Module p384_64

Autogenerated: ‘src/ExtractionOCaml/word_by_word_montgomery’ –lang Rust –inline p384 64 ‘2^384 - 2^128 - 2^96 + 2^32 - 1’ mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp curve description: p384 machine_wordsize = 64 (from “64”) requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp m = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff (from “2^384 - 2^128 - 2^96 + 2^32 - 1”)

NOTE: In addition to the bounds specified above each function, all functions synthesized for this Montgomery arithmetic require the input to be strictly less than the prime modulus (m), and also require the input to be in the unique saturated representation. All functions also ensure that these two properties are true of return values.

Computed values: eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) + (z[4] << 256) + (z[5] << 0x140) bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) + (z[32] << 256) + (z[33] << 0x108) + (z[34] << 0x110) + (z[35] << 0x118) + (z[36] << 0x120) + (z[37] << 0x128) + (z[38] << 0x130) + (z[39] << 0x138) + (z[40] << 0x140) + (z[41] << 0x148) + (z[42] << 0x150) + (z[43] << 0x158) + (z[44] << 0x160) + (z[45] << 0x168) + (z[46] << 0x170) + (z[47] << 0x178) twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) + (z[4] << 256) + (z[5] << 0x140) in if x1 & (2^384-1) < 2^383 then x1 & (2^384-1) else (x1 & (2^384-1)) - 2^384

Structs

fiat_p384_montgomery_domain_field_element

The type fiat_p384_montgomery_domain_field_element is a field element in the Montgomery domain. Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]

fiat_p384_non_montgomery_domain_field_element

The type fiat_p384_non_montgomery_domain_field_element is a field element NOT in the Montgomery domain. Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]

Functions

fiat_p384_add

The function fiat_p384_add adds two field elements in the Montgomery domain.

fiat_p384_addcarryx_u64

The function fiat_p384_addcarryx_u64 is an addition with carry.

fiat_p384_cmovznz_u64

The function fiat_p384_cmovznz_u64 is a single-word conditional move.

fiat_p384_divstep

The function fiat_p384_divstep computes a divstep.

fiat_p384_divstep_precomp

The function fiat_p384_divstep_precomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form).

fiat_p384_from_bytes

The function fiat_p384_from_bytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.

fiat_p384_from_montgomery

The function fiat_p384_from_montgomery translates a field element out of the Montgomery domain.

fiat_p384_msat

The function fiat_p384_msat returns the saturated representation of the prime modulus.

fiat_p384_mul

The function fiat_p384_mul multiplies two field elements in the Montgomery domain.

fiat_p384_mulx_u64

The function fiat_p384_mulx_u64 is a multiplication, returning the full double-width result.

fiat_p384_nonzero

The function fiat_p384_nonzero outputs a single non-zero word if the input is non-zero and zero otherwise.

fiat_p384_opp

The function fiat_p384_opp negates a field element in the Montgomery domain.

fiat_p384_selectznz

The function fiat_p384_selectznz is a multi-limb conditional select.

fiat_p384_set_one

The function fiat_p384_set_one returns the field element one in the Montgomery domain.

fiat_p384_square

The function fiat_p384_square squares a field element in the Montgomery domain.

fiat_p384_sub

The function fiat_p384_sub subtracts two field elements in the Montgomery domain.

fiat_p384_subborrowx_u64

The function fiat_p384_subborrowx_u64 is a subtraction with borrow.

fiat_p384_to_bytes

The function fiat_p384_to_bytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.

fiat_p384_to_montgomery

The function fiat_p384_to_montgomery translates a field element into the Montgomery domain.

Type Aliases

fiat_p384_i1

fiat_p384_i1 represents values of 1 bits, stored in one byte.

fiat_p384_i2

fiat_p384_i2 represents values of 2 bits, stored in one byte.

fiat_p384_u1

fiat_p384_u1 represents values of 1 bits, stored in one byte.

fiat_p384_u2

fiat_p384_u2 represents values of 2 bits, stored in one byte.