This repository contains documentation and example code that demonstrates a practical optimization on the implementation of the binary GCD algorithm, for the purpose of computing modular inverses. The sample code computes inverses modulo the well-known prime 2^255-19. This is C code with intrinsics and inline assembly; it requires GCC or Clang, a 64-bit x86 architecture, and a target CPU that supports the BMI2 opcodes (i.e. Haswell or later, in the line of Intel CPU).
On an Intel Core i5-8259U (Coffee Lake), this code was measured to perform an inversion in 7490 cycles, which is faster than using Fermat's little theorem. This code is constant-time, i.e. its execution time and memory access pattern does not depend on the value to invert (even if the value is not invertible, in which case the computed "inverse" is zero).
The implementation of computations modulo 2^255-19 is in
src/gf25519.c, with an API in src/gf25519.h. All other files are for
test and benchmarking purposes only. Tests also use
gmplib to verify that we compute correct values
(i.e. install the libgmp-dev package on your system if you want to
compile and run the tests).