Trait snarkvm_wasm::FieldParameters

pub trait FieldParameters: 'static + FftParameters + PoseidonDefaultParameters {
    const MODULUS: <Self as FftParameters>::BigInteger;
    const MODULUS_BITS: u32;
    const REPR_SHAVE_BITS: u32;
    const R: <Self as FftParameters>::BigInteger;
    const R2: <Self as FftParameters>::BigInteger;
    const INV: u64;
    const GENERATOR: <Self as FftParameters>::BigInteger;
    const CAPACITY: u32;
    const T: <Self as FftParameters>::BigInteger;
    const T_MINUS_ONE_DIV_TWO: <Self as FftParameters>::BigInteger;
    const MODULUS_MINUS_ONE_DIV_TWO: <Self as FftParameters>::BigInteger;
}

A trait that defines parameters for a prime field.

Required Associated Constants

const MODULUS: <Self as FftParameters>::BigInteger

The modulus of the field.

const MODULUS_BITS: u32

The number of bits needed to represent the Self::MODULUS.

const REPR_SHAVE_BITS: u32

The number of bits that must be shaved from the beginning of the representation when randomly sampling.

const R: <Self as FftParameters>::BigInteger

R = 2^256 % Self::MODULUS

const R2: <Self as FftParameters>::BigInteger

R2 = R^2 % Self::MODULUS

const INV: u64

INV = -(MODULUS^{-1} mod MODULUS) mod MODULUS

const GENERATOR: <Self as FftParameters>::BigInteger

A multiplicative generator that is also a quadratic nonresidue. Self::GENERATOR is an element having multiplicative order Self::MODULUS - 1. There also does not exist x such that Self::GENERATOR = x^2 % Self::MODULUS

const CAPACITY: u32

The number of bits that can be reliably stored. (Should equal SELF::MODULUS_BITS - 1)

const T: <Self as FftParameters>::BigInteger

t for 2^s * t = MODULUS - 1

const T_MINUS_ONE_DIV_TWO: <Self as FftParameters>::BigInteger

(t - 1) / 2

const MODULUS_MINUS_ONE_DIV_TWO: <Self as FftParameters>::BigInteger

(Self::MODULUS - 1) / 2

Implementations on Foreign Types

impl FieldParameters for FrParameters

const GENERATOR: BigInteger256 = BigInteger([11289572479685143826u64, 11383637369941080925u64, 2288212753973340071u64, 82014976407880291u64])

70865795004005329077606947863872807680085016823885970091001235374859923341923

const MODULUS: BigInteger256 = BigInteger([13356249993388743167u64, 5950279507993463550u64, 10965441865914903552u64, 336320092672043349u64])

MODULUS = 2111115437357092606062206234695386632838870926408408195193685246394721360383

const CAPACITY: u32 = 250u32

const INV: u64 = 9_659_935_179_256_617_473u64

const MODULUS_BITS: u32 = 251u32

const MODULUS_MINUS_ONE_DIV_TWO: BigInteger256 = BigInteger([6678124996694371583u64, 2975139753996731775u64, 14706092969812227584u64, 168160046336021674u64])

const R: BigInteger256 = BigInteger([16632263305389933622u64, 10726299895124897348u64, 16608693673010411502u64, 285459069419210737u64])

const R2: BigInteger256 = BigInteger([3987543627614508126u64, 17742427666091596403u64, 14557327917022607905u64, 322810149704226881u64])

const REPR_SHAVE_BITS: u32 = 5u32

const T: BigInteger256 = BigInteger([6678124996694371583, 2975139753996731775, 14706092969812227584, 168160046336021674])

const T_MINUS_ONE_DIV_TWO: BigInteger256 = BigInteger([12562434535201961599, 1487569876998365887, 7353046484906113792, 84080023168010837])

Implementors

impl FieldParameters for FqParameters

const CAPACITY: u32 = 376u32

const GENERATOR: BigInteger384 = BigInteger([18161750659790013178, 10940260503947051403, 2338003791965605956, 14680817040264804354, 841925479686732267, 43193913801202386])

const INV: u64 = 9_586_122_913_090_633_727u64

const MODULUS: BigInteger384 = BigInteger([9586122913090633729, 1660523435060625408, 2230234197602682880, 1883307231910630287, 14284016967150029115, 121098312706494698])

const MODULUS_BITS: u32 = 377u32

const MODULUS_MINUS_ONE_DIV_TWO: BigInteger384 = BigInteger([4793061456545316864, 830261717530312704, 10338489135656117248, 10165025652810090951, 7142008483575014557, 60549156353247349])

const R: BigInteger384 = BigInteger([202099033278250856u64, 5854854902718660529u64, 11492539364873682930u64, 8885205928937022213u64, 5545221690922665192u64, 39800542322357402u64])

const R2: BigInteger384 = BigInteger([13224372171368877346, 227991066186625457, 2496666625421784173, 13825906835078366124, 9475172226622360569, 30958721782860680])

const REPR_SHAVE_BITS: u32 = 7u32

const T: BigInteger384 = BigInteger([8435453208297608227, 9853568280881552429, 7479357291536088013, 1657802422768920715, 16796279350917535980, 1720])

const T_MINUS_ONE_DIV_TWO: BigInteger384 = BigInteger([13441098641003579921, 14150156177295552022, 12963050682622819814, 828901211384460357, 8398139675458767990, 860])

impl FieldParameters for snarkvm_wasm::FrParameters

const CAPACITY: u32 = 252u32

const GENERATOR: BigInteger256 = BigInteger([2984901390528151251u64, 10561528701063790279u64, 5476750214495080041u64, 898978044469942640u64])

const INV: u64 = 725_501_752_471_715_839u64

const MODULUS: BigInteger256 = BigInteger([725501752471715841u64, 6461107452199829505u64, 6968279316240510977u64, 1345280370688173398u64])

const MODULUS_BITS: u32 = 253u32

const MODULUS_MINUS_ONE_DIV_TWO: BigInteger256 = BigInteger([9586122913090633728, 12453925762954690560, 3484139658120255488, 672640185344086699])

const R: BigInteger256 = BigInteger([9015221291577245683u64, 8239323489949974514u64, 1646089257421115374u64, 958099254763297437u64])

const R2: BigInteger256 = BigInteger([2726216793283724667u64, 14712177743343147295u64, 12091039717619697043u64, 81024008013859129u64])

const REPR_SHAVE_BITS: u32 = 3u32

const T: BigInteger256 = BigInteger([17149038877957297187, 11113960768935211860, 14608890324369326440, 9558])

const T_MINUS_ONE_DIV_TWO: BigInteger256 = BigInteger([8574519438978648593, 5556980384467605930, 7304445162184663220, 4779])