primitives.goldilocks_jit

Fast Goldilocks field arithmetic via Numba JIT.

Provides scalar and vectorized operations for GF(p) and GF(p³) that bypass galois library’s python-calculate mode for significant performance gains.

GF(p): Goldilocks prime p = 2^64 - 2^32 + 1 = 0xFFFFFFFF00000001 GF(p³): cubic extension with irreducible polynomial x³ - x - 1 (so x³ = x + 1)

FF3 multiplication formula (derived from x³ = x + 1):

Let t = a1*b2 + a2*b1 c0 = a0*b0 + t c1 = a0*b1 + a1*b0 + t + a2*b2 c2 = a0*b2 + a1*b1 + a2*b0 + a2*b2

Functions

gl_add_vec(a, b)	Element-wise (a + b) mod p over uint64 arrays.
gl_sub_vec(a, b)	Element-wise (a - b) mod p over uint64 arrays.
gl_mul_vec(a, b)	Element-wise (a * b) mod p over uint64 arrays.
gl_inv_vec(a)	Element-wise a^(p-2) mod p over uint64 arrays.
ff3_batch_inverse(c0s, c1s, c2s)	Batch-invert N FF3 elements using Montgomery's trick.

Module Contents

primitives.goldilocks_jit.gl_add_vec(a, b)

Element-wise (a + b) mod p over uint64 arrays.

primitives.goldilocks_jit.gl_sub_vec(a, b)

Element-wise (a - b) mod p over uint64 arrays.

primitives.goldilocks_jit.gl_mul_vec(a, b)

Element-wise (a * b) mod p over uint64 arrays.

primitives.goldilocks_jit.gl_inv_vec(a)

Element-wise a^(p-2) mod p over uint64 arrays.

primitives.goldilocks_jit.ff3_batch_inverse(c0s, c1s, c2s)

Batch-invert N FF3 elements using Montgomery’s trick.

Cost: 2(N-1) FF3 multiplications + 1 FF3 inversion (vs N inversions). Each of the three component arrays must have the same length N > 0.