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<ul class="chapter"><li><a href="./Intro.html"><strong>1.</strong> Intro</a></li><li><a href="./DagHistory.html"><strong>2.</strong> History</a></li><li><a href="./Wallet.html"><strong>3.</strong> Wallet</a></li><li><ul class="section"><li><a href="./Deterministic_wallet.html"><strong>3.1.</strong> Deterministic Wallet</a></li><li><a href="./Mnemonic.html"><strong>3.2.</strong> Mnemonic</a></li></ul></li><li><a href="./Testnet.html"><strong>4.</strong> Testnet & faucet</a></li><li><ul class="section"><li><a href="./BTC_testnet.html"><strong>4.1.</strong> Bitcoin Testnet</a></li><li><a href="./ETH_testnet.html"><strong>4.2.</strong> Ethereum Testnet</a></li><li><a href="./GByte_testnet.html"><strong>4.3.</strong> Byteball Testnet</a></li></ul></li><li><a href="./Address.html"><strong>5.</strong> Address</a></li><li><ul class="section"><li><a href="./btc_addr.html"><strong>5.1.</strong> Bitcoin Address</a></li></ul></li><li><a href="./Data_Structure.html"><strong>6.</strong> Data Structure</a></li><li><ul class="section"><li><a href="./Transcation.html"><strong>6.1.</strong> Transcation</a></li><li><a href="./btc_tx.html"><strong>6.2.</strong> Bitcoin Transaction</a></li><li><a href="./MerkleTree.html"><strong>6.3.</strong> MerkleTree</a></li><li><a href="./PatriciaTree.html"><strong>6.4.</strong> PatriciaTree</a></li><li><a href="./IAVL_Tree.html"><strong>6.5.</strong> Merkleized IAVL+ Tree</a></li><li><a href="./MerkleDAG.html"><strong>6.6.</strong> MerkleDAG</a></li></ul></li><li><a href="./Data_Storage.html"><strong>7.</strong> Data Storage</a></li><li><ul class="section"><li><a href="./btc_datastore.html"><strong>7.1.</strong> Bitcoin</a></li></ul></li><li><a href="./Consensus.html"><strong>8.</strong> Consensus algorithm</a></li><li><ul class="section"><li><a href="./Consensus_POS_Ouroboros.html"><strong>8.1.</strong> IOHK/Ouroboros</a></li><li><a href="./DFINITY.html"><strong>8.2.</strong> DFINITY</a></li><li><a href="./Stellar.html"><strong>8.3.</strong> Stellar(SCP)</a></li><li><a href="./Matrix.html"><strong>8.4.</strong> Matrix</a></li><li><a href="./Ripple.html"><strong>8.5.</strong> Ripple</a></li><li><a href="./Casper.html"><strong>8.6.</strong> Casper</a></li><li><a href="./PoA.html"><strong>8.7.</strong> POA(Parity)</a></li><li><a href="./Terndermint.html"><strong>8.8.</strong> Tendermint</a></li><li><a href="./Delegated_Consensus.html"><strong>8.9.</strong> dBFT(NEO/Antshare)/dPOS(BTS/Steem/EOS/Lisk)</a></li><li><a href="./Algorand.html"><strong>8.10.</strong> Algorand</a></li></ul></li><li><a href="./Scalability.html"><strong>9.</strong> Scalability</a></li><li><ul class="section"><li><a href="./Ouroboros_Praos.html"><strong>9.1.</strong> Ouroboros Praos</a></li><li><a href="./EOS.html"><strong>9.2.</strong> EOS</a></li><li><a href="./eth_parallelizability.html"><strong>9.3.</strong> Ethereum Parallelizability</a></li></ul></li><li><a href="./Validation.html"><strong>10.</strong> Validation</a></li><li><ul class="section"><li><a href="./Segwit.html"><strong>10.1.</strong> Segwit</a></li><li><a href="./Multisignature.html"><strong>10.2.</strong> Multisignature</a></li><li><a href="./Tx_Malleability.html"><strong>10.3.</strong> Transaction Malleability</a></li><li><a href="./Double_Spend.html"><strong>10.4.</strong> Double Spend</a></li><li><a href="./Peplay_Protect.html"><strong>10.5.</strong> Replay Protection</a></li><li><a href="./TrueBit.html"><strong>10.6.</strong> Truebit</a></li></ul></li><li><a href="./Money_Denomiation_Token.html"><strong>11.</strong> Money & Token</a></li><li><ul class="section"><li><a href="./TxFee_BTC.html"><strong>11.1.</strong> Bitcoin TxFee</a></li><li><a href="./RBF.html"><strong>11.2.</strong> Bitcoin Replace by fee</a></li><li><a href="./TxFee_ETH.html"><strong>11.3.</strong> Ethereum TxFee</a></li><li><a href="./ERC20.html"><strong>11.4.</strong> ERC20/ERC223/ERC721</a></li></ul></li><li><a href="./Crypto.html"><strong>12.</strong> Crypto Algorithm</a></li><li><ul class="section"><li><a href="./secp256k1.html" class="active"><strong>12.1.</strong> secp256k1</a></li><li><a href="./ZK-SNARKs.html"><strong>12.2.</strong> ZKP/ZK-SNARKs</a></li><li><a href="./CoinJoin.html"><strong>12.3.</strong> CoinJoin</a></li><li><a href="./RingSig.html"><strong>12.4.</strong> RingSig</a></li><li><a href="./Crypto_SM.html"><strong>12.5.</strong> SMx</a></li><li><a href="./PQC.html"><strong>12.6.</strong> Post-Quantum Cryptography</a></li></ul></li><li><a href="./Messaging.html"><strong>13.</strong> Messaging</a></li><li><a href="./Node_Discovery.html"><strong>14.</strong> Node discovery</a></li><li><ul class="section"><li><a href="./Gossip_Protocol.html"><strong>14.1.</strong> Gossip Protocol</a></li><li><a href="./DHT_Protocol.html"><strong>14.2.</strong> DHT Protocol</a></li></ul></li><li><a href="./Sync.html"><strong>15.</strong> Synchronization</a></li><li><ul class="section"><li><a href="./btc_sync.html"><strong>15.1.</strong> Bitcoin Header frist</a></li></ul></li><li><a href="./Interconnecting.html"><strong>16.</strong> Interconnect & Cross-chain</a></li><li><ul class="section"><li><a href="./ILP.html"><strong>16.1.</strong> Interledger Protocol (ILP)</a></li><li><a href="./DID.html"><strong>16.2.</strong> Decentralized Identifiers (DIDs)</a></li><li><a href="./0xProtocol.html"><strong>16.3.</strong> 0x Protocol</a></li><li><a href="./Polkadot.html"><strong>16.4.</strong> Polkadot</a></li><li><a href="./Cosmos.html"><strong>16.5.</strong> Cosmos</a></li><li><a href="./OmiseGO.html"><strong>16.6.</strong> OmiseGO</a></li></ul></li><li><a href="./Oracle.html"><strong>17.</strong> Oracle</a></li><li><ul class="section"><li><a href="./Gnosis.html"><strong>17.1.</strong> Gnosis</a></li><li><a href="./Augur.html"><strong>17.2.</strong> Augur</a></li><li><a href="./Amoveo.html"><strong>17.3.</strong> Amoveo</a></li><li><a href="./ZenProtocol.html"><strong>17.4.</strong> Zen Protocal</a></li></ul></li><li><a href="./SmartContract.html"><strong>18.</strong> SmartContract</a></li><li><ul class="section"><li><a href="./Asset_Contract.html"><strong>18.1.</strong> Asset</a></li><li><a href="./Loan_Contract.html"><strong>18.2.</strong> Loan</a></li></ul></li><li><a href="./VM.html"><strong>19.</strong> VM</a></li></ul>
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<a class="header" href="./secp256k1.html#signatures" id="signatures"><h2>signatures</h2></a>
<p>https://bitcoin.stackexchange.com/a/12556</p>
<p>There are two different encodings used. <strong>DER</strong> and <strong>compact</strong></p>
<p>Everything in the Bitcoin protocol, including <strong>transaction signatures</strong> and <strong>alert signatures</strong>, uses DER encoding. This results in 71 bytes signatures (on average), as there are several header bytes, and the R and S valued are variable length.</p>
<p>For <strong>message signatures</strong>, a custom encoding is used which is more compact (and more recent) and supports public key recovery (given a message and a signature, find which public key would have created it). The code you're referring to in the question is for creating such signatures.</p>
<p>A correct DER-encoded signature has the following form:</p>
<ul>
<li>0x30: a header byte indicating a compound structure.
A 1-byte length descriptor for all what follows.</li>
<li>0x02: a header byte indicating an integer.
A 1-byte length descriptor for the R value
The R coordinate, as a big-endian integer.</li>
<li>0x02: a header byte indicating an integer.
A 1-byte length descriptor for the S value.
The S coordinate, as a big-endian integer.</li>
</ul>
<p>Where initial 0x00 bytes for R and S are not allowed, except when their first byte would otherwise be above 0x7F (in which case a single 0x00 in front is required). Also note that inside transaction signatures, an extra hashtype byte follows the actual signature data.</p>
<a class="header" href="./secp256k1.html#ri" id="ri"><h2>RI</h2></a>
<a class="header" href="./secp256k1.html#cc" id="cc"><h3>C/C++</h3></a>
<ul>
<li>https://github.com/bitcoin-core/secp256k1</li>
<li>by Peter Wuille</li>
<li>又名 libsecp256k1</li>
</ul>
<a class="header" href="./secp256k1.html#how-bitcoin-using-secp256k1" id="how-bitcoin-using-secp256k1"><h4>How bitcoin using secp256k1</h4></a>
<ul>
<li>https://github.com/bitcoin/bitcoin/blob/v0.15.1/src/wallet/rpcwallet.cpp#L163-L171
<ul>
<li>https://github.com/bitcoin/bitcoin/blob/v0.15.1/src/wallet/wallet.cpp#L3437 (pubkey from pool)
<ul>
<li>https://github.com/bitcoin/bitcoin/blob/v0.15.1/src/wallet/wallet.cpp#L125-L158 (how pubkey gen)
<ul>
<li>https://github.com/bitcoin/bitcoin/blob/v0.15.1/src/key.cpp#L152 (<strong>use secp256k1 to create pubkey</strong>)</li>
</ul>
</li>
</ul>
</li>
<li>https://github.com/bitcoin/bitcoin/blob/v0.15.1/src/pubkey.h#L144 (hash160)</li>
<li>https://github.com/bitcoin/bitcoin/blob/v0.15.1/src/base58.cpp#L197 ( <code>CBitcoinAddress(keyID).ToString()</code> -> base58check)</li>
</ul>
</li>
</ul>
<pre><code>$ src/bitcoin-cli getnewaddress
1Fop9P6BvWX5PdYcnABur6vXYbRVK2zjXp
$ src/bitcoin-cli dumpprivkey 1Fop9P6BvWX5PdYcnABur6vXYbRVK2zjXp
L3o684tsf6E4ZKwHXWwLd3pzjRksG7e9eeknqQP8XBytjTv8utje
$ echo L3o684tsf6E4ZKwHXWwLd3pzjRksG7e9eeknqQP8XBytjTv8utje|bx wif-to-public|bx ec-to-address
1Fop9P6BvWX5PdYcnABur6vXYbRVK2zjXp
</code></pre>
<a class="header" href="./secp256k1.html#how-ex-using-secp256k1" id="how-ex-using-secp256k1"><h4>How ex using secp256k1</h4></a>
<ul>
<li>https://github.com/libbitcoin/secp256k1 (is fork of bitcoin-core/secp256k1)
<ul>
<li>https://github.com/libbitcoin/libbitcoin/blob/v3.3.0/src/math/elliptic_curve.cpp</li>
<li>https://github.com/libbitcoin/libbitcoin/blob/v3.3.0/src/math/elliptic_curve.cpp#L85</li>
<li>https://github.com/libbitcoin/libbitcoin/blob/v3.3.0/src/wallet/ec_private.cpp#L201</li>
<li>https://github.com/libbitcoin/libbitcoin-explorer/blob/v3.3.0/src/commands/ec-new.cpp#L53</li>
</ul>
</li>
</ul>
<pre><code>$ echo 000000000000000000000000000000000000000000000000 |bx ec-new
f00ccc9dae46346963a579b2ffb3deb67a1cb0da158aef9c7b839ac05640d190
$ echo 000000000000000000000000000000000000000000000000 |bx ec-new |bx ec-to-public
03dc8335336fe1ea6936f2c13c5ac06b5ab585e5c72434f8bc74829349c9d14054
$ echo 000000000000000000000000000000000000000000000000 |bx ec-new |bx ec-to-public |bx ec-to-address
12KWaMA14HonuGKvEruKwe7rAFPbUzpwVM
$ echo 000000000000000000000000000000000000000000000000 |bx ec-new |bx ec-to-wif
L5GLUwKZA1VLu1u85n4ZqViWcDFrvh7nDzENesWwsk1Ed4wCHBXe
$ echo 000000000000000000000000000000000000000000000000 |bx ec-new |bx ec-to-wif |bx wif-to-ec
f00ccc9dae46346963a579b2ffb3deb67a1cb0da158aef9c7b839ac05640d190
$ echo 000000000000000000000000000000000000000000000000 |bx ec-new |bx ec-to-wif |bx wif-to-ec|bx ec-to-public
03dc8335336fe1ea6936f2c13c5ac06b5ab585e5c72434f8bc74829349c9d14054
$ echo 000000000000000000000000000000000000000000000000 |bx ec-new |bx ec-to-wif |bx wif-to-ec|bx ec-to-public|bx ec-to-address
12KWaMA14HonuGKvEruKwe7rAFPbUzpwVM
</code></pre>
<a class="header" href="./secp256k1.html#how-picocoin-works-with-secp256k1" id="how-picocoin-works-with-secp256k1"><h4>How picocoin works with secp256k1</h4></a>
<ul>
<li>picocoin is C light lib by Jeff Garzik ( Gavin Andresen的朋友，<a href="https://github.com/btc1/bitcoin">segwit2x</a>的主要开发）</li>
<li>https://github.com/jgarzik/picocoin/blob/v0.5/lib/key.c#L57-L73</li>
</ul>
<a class="header" href="./secp256k1.html#how-rust-bitcoin-works-with-libsecp256k1" id="how-rust-bitcoin-works-with-libsecp256k1"><h4>how rust-bitcoin works with libsecp256k1</h4></a>
<ul>
<li>https://github.com/apoelstra/rust-bitcoin/blob/master/src/util/address.rs#L55-L64</li>
<li>https://github.com/apoelstra/rust-secp256k1/blob/master/src/key.rs#L146-L160</li>
<li>https://github.com/apoelstra/rust-secp256k1 is a wrapper around libsecp256k1,</li>
</ul>
<a class="header" href="./secp256k1.html#how-bitcoinj-works-with-libsecp256k1" id="how-bitcoinj-works-with-libsecp256k1"><h4>how bitcoinj works with libsecp256k1</h4></a>
<ul>
<li>Using JNI (which provided by <code>libsecp256k1</code> officially)
<ul>
<li>https://github.com/bitcoin-core/secp256k1/tree/master/src/java/</li>
</ul>
</li>
<li>https://github.com/bitcoinj/bitcoinj/blob/v0.14.5/core/src/main/java/org/bitcoin/NativeSecp256k1.java</li>
<li>Note: <a href="https://github.com/bitcoinj">bitcoinj</a> looks maintained by <a href="https://github.com/greenaddress">greenaddress</a></li>
</ul>
<a class="header" href="./secp256k1.html#python" id="python"><h3>Python</h3></a>
<ul>
<li>https://github.com/vbuterin/pybitcointools By VB</li>
</ul>
<pre><code>>>> sha256('some big long brainwallet password')
'57c617d9b4e1f7af6ec97ca2ff57e94a28279a7eedd4d12a99fa11170e94f5a4'
>>> decoded_private_key = bitcoin.decode_privkey(sha256('some big long brainwallet password'), 'hex')
>>> public_key = bitcoin.fast_multiply(bitcoin.G, decoded_private_key)
>>> hex_encoded_public_key = bitcoin.encode_pubkey(public_key, 'hex')
>>> bitcoin.pubkey_to_address(public_key)
'1CQLd3bhw4EzaURHbKCwM5YZbUQfA4ReY6'
>>> (public_key_x, public_key_y) = public_key
>>> compressed_prefix = '02' if (public_key_y % 2) == 0 else '03'
>>> hex_compressed_public_key = compressed_prefix + bitcoin.encode(public_key_x, 16)
>>> bitcoin.pubkey_to_address(hex_compressed_public_key)
'1EHw4jytKnzMSX8szNrXJ9FQiahKYnuuji'
</code></pre>
<pre><code>$ echo 57c617d9b4e1f7af6ec97ca2ff57e94a28279a7eedd4d12a99fa11170e94f5a4|bx ec-to-public|bx ec-to-address
1EHw4jytKnzMSX8szNrXJ9FQiahKYnuuji
</code></pre>
<a class="header" href="./secp256k1.html#javascript" id="javascript"><h3>Javascript</h3></a>
<ul>
<li>https://github.com/cryptocoinjs/secp256k1-node</li>
</ul>
<a class="header" href="./secp256k1.html#go" id="go"><h3>Go</h3></a>
<ul>
<li>Package btcec implements elliptic curve cryptography needed for working with Bitcoin (secp256k1 only for now).</li>
<li>https://github.com/btcsuite/btcd/tree/master/btcec
<ul>
<li>https://github.com/btcsuite/btcd/blob/master/btcec/pubkey.go#L69-L122</li>
</ul>
</li>
</ul>
<a class="header" href="./secp256k1.html#how-ethereum-works-with-secp256k1" id="how-ethereum-works-with-secp256k1"><h4>How Ethereum works with secp256k1</h4></a>
<ul>
<li>Ethereum use the hybrid solution
<ul>
<li>公钥生成使用标准go api (<code>crypto/ecdsa</code>)
<ul>
<li>https://github.com/ethereum/go-ethereum/blob/v1.7.2/accounts/keystore/key.go#L161-L167</li>
</ul>
</li>
<li>签名使用cgo来调用libsecp256k1的c代码 （性能考虑）
<ul>
<li>https://github.com/ethereum/go-ethereum/blob/v1.7.2/crypto/secp256k1/secp256.go#L68-L97</li>
</ul>
</li>
<li>同时集成了btcec包, 当使用non-cgo模式时候，则使用这种方式（https://github.com/ethereum/go-ethereum/pull/3680 non-cgo fallback implementation of secp256k1
operations. The fallback implementation is not used when cgo is available. ）
<ul>
<li>https://github.com/ethereum/go-ethereum/blob/v1.7.2/crypto/signature_nocgo.go#L48-L72</li>
</ul>
</li>
</ul>
</li>
</ul>
<a class="header" href="./secp256k1.html#c" id="c"><h3>C#</h3></a>
<ul>
<li>https://github.com/MetacoSA/NBitcoin/blob/v4.0.0.42/NBitcoin/Crypto/ECKey.cs#L98</li>
<li>https://github.com/MetacoSA/NBitcoin/blob/v4.0.0.42/NBitcoin/BouncyCastle/math/ec/custom/sec/SecP256K1Curve.cs</li>
</ul>
<a class="header" href="./secp256k1.html#object-c" id="object-c"><h3>Object-C</h3></a>
<ul>
<li>https://github.com/oleganza/CoreBitcoin/blob/0.6.8.1/openssl/include/openssl/obj_mac.h#L384-L386</li>
<li>https://github.com/oleganza/CoreBitcoin/blob/0.6.8.1/CoreBitcoin/BTCKey.h</li>
<li>https://github.com/oleganza/CoreBitcoin/blob/0.6.8.1/CoreBitcoin/BTCKey.m</li>
<li>https://github.com/oleganza/CoreBitcoin/blob/0.6.8.1/CoreBitcoin/BTCCurvePoint.h</li>
<li>https://github.com/oleganza/CoreBitcoin/blob/0.6.8.1/CoreBitcoin/BTCCurvePoint.m</li>
</ul>
<a class="header" href="./secp256k1.html#reference" id="reference"><h2>Reference</h2></a>
<ul>
<li>https://en.bitcoin.it/wiki/Secp256k1</li>
<li>https://bitcoin.stackexchange.com/a/21911</li>
<li>https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch04.asciidoc</li>
<li>https://github.com/bitcoinbook/bitcoinbook/blob/develop/code/key-to-address-ecc-example.py</li>
</ul>
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