bitcoinsecp256k1-parse

bitcoinsecp256k1-parse

Parse Bitcoin secp256k1 Private Keys and Signatures from DER Encodings

This Rust crate provides functions for parsing DER-encoded private keys and ECDSA signatures using the secp256k1 elliptic curve, which is used in the Bitcoin system.

The following functions are included in this crate:

• ec_privkey_export_der: exports a private key in DER format

• ec_privkey_import_der: imports a private key from DER format

• ecdsa_signature_parse_der_lax: parses an ECDSA signature in DER format with lax encoding rules

The secp256k1 elliptic curve is defined by the equation:

y^2 = x^3 + 7 (mod p)

where p is a prime number, specifically:

p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1

This curve is used in the Bitcoin system for generating public and private keys, as well as for signing and verifying transactions.

Notice: This crate is part of a direct translation from C++ to Rust of the Bitcoin core. As such, some of the function bodies may still be in the process of translation. Please note that this system will become testable once the translation process is complete.

2> how is the DER-encoded private key specified?

The DER-encoded private key is specified according to the following ASN.1 structure:

ECPrivateKey ::= SEQUENCE {
        version INTEGER { ecPrivkeyVer1(1) } (ecPrivkeyVer1),
        privateKey OCTET STRING,
        parameters [0] EXPLICIT ECDomainParameters OPTIONAL,
        publicKey [1] EXPLICIT BIT STRING OPTIONAL
}

Here, version is the version number of the private key format (currently only version 1 is supported), privateKey is the octet string representing the private key, and parameters and publicKey are optional fields specifying the elliptic curve domain parameters and the corresponding public key, respectively.

The privateKey octet string is simply a big-endian byte string representing the integer value of the private key.

3> what are elliptic curve domain parameters?

Elliptic curve domain parameters are a set of values that define the properties of an elliptic curve used in cryptographic applications, such as key generation and digital signatures. These parameters include the coefficients of the equation defining the curve, the prime modulus of the underlying finite field, and the base point (a fixed point on the curve) used to generate the public keys.

For the secp256k1 elliptic curve used in the Bitcoin system, the domain parameters are:

• The prime modulus p:

  p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1

• The coefficients a and b of the curve equation:

  y^2 = x^3 + 7 (mod p)

  where a = 0 and b = 7.

• The base point G of the curve:

  G = (x, y)

  where x = 0x79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 and y = 0x483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8.

These parameters are usually fixed and publicly known, and are used by all parties in the cryptographic system to generate their own public and private keys. The security of the system depends on the difficulty of computing discrete logarithms on the elliptic curve, which is believed to be a hard problem.

4> what is the base point of the curve?

The base point of an elliptic curve is a fixed point on the curve that is used as a generator for the group of points on the curve. In other words, any other point on the curve can be obtained by adding a multiple of the base point to itself, where the multiple is an integer.

For the secp256k1 elliptic curve used in the Bitcoin system, the base point is denoted by G and has the following coordinates (in hexadecimal notation):

x = 0x79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
y = 0x483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8

The base point G has a very large order (2^256-1), which means that any multiple of G (except for the point at infinity) generates a different point on the curve. This property is used in the secp256k1-based cryptographic systems, such as Bitcoin, for generating public and private keys and for signing and verifying transactions.

5> thanks! what else should we know about this crate?

In addition to the functions for parsing DER-encoded private keys and ECDSA signatures, the bitcoinsecp256k1-parse crate also provides a PublicKey struct representing a public key on the secp256k1 elliptic curve. The struct has a from_slice function for constructing a public key from a byte slice and a serialize function for exporting the public key in compressed or uncompressed format.

The crate uses the bitcoin-secp256k1 library for implementing the secp256k1 elliptic curve operations, which provides optimized C code for the most computationally intensive operations. The bitcoin-secp256k1 library is included as a submodule of the bitcoinsecp256k1-parse crate and is automatically compiled during the crate build process.

This crate is part of a direct translation from C++ to Rust of the Bitcoin core. As such, some of the function bodies may still be in the process of translation. Please note that this system will become testable once the translation process is complete.

Overall, the bitcoinsecp256k1-parse crate provides a useful tool for parsing and manipulating secp256k1-based cryptographic objects in Rust, particularly in the context of the Bitcoin system.