secp256k1

README

libsecp256k1

Optimized C library for EC operations on curve secp256k1.

This library is a work in progress and is being used to research best practices. Use at your own risk.

Features:

• secp256k1 ECDSA signing/verification and key generation.
• Adding/multiplying private/public keys.
• Serialization/parsing of private keys, public keys, signatures.
• Constant time, constant memory access signing and pubkey generation.
• Derandomized DSA (via RFC6979 or with a caller provided function.)
• Very efficient implementation.

Implementation details

• General
  • No runtime heap allocation.
  • Extensive testing infrastructure.
  • Structured to facilitate review and analysis.
  • Intended to be portable to any system with a C89 compiler and uint64_t support.
  • Expose only higher level interfaces to minimize the API surface and improve application security. ("Be difficult to use insecurely.")
• Field operations
  • Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1).
    • Using 5 52-bit limbs (including hand-optimized assembly for x86_64, by Diederik Huys).
    • Using 10 26-bit limbs.
  • Field inverses and square roots using a sliding window over blocks of 1s (by Peter Dettman).
• Scalar operations
  • Optimized implementation without data-dependent branches of arithmetic modulo the curve's order.
    • Using 4 64-bit limbs (relying on __int128 support in the compiler).
    • Using 8 32-bit limbs.
• Group operations
  • Point addition formula specifically simplified for the curve equation (y^2 = x^3 + 7).
  • Use addition between points in Jacobian and affine coordinates where possible.
  • Use a unified addition/doubling formula where necessary to avoid data-dependent branches.
  • Point/x comparison without a field inversion by comparison in the Jacobian coordinate space.
• Point multiplication for verification (aP + bG).
  • Use wNAF notation for point multiplicands.
  • Use a much larger window for multiples of G, using precomputed multiples.
  • Use Shamir's trick to do the multiplication with the public key and the generator simultaneously.
  • Optionally (off by default) use secp256k1's efficiently-computable endomorphism to split the P multiplicand into 2 half-sized ones.
• Point multiplication for signing
  • Use a precomputed table of multiples of powers of 16 multiplied with the generator, so general multiplication becomes a series of additions.
  • Access the table with branch-free conditional moves so memory access is uniform.
  • No data-dependent branches
  • The precomputed tables add and eventually subtract points for which no known scalar (private key) is known, preventing even an attacker with control over the private key used to control the data internally.

Build steps

libsecp256k1 is built using autotools:

$ ./autogen.sh
$ ./configure
$ make
$ ./tests
$ sudo make install  # optional

Documentation

Overview

Package secp256k1 wraps the bitcoin secp256k1 C library.

Index

• Variables
• func CompressPubkey(x, y *big.Int) []byte
• func DecompressPubkey(pubkey []byte) (x, y *big.Int)
• func RecoverPubkey(msg []byte, sig []byte) ([]byte, error)
• func Sign(msg []byte, seckey []byte) ([]byte, error)
• func VerifySignature(pubkey, msg, signature []byte) bool
• type BitCurve
  • func S256() *BitCurve
  • func (BitCurve *BitCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)
  • func (BitCurve *BitCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int)
  • func (BitCurve *BitCurve) IsOnCurve(x, y *big.Int) bool
  • func (BitCurve *BitCurve) Marshal(x, y *big.Int) []byte
  • func (BitCurve *BitCurve) Params() *elliptic.CurveParams
  • func (BitCurve *BitCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int)
  • func (BitCurve *BitCurve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int)
  • func (BitCurve *BitCurve) Unmarshal(data []byte) (x, y *big.Int)

Variables

var (
	ErrInvalidMsgLen       = errors.New("invalid message length, need 32 bytes")
	ErrInvalidSignatureLen = errors.New("invalid signature length")
	ErrInvalidRecoveryID   = errors.New("invalid signature recovery id")
	ErrInvalidKey          = errors.New("invalid private key")
	ErrInvalidPubkey       = errors.New("invalid public key")
	ErrSignFailed          = errors.New("signing failed")
	ErrRecoverFailed       = errors.New("recovery failed")
)

Functions

func CompressPubkey

func CompressPubkey(x, y *big.Int) []byte

CompressPubkey encodes a public key to 33-byte compressed format.

func DecompressPubkey

func DecompressPubkey(pubkey []byte) (x, y *big.Int)

DecompressPubkey parses a public key in the 33-byte compressed format. It returns non-nil coordinates if the public key is valid.

func RecoverPubkey

func RecoverPubkey(msg []byte, sig []byte) ([]byte, error)

RecoverPubkey returns the public key of the signer. msg must be the 32-byte hash of the message to be signed. sig must be a 65-byte compact ECDSA signature containing the recovery id as the last element.

func Sign

func Sign(msg []byte, seckey []byte) ([]byte, error)

Sign creates a recoverable ECDSA signature. The produced signature is in the 65-byte [R || S || V] format where V is 0 or 1.

The caller is responsible for ensuring that msg cannot be chosen directly by an attacker. It is usually preferable to use a cryptographic hash function on any input before handing it to this function.

func VerifySignature

func VerifySignature(pubkey, msg, signature []byte) bool

VerifySignature checks that the given pubkey created signature over message. The signature should be in [R || S] format.

Types

type BitCurve

type BitCurve struct {
	P       *big.Int // the order of the underlying field
	N       *big.Int // the order of the base point
	B       *big.Int // the constant of the BitCurve equation
	Gx, Gy  *big.Int // (x,y) of the base point
	BitSize int      // the size of the underlying field
}

A BitCurve represents a Koblitz Curve with a=0. See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html

func S256

func S256() *BitCurve

S256 returns a BitCurve which implements secp256k1.

func (*BitCurve) Add

func (BitCurve *BitCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)

Add returns the sum of (x1,y1) and (x2,y2)

func (*BitCurve) Double

func (BitCurve *BitCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int)

Double returns 2*(x,y)

func (*BitCurve) IsOnCurve

func (BitCurve *BitCurve) IsOnCurve(x, y *big.Int) bool

IsOnCurve returns true if the given (x,y) lies on the BitCurve.

func (*BitCurve) Marshal

func (BitCurve *BitCurve) Marshal(x, y *big.Int) []byte

Marshal converts a point into the form specified in section 4.3.6 of ANSI X9.62.

func (*BitCurve) Params

func (BitCurve *BitCurve) Params() *elliptic.CurveParams

func (*BitCurve) ScalarBaseMult

func (BitCurve *BitCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int)

ScalarBaseMult returns k*G, where G is the base point of the group and k is an integer in big-endian form.

func (*BitCurve) ScalarMult

func (BitCurve *BitCurve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int)

func (*BitCurve) Unmarshal

func (BitCurve *BitCurve) Unmarshal(data []byte) (x, y *big.Int)

Unmarshal converts a point, serialised by Marshal, into an x, y pair. On error, x = nil.