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// Copyright (C) 2019-2021 Aleo Systems Inc. // This file is part of the snarkVM library. // The snarkVM library is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // The snarkVM library is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // You should have received a copy of the GNU General Public License // along with the snarkVM library. If not, see <https://www.gnu.org/licenses/>. use crate::traits::FftParameters; /// A trait that defines parameters for a prime field. pub trait FieldParameters: 'static + FftParameters { /// The modulus of the field. const MODULUS: Self::BigInteger; /// The number of bits needed to represent the `Self::MODULUS`. const MODULUS_BITS: u32; /// The number of bits that must be shaved from the beginning of /// the representation when randomly sampling. const REPR_SHAVE_BITS: u32; /// R = 2^256 % Self::MODULUS const R: Self::BigInteger; /// R2 = R^2 % Self::MODULUS const R2: Self::BigInteger; /// INV = -(MODULUS^{-1} mod MODULUS) mod MODULUS const INV: u64; /// 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 GENERATOR: Self::BigInteger; /// The number of bits that can be reliably stored. /// (Should equal `SELF::MODULUS_BITS - 1`) const CAPACITY: u32; /// t for 2^s * t = MODULUS - 1 const T: Self::BigInteger; /// (t - 1) / 2 const T_MINUS_ONE_DIV_TWO: Self::BigInteger; /// (Self::MODULUS - 1) / 2 const MODULUS_MINUS_ONE_DIV_TWO: Self::BigInteger; }