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README.md
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 52bit limbs (including handoptimized assembly for x86_64, by Diederik Huys).
 Using 10 26bit limbs.
 Field inverses and square roots using a sliding window over blocks of 1s (by Peter Dettman).
 Optimized implementation of arithmetic modulo the curve's field size (2^256  0x1000003D1).
 Scalar operations
 Optimized implementation without datadependent branches of arithmetic modulo the curve's order.
 Using 4 64bit limbs (relying on __int128 support in the compiler).
 Using 8 32bit limbs.
 Optimized implementation without datadependent branches of arithmetic modulo the curve's order.
 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 datadependent 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 efficientlycomputable endomorphism to split the P multiplicand into 2 halfsized 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 branchfree conditional moves so memory access is uniform.
 No datadependent 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