEMD-160)
  2. Public Key Cryptography (i.e. ECDSA — the Elliptic Curve Digital Signature Algorithm)
While Public Key Cryptography, bitcoin addresses, and digital signatures are used to provide ownership of bitcoins, the SHA-256 hash function is used to verify data and block integrity and to establish the chronological order of the blockchain. A cryptographic hash function is a mathematical function that verifies the integrity of data by transforming it into a unique unidentifiable code.
Here is a graphic example to make things more clear:

– Extract from the MOOC (Massive Open Online Course) in Digital Currencies at the University of Nicosia.
Furthermore, hash functions are used as part of the PoW algorithm, which is a prominent part of the Bitcoin mining algorithm and this is what is of more interest to understand the security of the network. Mining creates new bitcoins in each block, almost like a central bank printing new money and creates trust by ensuring that transactions are confirmed only when enough computational power is devoted to the block that contains them. More blocks mean more computation, which means more trust.
With PoW, miners compete against each other to complete transactions on the network and get rewarded. Basically they need to solve a complicated mathematical puzzle and a possibility to easily prove the solution. The more hashing power, the higher the chance to resolve the puzzle and therefore perform the proof of work. In more simple words, bitcoins exist thanks to a peer to peer network that helps validate transactions in the ledger and provides enough trust to avoid that a third party is involved in the process. It also exists because miners give it life by resolving that computational puzzle, through the mining reward incentive they are receiving.
For more info, contact Block.co directly or email at [email protected].
Tel +357 70007828
Get the latest from Block.co, like and follow us on social media:
submitted by BlockDotCo to u/BlockDotCo [link] [comments]

[ShowerThoughts] There will come a day when computing is cheap enough that all the lost bitcoin will be found.

Just like most brainwallets have already been brute forced, I could foresee the day when ECDSA could be brute-forced at some marginal profitability. May be decades away. By then most of the UTXOs will be moved to a new signature algorithm, and the only ones left will be all the "lost coins" of people who forgot their seed or lost their harddrive. In this imaginary future, bitcoin mining will be brute-forcing old / legacy ECDSA UTXOs.
Take a look at the RSA Challenge, they have been ticking away at that over the last few decades quite nicely.
Bits Month-Year Cracked
300 4-1991
364 4-1992
397 7-1993
426 4-1994
430 4-1996
463 2-1999
512 8-1999
576 12-2003
663 5-2005
768 12-2009
And that is just for fame and $50k or so of prizes. The cash "prize" for ECSDA is much higher. I'd be amazed if ECDSA is still unfactorable in 80 years. Especially using made-to-order hardware.
Before the maximalists bury me, I'm anticipating innovation in methodologies, not Moore's Law.
Though there may be raw tech in the next century as well. Here's a proof-of-concept at defeating RSA 2048 in trivial time
Remember... the three bodies problem was considered unsolvable... till it wasn't.
submitted by brianddk to btc [link] [comments]

I'm writing a series about blockchain tech and possible future security risks. This is the third part of the series introducing Quantum resistant blockchains.

Part 1 and part 2 will give you usefull basic blockchain knowledge that is not explained in this part.
Part 1 here
Part 2 here
Quantum resistant blockchains explained.
- How would quantum computers pose a threat to blockchain?
- Expectations in the field of quantum computer development.
- Quantum resistant blockchains
- Why is it easier to change cryptography for centralized systems such as banks and websites than for blockchain?
- Conclusion
The fact that whatever is registered on a blockchain can’t be tampered with is one of the great reasons for the success of blockchain. Looking ahead, awareness is growing in the blockchain ecosystem that quantum computers might cause the need for some changes in the cryptography that is used by blockchains to prevent hackers from forging transactions.
How would quantum computers pose a threat to blockchain?
First, let’s get a misconception out of the way. When talking about the risk quantum computers could pose for blockchain, some people think about the risk of quantum computers out-hashing classical computers. This, however, is not expected to pose a real threat when the time comes.
This paper explains why: https://arxiv.org/pdf/1710.10377.pdf "In this section, we investigate the advantage a quantum computer would have in performing the hashcash PoW used by Bitcoin. Our findings can be summarized as follows: Using Grover search, a quantum computer can perform the hashcash PoW by performing quadratically fewer hashes than is needed by a classical computer. However, the extreme speed of current specialized ASIC hardware for performing the hashcash PoW, coupled with much slower projected gate speeds for current quantum architectures, essentially negates this quadratic speedup, at the current difficulty level, giving quantum computers no advantage. Future improvements to quantum technology allowing gate speeds up to 100GHz could allow quantum computers to solve the PoW about 100 times faster than current technology.
However, such a development is unlikely in the next decade, at which point classical hardware may be much faster, and quantum technology might be so widespread that no single quantum enabled agent could dominate the PoW problem."
The real point of vulnerability is this: attacks on signatures wherein the private key is derived from the public key. That means that if someone has your public key, they can also calculate your private key, which is unthinkable using even today’s most powerful classical computers. So in the days of quantum computers, the public-private keypair will be the weak link. Quantum computers have the potential to perform specific kinds of calculations significantly faster than any normal computer. Besides that, quantum computers can run algorithms that take fewer steps to get to an outcome, taking advantage of quantum phenomena like quantum entanglement and quantum superposition. So quantum computers can run these certain algorithms that could be used to make calculations that can crack cryptography used today. https://en.wikipedia.org/wiki/Elliptic-curve_cryptography#Quantum_computing_attacks and https://eprint.iacr.org/2017/598.pdf
Most blockchains use Elliptic Curve Digital Signature Algorithm (ECDSA) cryptography. Using a quantum computer, Shor's algorithm can be used to break ECDSA. (See for reference: https://arxiv.org/abs/quant-ph/0301141 and pdf: https://arxiv.org/pdf/quant-ph/0301141.pdf ) Meaning: they can derive the private key from the public key. So if they got your public key (and a quantum computer), then they got your private key and they can create a transaction and empty your wallet.
RSA has the same vulnerability while RSA will need a stronger quantum computer to be broken than ECDSA.
At this point in time, it is already possible to run Shor’s algorithm on a quantum computer. However, the amount of qubits available right now makes its application limited. But it has been proven to work, we have exited the era of pure theory and entered the era of practical applications:
So far Shor's algorithm has the most potential, but new algorithms might appear which are more efficient. Algorithms are another area of development that makes progress and pushes quantum computer progress forward. A new algorithm called Variational Quantum Factoring is being developed and it looks quite promising. " The advantage of this new approach is that it is much less sensitive to error, does not require massive error correction, and consumes far fewer resources than would be needed with Shor’s algorithm. As such, it may be more amenable for use with the current NISQ (Noisy Intermediate Scale Quantum) computers that will be available in the near and medium term." https://quantumcomputingreport.com/news/zapata-develops-potential-alternative-to-shors-factoring-algorithm-for-nisq-quantum-computers/
It is however still in development, and only works for 18 binary bits at the time of this writing, but it shows new developments that could mean that, rather than a speedup in quantum computing development posing the most imminent threat to RSA and ECDSA, a speedup in the mathematical developments could be even more consequential. More info on VQF here: https://arxiv.org/abs/1808.08927
It all comes down to this: when your public key is visible, which is always necessary to make transactions, you are at some point in the future vulnerable for quantum attacks. (This also goes for BTC, which uses the hash of the public key as an address, but more on that in the following articles.) If you would have keypairs based on post quantum cryptography, you would not have to worry about that since in that case not even a quantum computer could derive your private key from your public key.
The conclusion is that future blockchains should be quantum resistant, using post-quantum cryptography. It’s very important to realize that post quantum cryptography is not just adding some extra characters to standard signature schemes. It’s the mathematical concept that makes it quantum resistant. to become quantm resistant, the algorithm needs to be changed. “The problem with currently popular algorithms is that their security relies on one of three hard mathematical problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve discrete logarithm problem. All of these problems can be easily solved on a sufficiently powerful quantum computer running Shor's algorithm. Even though current, publicly known, experimental quantum computers lack processing power to break any real cryptographic algorithm, many cryptographers are designing new algorithms to prepare for a time when quantum computing becomes a threat.” https://en.wikipedia.org/wiki/Post-quantum_cryptography
Expectations in the field of quantum computer development.
To give you an idea what the expectations of quantum computer development are in the field (Take note of the fact that the type and error rate of the qubits is not specified in the article. It is not said these will be enough to break ECDSA or RSA, neither is it said these will not be enough. What these articles do show, is that a huge speed up in development is expected.):
When will ECDSA be at risk? Estimates are only estimates, there are several to be found so it's hard to really tell.
The National Academy of Sciences (NAS) has made a very thourough report on the development of quantum computing. The report came out in the end of 2018. They brought together a group of scientists of over 70 people from different interconnecting fields in quantum computing who, as a group, have come up with a close to 200 pages report on the development, funding, implications and upcoming challenges for quantum computing development. But, even though this report is one of the most thourough up to date, it doesn't make an estimate on when the risk for ECDSA or RSA would occur. They acknowledge this is quite impossible due to the fact there are a lot of unknowns and due to the fact that they have to base any findings only on publicly available information, obviously excluding any non available advancements from commercial companies and national efforts. So if this group of specialized scientists can’t make an estimate, who can make that assessment? Is there any credible source to make an accurate prediction?
The conclusion at this point of time can only be that we do not know the answer to the big question "when".
Now if we don't have an answer to the question "when", then why act? The answer is simple. If we’re talking about security, most take certainty over uncertainty. To answer the question when the threat materializes, we need to guess. Whether you guess soon, or you guess not for the next three decades, both are guesses. Going for certain means you'd have to plan for the worst, hope for the best. No matter how sceptical you are, having some sort of a plan ready is a responsible thing to do. Obviously not if you're just running a blog about knitting. But for systems that carry a lot of important, private and valuable information, planning starts today. The NAS describes it quite well. What they lack in guessing, they make up in advice. They have a very clear advice:
"Even if a quantum computer that can decrypt current cryptographic ciphers is more than a decade off, the hazard of such a machine is high enough—and the time frame for transitioning to a new security protocol is sufficiently long and uncertain—that prioritization of the development, standardization, and deployment of post-quantum cryptography is critical for minimizing the chance of a potential security and privacy disaster."
Another organization that looks ahead is the National Security Agency (NSA) They have made a threat assessment in 2015. In August 2015, NSA announced that it is planning to transition "in the not too distant future" (statement of 2015) to a new cipher suite that is resistant to quantum attacks. "Unfortunately, the growth of elliptic curve use has bumped up against the fact of continued progress in the research on quantum computing, necessitating a re-evaluation of our cryptographic strategy." NSA advised: "For those partners and vendors that have not yet made the transition to Suite B algorithms, we recommend not making a significant expenditure to do so at this point but instead to prepare for the upcoming quantum resistant algorithm transition.” https://en.wikipedia.org/wiki/NSA_Suite_B_Cryptography#cite_note-nsa-suite-b-1
What these organizations both advice is to start taking action. They don't say "implement this type of quantum resistant cryptography now". They don't say when at all. As said before, the "when" question is one that is a hard one to specify. It depends on the system you have, the value of the data, the consequences of postponing a security upgrade. Like I said before: you just run a blog, or a bank or a cryptocurrency? It's an individual risk assesment that's different for every organization and system. Assesments do need to be made now though. What time frame should organisationds think about when changing cryptography? How long would it take to go from the current level of security to fully quantum resistant security? What changes does it require to handle bigger signatures and is it possible to use certain types of cryptography that require to keep state? Do your users need to act, or can al work be done behind the user interface? These are important questions that one should start asking. I will elaborate on these challenges in the next articles.
Besides the unsnswered question on "when", the question on what type of quantum resistant cryptography to use is unanswered too. This also depends on the type of system you use. The NSA and NAS both point to NIST as the authority on developments and standardization of quantum resistant cryptography. NIST is running a competition right now that should end up in one or more standards for quantum resistant cryptography. The NIST competition handles criteria that should filter out a type of quantum resistant cryptography that is feasable for a wide range of systems. This takes time though. There are some new algorithms submitted and assessing the new and the more well known ones must be done thouroughly. They intend to wrap things up around 2022 - 2024. From a blockchain perspective it is important to notice that a specific type of quantum resistant cryptography is excluded from the NIST competition: Stateful Hash-Based Signatures. (LMS and XMSS) This is not because these are no good. In fact they are excelent and XMSS is accepted to be provable quantum resistant. It's due to the fact that implementations will need to be able to securely deal with the requirement to keep state. And this is not a given for most systems.
At this moment NIST intends to approve both LMS and XMSS for a specific group of applications that can deal with the statefull properties. The only loose end at this point is an advice for which applications LMS and XMSS will be adviced and for what applications it is discouraged. These questions will be answered in the beginning of april this year: https://csrc.nist.gov/news/2019/stateful-hbs-request-for-public-comments This means that quite likely LMS and XMSS will be the first type of standardized quantum resistant cryptography ever. To give a small hint: keeping state, is pretty much a naturally added property of blockchain.
Quantum resistant blockchains
“Quantum resistant” is only used to describe networks and cryptography that are secure against any attack by a quantum computer of any size in the sense that there is no algorithm known that makes it possible for a quantum computer to break the applied cryptography and thus that system.
Also, to determine if a project is fully quantum resistant, you would need to take in account not only how a separate element that is implemented in that blockchain is quantum resistant, but also the way it is implemented. As with any type of security check, there should be no backdoors, in which case your blockchain would be just a cardboard box with bulletproof glass windows. Sounds obvious, but since this is kind of new territory, there are still some misconceptions. What is considered safe now, might not be safe in the age of quantum computers. I will address some of these in the following chapters, but first I will elaborate a bit about the special vulnerability of blockchain compared to centralized systems.
Why is it easier to change cryptography for centralized systems such as banks and websites than for blockchain?
Developers of a centralized system can decide from one day to the other that they make changes and update the system without the need for consensus from the nodes. They are in charge, and they can dictate the future of the system. But a decentralized blockchain will need to reach consensus amongst the nodes to update. Meaning that the majority of the nodes will need to upgrade and thus force the blockchain to only have the new signatures to be valid. We can’t have the old signature scheme to be valid besides the new quantum resistant signature scheme. Because that would mean that the blockchain would still allow the use of vulnerable, old public- and private keys and thus the old vulnerable signatures for transactions. So at least the majority of the nodes need to upgrade to make sure that blocks which are constructed using the old rules and thus the old vulnerable signature scheme, are rejected by the network. This will eventually result in a fully upgraded network which only accepts the new post quantum signature scheme in transactions. So, consensus is needed. The most well-known example of how that can be a slow process is Bitcoin’s need to scale. Even though everybody agrees on the need for a certain result, reaching consensus amongst the community on how to get to that result is a slow and political process. Going quantum resistant will be no different, and since it will cause lesser performance due to bigger signatures and it will need hardware upgrades quite likely it will be postponed rather than be done fast and smooth due to lack of consensus. And because there are several quantum resistant signature schemes to choose from, agreement an automatic given. The discussion will be which one to use, and how and when to implement it. The need for consensus is exclusively a problem decentralized systems like blockchain will face.
Another issue for decentralized systems that change their signature scheme, is that users of decentralized blockchains will have to manually transfe migrate their coins/ tokens to a quantum safe address and that way decouple their old private key and activate a new quantum resistant private key that is part of an upgraded quantum resistant network. Users of centralized networks, on the other hand, do not need to do much, since it would be taken care of by their centralized managed system. As you know, for example, if you forget your password of your online bank account, or some website, they can always send you a link, or secret question, or in the worst case they can send you mail by post to your house address and you would be back in business. With the decentralized systems, there is no centralized entity who has your data. It is you who has this data, and only you. So in the centralized system there is a central entity who has access to all the data including all the private accessing data, and therefore this entity can pull all the strings. It can all be done behind your user interface, and you probably wouldn’t notice a thing.
And a third issue will be the lost addresses. Since no one but you has access to your funds, your funds will become inaccessible once you lose your private key. From that point, an address is lost, and the funds on that address can never be moved. So after an upgrade, those funds will never be moved to a quantum resistant address, and thus will always be vulnerable to a quantum hack.
To summarize: banks and websites are centralized systems, they will face challenges, but decentralized systems like blockchain will face some extra challenges that won't apply for centralized systems.
All issues specific for blockchain and not for banks or websites or any other centralized system.
Bitcoin and all currently running traditional cryptocurrencies are not excluded from this problem. In fact, it will be central to ensuring their continued existence over the coming decades. All cryptocurrencies will need to change their signature schemes in the future. When is the big guess here. I want to leave that for another discussion. There are enough certain specifics we can discuss right now on the subject of quantum resistant blockchains and the challenges that existing blockchains will face when they need to transfer. This won’t be an easy transfer. There are some huge challenges to overcome and this will not be done overnight. I will get to this in the next few articles.
Part 1, what makes blockchain reliable?
Part 2, The two most important mathematical concepts in blockchain.
Part 4A, The advantages of quantum resistance from genesis block, A
Part 4B, The advantages of quantum resistance from genesis block, B
Part 5, Why BTC will be vulnerable sooner than expected.
submitted by QRCollector to CryptoTechnology [link] [comments]

I decided to post this here as I saw some questions on the QRL discord.

Is elliptic curve cryptography quantum resistant?
No. Using a quantum computer, Shor's algorithm can be used to break Elliptic Curve Digital Signature Algorithm (ECDSA). Meaning: they can derive the private key from the public key. So if they got your public key, they got your private key, and they can empty your funds. https://en.wikipedia.org/wiki/Elliptic-curve_cryptography#Quantum_computing_attacks https://eprint.iacr.org/2017/598.pdf
Why do people say that BTC is quantum resistant, while they use elliptic curve cryptography? (Here comes the idea from that never reusing a private key from elliptic curve cryptography (and public key since they form a pair) would be quantum resistant.)
Ok, just gonna start with the basics here. Your address, where you have your coins stalled, is locked by your public- private key pair. See it as your e-mail address (public key) and your password (Private key). Many people got your email address, but only you have your password. If you got your address and your password, then you can access your mail and send emails (Transactions). Now if there would be a quantum computer, people could use that to calculate your password/ private key, if they have your email address/ public key.
What is the case with BTC: they don't show your public key anywhere, untill you make a transaction. So your public key is private untill you make a transaction. How do they do that while your funds must be registered on the ledger? Wel, they only show the Hash of your public key (A hash is an outcome of an equation. Usually one-way hash functions are used, where you can not derive the original input from the output. But everytime you use the same hash function on the same original input (For example IFUHE8392ISHF), you will always get the same output (For example G). That way you can have your coins on public key IFUHE8392ISHF, while on the chain, they are on G.) So your funds are registered on the blockchain on the "Hash" of the public key. The Hash of the public key is also your "email address" in this case. So you give "G" as your address to send BTC to.
By the way, in the early days you could use your actual public key as your address. And miners would receive coins on their public key, not on the hashed public key. That is why all the Satoshi funds are vulnerable to quantum attacks even though these addresses have never been used to make transactions from. These public keys are already public instead of hashed. Also certain hard forks have exposed the public keys of unused addresses. So it's really a false sense of security that most people hang on to in the first place.
But it's actually a false sense of security over all.
Since it is impossible to derive a public key from the Hash of a public key, your coins are safe for quantum computers as long as you don't make any transaction. Now here follows the biggest misconseption: Pretty much everyone will think, great, so BTC is quantum secure! It's not that simple. Here it is important to understand two things:
1 How is a transaction sent? The owner has the private key and the public key and uses that to log into the secured environment, the wallet. This can be online or offline. Once he is in his wallet, he states how much he wants to send and to what address.
When he sends the transaction, it will be broadcasted to the blockchain network. But before the actual transaction that will be sent, it is formed into a package, created by the wallet. This happens out of sight of the sender.
That package ends up carrying roughly the following info: The public key to point to the address where the funds will be coming from, the amount that will be transferred, the public key of the address the funds will be transferred to.
Then this package caries the most important thing: a signature, created by the wallet, derived from the private- public key combination. This signature proves to the miners that you are the rightfull owner and you can send funds from that public key.
So this package is then sent out of the secure wallet environment to multiple nodes. The nodes don’t need to trust the sender or establish the sender’s "identity." And because the transaction is signed and contains no confidential information, private keys, or credentials, it can be publicly broadcast using any underlying network transport that is convenient. As long as the transaction can reach a node that will propagate it into the network, it doesn’t matter how it is transported to the first node.
2 How is a transaction confirmed/ fullfilled and registered on the blockchain?
After the transaction is sent to the network, it is ready to be processed. The nodes have a bundle of transactions to verify and register on the next block. This is done during a period called the block time. In the case of BTC that is 10 minutes.
If you comprehend the information written above, you can see that there are two moments where you can actually see the public key, while the transaction is not fullfilled and registered on the blockchain yet.
1: during the time the transaction is sent from the sender to the nodes
2: during the time the nodes verify the transaction.
This paper describes how you could hijack a transaction and make a new transaction of your own, using someone elses address to send his coins to an address you own during moment 2: the time the nodes verify the transaction:
"(Unprocessed transactions) After a transaction has been broadcast to the network, but before it is placed on the blockchain it is at risk from a quantum attack. If the secret key can be derived from the broadcast public key before the transaction is placed on the blockchain, then an attacker could use this secret key to broadcast a new transaction from the same address to his own address. If the attacker then ensures that this new transaction is placed on the blockchain first, then he can effectively steal all the bitcoin behind the original address."
So this means that practically, you can't call BTC a quantum secure blockchain. Because as soon as you will touch your coins and use them for payment, or send them to another address, you will have to make a transaction and you risk a quantum attack.
Why would Nexus be any differtent?
If you ask the wrong person they will tell you "Nexus uses a combination of the Skein and Keccak algorithms which are the 2 recognized quantum resistant algorithms (keccal is used by the NSA) so instead of sha-256, Nexus has SK-1024 making it much harder to break." Which would be the same as saying BTC is quantum resistant because they use a Hashing function to hash the private key as long as no transaction is made.
No, this is their sollid try to be quantum resistant: Nexus states it's different because they have instant transactions (So there wouldn't be a period during which time the nodes verify the transaction. This period would be instant.) Also they use a particular order in which the miners verify transactions: First-In-First-Out (FIFO) (So even if instant is not instant after all, and you would be able to catch a public key and derive the private key, you would n't be able to have your transaction signed before the original one. The original one is first in line, and will therefore be confirmed first. Also for some reason Nexus has standardized fees which are burned after a transaction. So if FIFO wouldn't do the trick you would not be able to use a higher fee to get prioritized and get an earlyer confirmation.
So, during during the time the nodes verify the transaction, you would not be able to hijack a transaction. GREAT, you say? Yes, great-ish. Because there is still moment # 1: during the time the transaction is sent from the sender to the nodes. This is where network based attacks could do the trick:
There are network based attacks that can be used to delay or prevent transactions to reach nodes. In the mean time the transactions can be hijacked before they reach the nodes. And thus one could hijack the non quantum secure public keys (they are openly included in sent signed transactions) who then can be used to derive privatekeys before the original transaction is made. So this means that even if Nexus has instant transactions in FIFO order, it is totally useless, because the public key would be obtained by the attacker before they reach the nodes. Conclusion: Nexus is Nnot quantum resistant. You simply can't be without using a post quantum signature scheme.
Performing a DDoS attack or BGP routing attacks or NSA Quantum Insert attacks on a peer to peer newtork would be hard. But when provided with an opportunitiy to steal billions, hackers would find a way. For example:
For BTC:
"An eclipse attack is a network-level attack on a blockchain, where an attacker essentially takes control of the peer-to-peer network, obscuring a node’s view of the blockchain."
That is exactly the receipe for what you would need to create extra time to find public keys and derive private keys from them. Then you could sign transactions of your own and confirm them before the originals do.
By the way, yes this seems to be fixed now, but it most definately shows it's possible. And there are other creative options. Either you stop tranasctions from the base to get out, while the sender thinks they're sent, or you blind the network and catch transactions there. There are always options, and they will be exploited when billions are at stake. The keys can also be hijacked when a transaction is sent from the users device to the blockchain network using a MITM attack. The result is the same as for network based attacks, only now you don't mess with the network itself. These attacks make it possible to 1) retrieve the original public key that is included in the transaction message. 2) Stop or delay the transaction message to arrive at the blockchain network. So, using a quantum computer, you could hijack transactions and create forged transactions, which you then send to the nodes to be confirmed before the nodes even receive the original transaction. There is nothing you could change to the Nexus network to prevent this. The only thing they can do is implement a quantum resistant signature scheme. They plan to do this in the future, like any other serious blockchain project. Yet Nexus is the only of these future quantum resistant projects to prematurely claim to be quantum resistant. There is only one way to get quantum resistancy: POST QUANTUM SIGNATURE SCHEMES. All the rest is just a shitty shortcut that won't work in the end.
(If you use this info on BTC, you will find that the 10 minutes blocktime that is used to estimate when BTC will be vulnerable for quantum attacks, can actually be more then 10 minutes if you catch the public key before the nodes receive them. This makes BTC vulnerable sooner thatn the 10 min blocktime would make you think.)
By the way, Nexus using FIFO and standadrized fees which are burned after the transaction comes with some huge downsides:
Why are WOTS+ signatures (and by extension XMSS) more quantum resistant?
First of all, this is where the top notch mathematicians work their magic. Cryptography is mostly maths. As Jackalyst puts it talking about post quantum signature schemes: "Having papers written and cryptographers review and discuss it to nauseating levels might not be important for butler, but it's really important with signature schemes and other cryptocraphic methods, as they're highly technical in nature."
If you don't believe in math, think about Einstein using math predicting things most coudldn't even emagine, let alone measure back then.
Then there is implementing it the right way into your blockchain without leaving any backdoors open.
So why is WOTS+ and by extension XMSS quantum resistant? Because math papers say so. With WOTS it would even take a quantum computer too much time to derive a private key from a public key. https://en.wikipedia.org/wiki/Hash-based_cryptography https://eprint.iacr.org/2011/484.pdf
What is WOTS+?
It's basiclally an optimized version of Lamport-signatures. WOTS+ (Winternitz one-time signature) is a hash-based, post-quantum signature scheme. So it's a post quantum signature scheme meant to be used once.
What are the risks of WOTS+?
Because each WOTS publishes some part of the private key, they rapidly become less secure as more signatures created by the same public/private key are published. The first signature won't have enough info to work with, but after two or three signatures you will be in trouble.
IOTA uses WOTS. Here's what the people over at the cryptography subreddit have to say about that:
With the article:
Mochimo uses WOTS+. They kinda solved the problem: A transaction consists of a "Source Address", a "Destination Address" and a "Change Address". When you transact to a Destination Address, any remaining funds in your Source Address will move to the Change Address. To transact again, your Change Address then becomes your Source Address.
But what if someone already has your first address and is unaware of the fact you already send funds from that address? He might just send funds there. (I mean in a business environment this would make Mochimo highly impractical.) They need to solve that. Who knows, it's still a young project. But then again, for some reason they also use FIFO and fixed fees, so there I have the same objections as for Nexus.
How is XMSS different?
XMSS uses WOTS in a way that you can actually reuse your address. WOTS creates a quantum resistant one time signature and XMSS creates a tree of those signatures attached to one address so that the address can be reused for sending an asset.
submitted by QRCollector to QRL [link] [comments]

How the core developers are working to further scale Bitcoin.

Following the implementation of Segwit, it's time to talk about Schnorr signatures and how they are going to aid in scaling Bitcoin. Segwit works by altering the composition of Bitcoin blocks. It moves the signature data to another part of the block, hence the name "Segregated Witness". Now that the signature data has been reorganized, Schnorr signatures can be applied to them, where they are signed at once rather than individually. According to coindesk, "Under the ECDSA scheme, each piece of a bitcoin transaction is signed individually, while with Schnorr signatures, all of this data can be signed once"[3].
What are Schnorr Signatures?
How is this going to change/improve Bitcoin?
How are these changes going to implemented?
How is the work coming along?
The meat and potatoes of the matter
The verification equation:
sG = R - H(R || P1 || C || m)P1 - H(R || P2 || C || m)P2 
The signature equation:
R = H(R || P1 || C || m)P1 + … + s*G 
Summations are fundamentally faster to compute on computers than multiplication. This is because each multiplication operation is the sum of the terms where the n is the number of terms. So 5 * 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 (or vice versa for 7). computers only have the capacity to perform two operations - addition and bitwise shifts. Algorithms that maximize the use of these operations are comparitively faster than algorithms that use multiplication, division, or modulus even when the time complexity of the two problems are equal. This is why "For 100000 keys, the speedup is approximately 8x"[1].
"And aggregation shrinks the transaction sizes by the amounts of inputs they have. In our paper, we went and ran numbers on the shrinkage based on existing transaction patterns, there was a 28% reduction based on the existing history"[1].
This is VERY SIGNIFICANT. The "aggregation shrinks the transaction sizes by the amounts of inputs they have"[1]. This means the "more inputs you have, the more you gain because you add a shared cost of paying for one signature"[1].
"Validation time regardless of how complex your script is. You just prove that the script existed, it is valid, and the hash. But anything that further complicates the structure of transaction. This helps fungibility, privacy, and bandwidth"[1].
What can you do to help?
[1] http://diyhpl.us/wiki/transcripts/bitcoin-core-dev-tech/2017-09-06-signature-aggregation/
[2] https://github.com/bitcoin-core/secp256k1
[3] https://www.coindesk.com/just-segwit-bitcoin-core-already-working-new-scaling-upgrade/
Edit: Finally got formatting to work.
submitted by RussianHacker1011101 to Bitcoin [link] [comments]

How can Bitcoin not be exploited by an algorithm that was made to solve math problems in order to make value?

I dont know how to put it into words, but since there was an algorithm created, how can their not be a zero day out there for this
submitted by iamyounow to Bitcoin [link] [comments]

Descripción general de Taurus0x

Descripción general de Taurus0x
Protocolo distribuido fuera de cadena / en cadena que impulsa derivados inteligentes de principio a fin, para cualquier activo sobre cualquier red.
Antecedentes de Taurus0x
¿Recuerdas alrededor de septiembre de 2017 cuando el mundo perdió la calma por los precios de Bitcoin? Fue casi una guerra ideológica para muchos. Se me ocurrió crear una aplicación para que las personas puje por los precios de Bitcoin, y conectaría esa aplicación a un contrato inteligente para ejecutar las ofertas en la cadena de bloques. Me llevó un par de semanas calcular la cantidad de licencias que tendría que adquirir para administrar un negocio de este tipo en los Estados Unidos. Se hizo evidente que la creación de mercado es una gran empresa y está mejor descentralizada en un protocolo de estándar abierto para generar liquidez.
El protocolo debe descentralizarse por completo como requisito principal. ¿Por qué? porque creo en la filosofía de la descentralización y en la creación de creadores de mercado justos, gobernados por una comunidad pública. Es lo que se debe hacer para crear igualdad de oportunidades para los consumidores sin control centralizado y privilegios especiales.
No sorprende a nadie en este momento que la gran mayoría de las "OIC" fueran promesas vacías. La utilidad de la vida real era y es una necesidad para cualquier proyecto viable. La transición de un mundo centralizado a uno centralizado y descentralizado no puede ser abrupto. El protocolo necesitaba apoyar ambos mundos y permitir un resultado de libre mercado en cuanto a la adopción. Escalable en términos de escalabilidad y hasta el día de hoy, Ethereum no podía manejar un DEX completo en tiempo real que pudiera competir con intercambios centralizados avanzados y conocidos. Y, francamente, tal vez no sea su intención. Aquí es cuando comenzó el pensamiento fuera de la cadena, especialmente después de presenciar algunos de los proyectos más exitosos que adoptaron este enfoque, como Lighting y 0xProject..La compensación fue la complejidad del manejo de las comunicaciones criptográficas sin la ayuda de la cadena de bloques.
Conocí a mi cofundador Brett Hayes en ese momento. Necesitaría otros 3 o 4 artículos para explicarle a Brett por usted.
¿Qué es la Criptografía Asimétrica?
La criptografía asimétrica es una forma de criptografía que usa pares de claves públicas y privadas. Cada clave pública viene con su clave privada asociada y única. Si encriptas un dato con un privado, solo la clave pública asociada se puede usar para descifrar los datos. Y viceversa.
Si le envío un "hola" cifrado con mi clave privada, e intenta descifrarlo con mi clave pública (lo cual no es ningún secreto). Si descifra bien, entonces estás seguro de que este "hola" vino de mí. Esto es lo que llamamos firmas digitales.
La siguiente figura es del documento técnico Taurus0x y describe el algoritmo de firma digital elegido ( ECDSA).
¿Qué son los derivados inteligentes?
Bueno, ¿qué son los derivados en primer lugar?
En el mundo financiero, un derivado es un contrato entre dos o más partes basado en un activo. Su precio está determinado por las fluctuaciones en el activo subyacente. Los activos subyacentes más comunes incluyen acciones, bonos, materias primas, divisas, tasas de interés e índices de mercado. Los contratos de futuros, contratos a plazo, opciones, swaps, precios de criptomonedas y warrants son derivados comunes.
Los derivados inteligentes son contratos inteligentes que se comportan como derivados financieros. Poseen suficiente información y fondos para permitir la ejecución con resultados garantizados y confiables.
¿Qué es Taurus0x?
Taurus0x es un protocolo distribuido fuera de cadena / en cadena que alimenta derivados inteligentes de extremo a extremo.Taurus0x es tanto de activos como de agnóstico de red. La filosofía es convertirse también en agnóstico de cadenas de bloques a medida que cobran vida más blockchains.
Distribuido= conjunto totalmente descentralizado de contratos y bibliotecas inteligentes.
Fuera de cadena= protocolo ad-hoc no limitado a una cadena de bloques.
En cadena= resultado confiable sin intermediarios.
Asset-agnostic= admite cualquier activo, no limitado a criptomonedas.
Network-agnostic= los contratos se pueden transmitir a través de cualquier red (correo electrónico, texto, twitter, facebook, lápiz y papel, etc.)
¿Quién puede usar Taurus0x?
El protocolo Taurus0x finalmente se construye para servir a los consumidores finales que negocian contratos de derivados. Los participantes pueden participar en contratos de derivados de igual a igual sin la necesidad de una casa en el medio.
El equipo y el asesoramiento de Taurus0x se dan cuenta de que la migración de un mundo centralizado a uno descentralizado no puede ser abrupta, específicamente en FinTech. Taurus0x está diseñado para admitir modelos comerciales existentes así como C2C punto a punto. Los intercambios que deseen asumir el mercado de derivados pueden usar un protocolo de fuente abierta sin preocuparse por construir un back-end completo para manejar el compromiso y la liquidación del contrato. Los intercambios Taurus0x simplemente conectan a los participantes entre sí, usando algoritmos de coincidencia.
Taurus0x tiene la intención de estandarizar el comercio de derivados de una manera abierta. Tener más intercambios usando el protocolo permite la creación de grupos públicos y de permisos para generar liquidez compuesta de contratos. Esto ayuda a los intercambios más pequeños al reducir la barrera de entrada al mercado.
¿Cómo funciona Taurus0x?
El proceso es simple y directo. Los detalles de implementación están enmascarados por el protocolo, lo que hace que sea muy fácil de construir en la parte superior. Los primeros 2 pasos representan el acuerdo de contrato fuera de la cadena, mientras que 3 y 4 solidifican y ejecutan el contrato en cadena.
1- Crear
Un productor crea un contrato de cualquier cliente que utiliza el protocolo Taurus0x, ya sea desde una aplicación, un sitio web o una extensión de navegador. El productor especifica una condición que se espera que ocurra en algún momento en el futuro. Por ejemplo, I (el productor) podría crear un contrato binario con la siguiente condición:
Stock de Apple> $ 200 para el 1 de julio de 2018 con una prima de 10 TESTIGOS (cualquier token ERC20)
El contrato se firmará automáticamente con mi clave privada, lo que confirma que lo creé. Luego puedo compartirlo (un texto hexadecimal largo) con cualquier persona en cualquier red que elija.
2- Signo
Cuando el consumidor recibe el contrato firmado, podrá cargarlo a través de cualquier cliente que use Taurus0x. Si el consumidor no está de acuerdo con el productor en la condición especificada, seguirá adelante y firmará el contrato con su clave privada. Volviendo a nuestro ejemplo anterior, el consumidor podría pensar que las acciones de Apple permanecerán por debajo de los $ 200 el 1 de julio de 2018. Ahora que hemos recopilado ambas firmas, el contrato está listo para publicarse en blockchain.
3- Publicar
Cualquiera que posea el contrato MultiSig y sus 2 firmas puede continuar y publicarlo en el blockchain de Ethereum. Lo más probable es que sea el productor, el consumidor o una parte como un intercambio en el medio que recibe órdenes fuera de la cadena. Tan pronto como se publique el contrato, el proxy Taurus0x (un contrato inteligente de fuente abierta) extraerá los fondos necesarios de los monederos participantes en la Derivada inteligente recién creada. Los fondos vivirán en el contrato derivado hasta la ejecución exitosa.
4- Ejecutar
Si en algún momento antes de la fecha de vencimiento del contrato se cumple la condición especificada (es decir, Apple Stock> $ 200 ), el productor puede seguir adelante y ejecutar el contrato derivado. El contrato calculará el resultado y transferirá los fondos en consecuencia. En este ejemplo binario derivado, el productor recibirá 20 TESTIGOS en su billetera al ejecutar el contrato. Si llega la fecha de vencimiento y el productor nunca ha ejecutado con éxito el contrato, el consumidor puede ejecutarlo y recoger los 20 TESTIGOS.
Esta figura es del documento técnico de Taurus0x que muestra el proceso:
Taurus0x es un protocolo altamente versátil y modular construido usando contratos inteligentes basados ​​en Ethereum y bibliotecas JS wrapper para la adopción del desarrollador bootstrap. Si bien Derivados Inteligentes es la primera aplicación de Taurus0x, vale la pena señalar que el protocolo no se limita a las criptomonedas o incluso derivados para el caso. Es una solución de administración de contratos escalable y ad-hoc que garantiza resultados de confianza en el futuro en base a las condiciones especificadas en el día de hoy. La naturaleza semi-fuera de la cadena del protocolo ayuda a remediar las limitaciones de escalabilidad de Ethereum y lo convierte en un producto viable.
Finalmente, el plan para Taurus0x debe ser gobernado por una Organización Autónoma Descentralizada o DAO como se describe en la hoja de ruta en https://taurus0x.com. Esta es un área de investigación y desarrollo a partir de hoy. La descentralización no cumple su propósito si la gobernanza se mantiene centralizada, por lo tanto, sin compromiso, Taurus0x sigue una estructura de gobierno descentralizado.
Nos gustaría expresar nuestra gratitud a nuestros mentores y asesores que ayudaron constantemente a revisar y proporcionar comentarios sobre nuestro trabajo. También nos gustaría agradecer a los miembros de la comunidad de Ethereum cuyas innovaciones nos ayudan a crear una economía descentralizada y simbólica. También nos gustaría reconocer el trabajo de equipos como Lightning, 0x Project y Oraclize que allanaron el camino para una mentalidad fuera de la cadena / en la cadena. Un agradecimiento especial a Bernard Abdo, Rees Morgan y Henry Park, cuyo conocimiento y experiencia ayudaron a proporcionar información valiosa a lo largo de este proyecto.
Autor:Rawad Rifai - Cofundador, Taurus0x
Etiquetas (tags): Blockchain Ethereum Taurus0x Decentralized Derivatives
submitted by Taurus0x to Taurus0x [link] [comments]

The myths behind Schnorr signatures

TLDR: To sum it up, Schnorr signature bring nothing and it creates a lot of problems to implement.


I made another post regarding the history of Schnorr signatures, it contains archived link to almost everything there is to know about the topic, it can be found here:
This post is instead about what I have learned through my inquiries and my personal opinion on Schnorr signatures.

Myth 1: Signature aggregation

Schnorr can do multisignature in a very straightforward and scalable way
-Gregory Maxwell, 2015
The theory is that Schnorr signatures are linear so if (r1,s1) and (r2,s2) are two signatures, then (r1+r2,s1+s2) is the signature of both signatures put together.
This is cannot be applied directly to Bitcoin multisig because if the signature work linearly it means someone could forge a signature using the other public keys and “cancel out” the other signature. This problem is best described by Pieter Wuille:
This would mean that he could sign for both of them while everyone is assuming that we have created an address that is multisig that actually requires both of their signatures. This is the cancellation problem. You can choose your keys in such a way that other people's keys get canceled out.
-Pieter Wuille, 2016.
So the linear formula which allow native supports of multisig wallets also native support of one member of a multisig wallet taking over the whole wallet. This problem could be fixed through delinearization but this introduces new issues. Specifically that it isn’t proven to be secure or not to be a breaking change to the cryptographic algorithm. Which is why the Schnorr signatures implementation has been delayed over and over (it is now, I believe, 18 months away at least).

Myth 2: reduction of at least a 25% in terms of storage and bandwidth

Estimates are that this upgrade would reduce the use of storage and bandwidth by at least 25%.
-Bitcoincore.org, March 2017.
This estimate is pure fantasy. The same article states “Assuming every historical signature would be reduced to 1 byte”.
Never, ever, Schnorr signatures will reduce signatures to 1 Byte. Just never. But do not believe me, once again Pieter Wuille says it: Schnorr signature are of 64 bytes fixed size. For comparison, current signatures are at max 73 bytes (12% bigger). This assumes that the delinearization process described in myth 1 does not incur a bigger signature than that or some additional data transfer. Also, This is of course assuming that everyone that use multisig decides to use the Schnorr alternative.

Myth 3: Schnorr signature will improve privacy

This one is a bit tricky and to be fair it is highly dependent on actual implementation.
Schnorr allows the entire policy of the multisig to be obscured and indistinguishable from a conventional single pubkey. In a threshold setup, it also becomes impossible for participants to reveal which of them authorized, or not, a transaction.
-Bitcoincore.org, March 2017.
By design 1 Schnorr signature would replace all the signatures that would normally be involved in a multisig transaction. Thus hiding them. But this is only the theory. In practice the holders of the keys in the multisig still need to communicate and exchange their signature in order to generate that one Schnorr signature. It is extremely naive to believe that this communication step would not leave any public traces. This is particularly true if (as it has been mentioned) a bitcoin node acts as an aggregator.
The idea behind signature aggregation is to enable system validators ie. Bitcoin nodes to compute a single key and signature for every inputs of all transactions at the protocol level.
-Bitcoincore.org, March 2017.
In that use case, the privacy would disappear the instant the third party node is involved in the transaction. Let’s remember that anyone can run a node which by default is decentralized and permissionless.


Why remove the ECDSA for another cryptographic system?? This seems quite pointless and quite a waste of time. While it is undeniable that he could yield some bandwidth reduction (nowhere near 25%!), the gains are far from offsetting the efforts. If anything, the cryptographic system should be changed for a quantum computing secure algorithm but not for another variant of the same.
edit: spelling and link.
submitted by Azeroth7 to btc [link] [comments]

Dogecoin giveaway - Comment here to receive 100 doge. Also, AMA about cryptocurrency.

Once you get tipped, click the +accept link that the bot PMs you. You can then see your balance and recent dogetipbot transaction history with +history
I will also be answering any questions you have. I'm a moderator on /dogecoin and have been studying cryptocurrency for almost 3 years. Here's a glossary of terms you may not know which may help spark some questions if you don't know what to ask:
Hash: The result of an algorithm that takes any input data of arbitrary size and produces a fixed size output. It is impossible to discover the input data based on the resulting hash.
Private keys, public keys and addresses (privkey, pubkey, addr): Put simply, a private key is just a number. A really really big number. There are 2 ^ 160 possible private keys, each is a 256 bit integer in binary. Using the ECDSA your private keys correspond to a public key. And a hash of your public key is your wallet address.
Wallet: Software which generates and stores your keys and addresses.
Transaction (tx): A piece of data that contains where coins are coming from (inputs) and where they are going to (outputs). To be valid, your wallet software must sign the transaction with the private keys of all the inputs, this is how ownership of coins is proven.
Block: A data structure used by cryptocurrency networks which contains transactions.
Blockchain: The collection of blocks in a cryptocurrency network. Each new block contains the hash of the previous block, this is required for it to be valid. In this way, blocks are chained together, each one depends on the previous one to be valid.
Proof of work (POW): The process of hashing random data to discover a hash value that is lower than a predetermined number, that number is the "difficulty".
Mining: Miners collect all the transactions on the network and assemble them into a block. Using POW, miners insert random data (called a nonce, aka number used once) into the block and hash the block. When they find a hash value below the target difficulty, the block is considered valid by the rules of the network and miners broadcast the block to the network. The transactions in the block now have 1 confirmation. Miners are also allowed to claim a block reward (sort of a finder's fee) for their work. This incentivizes miners for their work. Mining is what secures the network from attack. If you have 51% of the entire network's mining power, then you can block transactions or even reverse transactions, so it is important that mining remains as decentralized as possible.
Node: A computer that is running cryptocurrency software which generates, validates and relays transactions and blocks. They download and validate the full blockchain. Nodes can also be wallets, this software is often called "core". The network of nodes IS the cryptocurrency network, they are what make the whole thing work. The node software also contains a friendly JSON API which can be used to perform many functions, such as looking up a transaction in the blockchain history.
submitted by peoplma to RedditDayOf [link] [comments]

Encrypt/Decrypt Message tool in Electron Cash

Encrypt/Decrypt Message tool in Electron Cash
Hi all, I have a question about the Encrypt/Decrypt Message tool in Electron Cash
I knew that I can use a public key to encrypt some plain text and decrypt with the corresponding private key

For example,
Public key: 03c8803b937bf4970fdcec5f43295c3adf4731aaa9287bd58612089480c096e8bd
message: hello-world-123
With the tool, I got the encrtyped text QklFMQKWrqTZYtpihiXAC/0HcPgZMlqoWxy3aREvX+jwKyAmMy93Y4uwz0bIDgQAu9A8RTv2SRy45mQOM5ryl7HiMr1NjVNNGAdKsv0+sMAq3IqV2g==
When I click the "Encrypt" button again, I got a brand new encrypted text QklFMQMA0EA3pYj7FD1+TPh0qqUb6QmO6fr+qs58jvrBWND9hCA7EzQr68TpgBnLrq2Oj0n00YSYOdFnMxa52pve3JKDtsxEuLTL1+/ck2MDNcFp/g==
This happens again and again, and I can decrypt all these different encrypted texts...

I knew that, Bitcoin and Bitcoin Cash
- use ECC, to be more specific, the secp256k1 curve, to generate public and private key pairs
- use ECDSA, aka Elliptic Curve Digital Signature Algorithm, to sign and verify messages
- did some google, the algorithm used in encrypt/decrypt text, has a name ECIES
Am I right?

For the encrypt and decrypt part, why the encrypted text changes every time...? What on earth happens inside this operation?

I also found a GitHub repository about the ECIES, it's from bitpay

But I am quite confused with its example
When we encrypt data, we should not need anyone's private keys, right?
If I wanna implement the encrypt/decrypt part, is there any libraries that I can use? Any recommendations?

Sorry to bother, but quite desire to know the truth.
Does anyone has an knowledge on this...? Thanks very much for helping and teaching me
submitted by aaron67_cc to electroncash [link] [comments]

Biased Nonce Sense: Lattice Attacks against Weak ECDSA Signatures in Cryptocurrencies

Cryptology ePrint Archive: Report 2019/023
Date: 2019-01-08
Author(s): Joachim Breitner, Nadia Heninger

Link to Paper

In this paper, we compute hundreds of Bitcoin private keys and dozens of Ethereum, Ripple, SSH, and HTTPS private keys by carrying out cryptanalytic attacks against digital signatures contained in public blockchains and Internet-wide scans. The ECDSA signature algorithm requires the generation of a per-message secret nonce. This nonce must be generated perfectly uniformly, or else an attacker can exploit the nonce biases to compute the long-term signing key. We use a lattice-based algorithm for solving the hidden number problem to efficiently compute private ECDSA keys that were used with biased signature nonces due to multiple apparent implementation vulnerabilities.

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  16. Dierks, T., Rescorla, E.: The Transport Layer Security (TLS) protocol. IETF RFC RFC5246 (2008)
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submitted by dj-gutz to myrXiv [link] [comments]

Pentesterlab. ECDSA challenge

Hi there,

I am struggling with Pentesterlab challenge: https://pentesterlab.com/exercises/ecdsa

I'm wondering who can give some lights on how to resolve some steps in this challenge. You can read about similar challenge there - https://ropnroll.co.uk/2017/05/breaking-ecdsa/
I suppose I have problems with extracting (r,s) from ESDCA (SECP256k1) signature (here details - https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm)

I even try to brute-force all possible (r,s) values but no luck. Every time I receive error 500.

def recover_key(c1, sig1, c2, sig2, r_len, s_len): n = SECP256k1.order cookies = {} for s_idx in range(s_len, s_len + 2): for r_idx in range(r_len, r_len + 2): s1 = string_to_number(sig1[0 - s_idx:]) s2 = string_to_number(sig2[0 - s_idx:]) # https://bitcoin.stackexchange.com/questions/58853/how-do-you-figure-out-the-r-and-s-out-of-a-signature-using-python r1 = string_to_number(sig1[0 - (s_idx + r_idx + 2):0 - (s_idx)]) r2 = string_to_number(sig2[0 - (s_idx + r_idx + 2):0 - (s_idx)]) z1 = string_to_number(sha2(c1)) z2 = string_to_number(sha2(c2)) # Find cryptographically secure random k = (((z1 - z2) % n) * inverse_mod((s1 - s2), n)) % n # k = len(login1) # Recover private key da1 = ((((s1 * k) % n) - z1) * inverse_mod(r1, n)) % n # da2 = ((((s2 * k) % n) - z2) * inverse_mod(r2, n)) % n # SECP256k1 is the Bitcoin elliptic curve sk = SigningKey.from_secret_exponent(da1, curve=SECP256k1, hashfunc=hashlib.sha256) # create the signature login_tgt = "admin" # Sign account login_hash = sha2(login_tgt) signature = sk.sign(login_hash, k=k) # Create signature key sig_dic_key = "r" + str(r_idx) + "s" + str(s_idx) try: # because who trusts python vk = sk.get_verifying_key() vk.verify(signature, login_hash) print(sig_dic_key, " - good signature") except BadSignatureError: print(sig_dic_key, " - BAD SIGNATURE") 

Its very interesting challenge and I want to break ECDSA finally.
Thanks in advance
submitted by unk1nd0n3 to webappsec [link] [comments]

Andreas Antonopoulos on Bitcoin Wallet Encryption Elliptic Curve Digital Signature Algorithm (ECDSA) in NS2 Dev++ 01-01-EN  Foundational Math, ECDSA and Transactions - Jimy Song Getting the ECDSA Z Value from a Single Input Multi Signature Transaction Elliptic Curve Digital Signature Algorithm (ECDSA) - Public Key Cryptography w/ JAVA (tutorial 10)

Elliptic Curve Digital Signature Algorithm or ECDSA is a cryptographic algorithm used by Bitcoin to ensure that funds can only be spent by their rightful owners.. A few concepts related to ECDSA: private key: A secret number, known only to the person that generated it.A private key is essentially a randomly generated number. Elliptic Curve Digital Signature Algorithm or ECDSA is a cryptographic algorithm used by Bitcoin to ensure the effective and secure control of ownership of funds.. A few concepts related to ECDSA: private key: A secret number, known only to the person that generated it.A private key can be a randomly generated number but in 2019 most wallets use deterministic key schemes derived from BIP 0032. (In particular Bitcoin uses the ECDSA algorithm with elliptic curve secp256k1 .) For both encryption and digital signatures, each user of the system generates apair of keys: a public key and a private key. The public and private keysare mathematically related, but (as far as we know) it is computationallyinfeasible to derive the private key ... In December 2010, a group calling itself fail0verflow announced recovery of the ECDSA private key used by Sony to sign software for the PlayStation 3 game console. However, this attack only worked because Sony did not properly implement the algorithm, because was static instead of random. As pointed out in the Signature generation algorithm section above, this makes solvable and the entire ... Elliptic Curve Digital Signature Algorithm (ECDSA) is a cryptographic algorithm used by Bitcoin to ensure that funds can only be spent by their rightful owners.

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Andreas Antonopoulos on Bitcoin Wallet Encryption

Elliptic Curve Digital Signature Algorithm ECDSA Part 10 Cryptography Crashcourse - Duration: 35:32. Dr. Julian Hosp - Blockchain, Krypto, Bitcoin 5,773 views This video is unavailable. Watch Queue Queue. Watch Queue Queue Elliptic Curve Digital Signature Algorithm (ECDSA) - Public Key Cryptography w/ JAVA (tutorial 10) zaneacademy. ... 34:30 Alice uses secp256k1 (the bitcoin curve) 35:22 Bob uses secp384r1 curve In this video, Andreas Antonopoulos covers Elliptic Curve Crypto (ECC) & EC Digital Signature Algorithm (ECDSA), Key formats (hex, compressed, b58, b58check, Key types, Key mnemonic word list ... In this video I demonstrate getting the ECDSA Z value from a bitcoin transaction containing a multi signature input. I also show the R and S values. The ECDSA R, S and Z values are used throughout ...