8de58308d8
This commit adds three new cryptosystems to libsecp256k1: Pedersen commitments are a system for making blinded commitments to a value. Functionally they work like: commit_b,v = H(blind_b || value_v), except they are additively homorphic, e.g. C(b1, v1) - C(b2, v2) = C(b1 - b2, v1 - v2) and C(b1, v1) - C(b1, v1) = 0, etc. The commitments themselves are EC points, serialized as 33 bytes. In addition to the commit function this implementation includes utility functions for verifying that a set of commitments sums to zero, and for picking blinding factors that sum to zero. If the blinding factors are uniformly random, pedersen commitments have information theoretic privacy. Borromean ring signatures are a novel efficient ring signature construction for AND/OR admissions policies (the code here implements an AND of ORs, each of any size). This construction requires 32 bytes of signature per pubkey used plus 32 bytes of constant overhead. With these you can construct signatures like "Given pubkeys A B C D E F G, the signer knows the discrete logs satisifying (A || B) & (C || D || E) & (F || G)". ZK range proofs allow someone to prove a pedersen commitment is in a particular range (e.g. [0..2^64)) without revealing the specific value. The construction here is based on the above borromean ring signature and uses a radix-4 encoding and other optimizations to maximize efficiency. It also supports encoding proofs with a non-private base-10 exponent and minimum-value to allow trading off secrecy for size and speed (or just avoiding wasting space keeping data private that was already public due to external constraints). A proof for a 32-bit mantissa takes 2564 bytes, but 2048 bytes of this can be used to communicate a private message to a receiver who shares a secret random seed with the prover.
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).
- Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1).
- 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.
- Optimized implementation without data-dependent 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 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