Expand description
Autogenerated: ‘src/ExtractionOCaml/word_by_word_montgomery’ –lang Rust –inline p256 32 ‘2^256 - 2^224 + 2^192 + 2^96 - 1’ mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp curve description: p256 machine_wordsize = 32 (from “32”) requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp m = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff (from “2^256 - 2^224 + 2^192 + 2^96 - 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] << 32) + (z[2] << 64) + (z[3] << 96) + (z[4] << 128) + (z[5] << 160) + (z[6] << 192) + (z[7] << 224) 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) twos_complement_eval z = let x1 := z[0] + (z[1] << 32) + (z[2] << 64) + (z[3] << 96) + (z[4] << 128) + (z[5] << 160) + (z[6] << 192) + (z[7] << 224) in if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256
Structs§
- fiat_
p256_ montgomery_ domain_ field_ element - The type fiat_p256_montgomery_domain_field_element is a field element in the Montgomery domain. Bounds: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]]
- fiat_
p256_ non_ montgomery_ domain_ field_ element - The type fiat_p256_non_montgomery_domain_field_element is a field element NOT in the Montgomery domain. Bounds: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]]
Functions§
- fiat_
p256_ add - The function fiat_p256_add adds two field elements in the Montgomery domain.
- fiat_
p256_ addcarryx_ u32 - The function fiat_p256_addcarryx_u32 is an addition with carry.
- fiat_
p256_ cmovznz_ u32 - The function fiat_p256_cmovznz_u32 is a single-word conditional move.
- fiat_
p256_ divstep - The function fiat_p256_divstep computes a divstep.
- fiat_
p256_ divstep_ precomp - The function fiat_p256_divstep_precomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form).
- fiat_
p256_ from_ bytes - The function fiat_p256_from_bytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.
- fiat_
p256_ from_ montgomery - The function fiat_p256_from_montgomery translates a field element out of the Montgomery domain.
- fiat_
p256_ msat - The function fiat_p256_msat returns the saturated representation of the prime modulus.
- fiat_
p256_ mul - The function fiat_p256_mul multiplies two field elements in the Montgomery domain.
- fiat_
p256_ mulx_ u32 - The function fiat_p256_mulx_u32 is a multiplication, returning the full double-width result.
- fiat_
p256_ nonzero - The function fiat_p256_nonzero outputs a single non-zero word if the input is non-zero and zero otherwise.
- fiat_
p256_ opp - The function fiat_p256_opp negates a field element in the Montgomery domain.
- fiat_
p256_ selectznz - The function fiat_p256_selectznz is a multi-limb conditional select.
- fiat_
p256_ set_ one - The function fiat_p256_set_one returns the field element one in the Montgomery domain.
- fiat_
p256_ square - The function fiat_p256_square squares a field element in the Montgomery domain.
- fiat_
p256_ sub - The function fiat_p256_sub subtracts two field elements in the Montgomery domain.
- fiat_
p256_ subborrowx_ u32 - The function fiat_p256_subborrowx_u32 is a subtraction with borrow.
- fiat_
p256_ to_ bytes - The function fiat_p256_to_bytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.
- fiat_
p256_ to_ montgomery - The function fiat_p256_to_montgomery translates a field element into the Montgomery domain.
Type Aliases§
- fiat_
p256_ i1 - fiat_p256_i1 represents values of 1 bits, stored in one byte.
- fiat_
p256_ i2 - fiat_p256_i2 represents values of 2 bits, stored in one byte.
- fiat_
p256_ u1 - fiat_p256_u1 represents values of 1 bits, stored in one byte.
- fiat_
p256_ u2 - fiat_p256_u2 represents values of 2 bits, stored in one byte.