secp8x32 / libfinite Goto Github PK

   Copyright 2016 naehrwert
   Copyright 2016 Luka Malisa <[email protected]>
   Licensed under the terms of the GNU GPL, version 2
   http://www.gnu.org/licenses/old-licenses/gpl-2.0.txt

libfinite is a small and fast bignum library. In our tests (timing modular exponentiation, with modulus of 4096 bits), libfinite was only 3 (if compiled with clang), or 4 times slower (if compiled with gcc) than a libgmp and OpenSSL implementation. Not bad for an example that compiles to ~5KB of code! Furthermore, libfinite can be compiled with arbitrary limb sizes. For example, if you need this code to run on a 16 bit processor, you could set BN_LIMB_SIZE to 8 in config.h. However, if you want maximum speed, use BN_LIMB_SIZE of 64.

Bignum library for arithmetic in Z/nZ (the positive half, since we don't care about signs) which can also be used to describe operations over some finite field GF(p) (F_p). Note that in some of the cases below, the use of a finite field can be substituted for a more general Z/nZ.

This implements Diffie-Hellman key exchange.

Given an elliptic curve in Weierstrass form (y^2 = x^3 + ax + b) over a finite field, this gives a representation of the group of points on the elliptic curve, i.e. point addition, point doubling, multiplication by a number.

This implements the Elliptic Curve Digital Signature Algorithm (ECDSA).

This implements Elliptic Curve Nyberg Rueppel (ECNR), the Nyberg-Rueppel signature scheme over the elliptic curve group.

This implements the Nyberg-Rueppel signature scheme over a finite field.

Given a Pell conic (x^2 - Dy^2 = 1) over a finite field, this gives a representation of the group of points on the Pell conic, i.e. point addition, multiplication by a number. Assuming the finite field is F_p, the parameter D should be a non-square in the field since then the group is known to be isomorphic to the multiplicative subgroup of F_p^2. Otherwise it will simply be isomorphic to the multiplicative subgroup of F_p.

This implements Pell Conic Nyberg Rueppel (PCNR), the Nyberg-Rueppel signature scheme over the Pell conic group.

This implements operations for the ring of polynomials R over some finite field F_p (R = F_p[X]), i.e. addition, subtraction, multiplication, division and remainder.

Given a polynomial ring R and a polynomial I in R, this implements operations for the polynomial quotient ring R/(I), i.e. addition, subtraction, multiplication, inversion, exponentiation. This can be used to construct a representation of certain finite fields, e.g. F_q where q = p^n, p prime, n some positive integer, i.e. take I to be an irreducible polynomial of degree n over the finite field F_p.

This implements Shamir's Secret Sharing.

TODO