Module fiat_crypto::p256_64

Autogenerated: ‘src/ExtractionOCaml/word_by_word_montgomery’ –lang Rust –inline p256 64 ‘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 = 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 = 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] << 64) + (z[2] << 128) + (z[3] << 192) 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] << 64) + (z[2] << 128) + (z[3] << 192) 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 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
• 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 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]

Functions

• fiat_p256_add
  The function fiat_p256_add adds two field elements in the Montgomery domain.
• fiat_p256_addcarryx_u64
  The function fiat_p256_addcarryx_u64 is an addition with carry.
• fiat_p256_cmovznz_u64
  The function fiat_p256_cmovznz_u64 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_u64
  The function fiat_p256_mulx_u64 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_u64
  The function fiat_p256_subborrowx_u64 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.