1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239
// -*- mode: rust; -*- // // This file is part of curve25519-dalek. // Copyright (c) 2016-2018 Isis Lovecruft, Henry de Valence // See LICENSE for licensing information. // // Authors: // - Isis Agora Lovecruft <isis@patternsinthevoid.net> // - Henry de Valence <hdevalence@hdevalence.ca> //! Module for common traits. use core::borrow::Borrow; use subtle; use scalar::Scalar; // ------------------------------------------------------------------------ // Public Traits // ------------------------------------------------------------------------ /// Trait for getting the identity element of a point type. pub trait Identity { /// Returns the identity element of the curve. /// Can be used as a constructor. fn identity() -> Self; } /// Trait for testing if a curve point is equivalent to the identity point. pub trait IsIdentity { /// Return true if this element is the identity element of the curve. fn is_identity(&self) -> bool; } /// Implement generic identity equality testing for a point representations /// which have constant-time equality testing and a defined identity /// constructor. impl<T> IsIdentity for T where T: subtle::ConstantTimeEq + Identity, { fn is_identity(&self) -> bool { self.ct_eq(&T::identity()).unwrap_u8() == 1u8 } } /// A trait for constant-time multiscalar multiplication without precomputation. pub trait MultiscalarMul { /// The type of point being multiplied, e.g., `RistrettoPoint`. type Point; /// Given an iterator of (possibly secret) scalars and an iterator of /// public points, compute /// $$ /// Q = c\_1 P\_1 + \cdots + c\_n P\_n. /// $$ /// /// It is an error to call this function with two iterators of different lengths. /// /// # Examples /// /// The trait bound aims for maximum flexibility: the inputs must be /// convertable to iterators (`I: IntoIter`), and the iterator's items /// must be `Borrow<Scalar>` (or `Borrow<Point>`), to allow /// iterators returning either `Scalar`s or `&Scalar`s. /// /// ``` /// use curve25519_dalek::constants; /// use curve25519_dalek::traits::MultiscalarMul; /// use curve25519_dalek::ristretto::RistrettoPoint; /// use curve25519_dalek::scalar::Scalar; /// /// // Some scalars /// let a = Scalar::from(87329482u64); /// let b = Scalar::from(37264829u64); /// let c = Scalar::from(98098098u64); /// /// // Some points /// let P = constants::RISTRETTO_BASEPOINT_POINT; /// let Q = P + P; /// let R = P + Q; /// /// // A1 = a*P + b*Q + c*R /// let abc = [a,b,c]; /// let A1 = RistrettoPoint::multiscalar_mul(&abc, &[P,Q,R]); /// // Note: (&abc).into_iter(): Iterator<Item=&Scalar> /// /// // A2 = (-a)*P + (-b)*Q + (-c)*R /// let minus_abc = abc.iter().map(|x| -x); /// let A2 = RistrettoPoint::multiscalar_mul(minus_abc, &[P,Q,R]); /// // Note: minus_abc.into_iter(): Iterator<Item=Scalar> /// /// assert_eq!(A1.compress(), (-A2).compress()); /// ``` fn multiscalar_mul<I, J>(scalars: I, points: J) -> Self::Point where I: IntoIterator, I::Item: Borrow<Scalar>, J: IntoIterator, J::Item: Borrow<Self::Point>; } /// A trait for variable-time multiscalar multiplication without precomputation. pub trait VartimeMultiscalarMul { /// The type of point being multiplied, e.g., `RistrettoPoint`. type Point; /// Given an iterator of public scalars and an iterator of /// `Option`s of points, compute either `Some(Q)`, where /// $$ /// Q = c\_1 P\_1 + \cdots + c\_n P\_n, /// $$ /// if all points were `Some(P_i)`, or else return `None`. /// /// This function is particularly useful when verifying statements /// involving compressed points. Accepting `Option<Point>` allows /// inlining point decompression into the multiscalar call, /// avoiding the need for temporary buffers. /// ``` /// use curve25519_dalek::constants; /// use curve25519_dalek::traits::VartimeMultiscalarMul; /// use curve25519_dalek::ristretto::RistrettoPoint; /// use curve25519_dalek::scalar::Scalar; /// /// // Some scalars /// let a = Scalar::from(87329482u64); /// let b = Scalar::from(37264829u64); /// let c = Scalar::from(98098098u64); /// let abc = [a,b,c]; /// /// // Some points /// let P = constants::RISTRETTO_BASEPOINT_POINT; /// let Q = P + P; /// let R = P + Q; /// let PQR = [P, Q, R]; /// /// let compressed = [P.compress(), Q.compress(), R.compress()]; /// /// // Now we can compute A1 = a*P + b*Q + c*R using P, Q, R: /// let A1 = RistrettoPoint::vartime_multiscalar_mul(&abc, &PQR); /// /// // Or using the compressed points: /// let A2 = RistrettoPoint::optional_multiscalar_mul( /// &abc, /// compressed.iter().map(|pt| pt.decompress()), /// ); /// /// assert_eq!(A2, Some(A1)); /// /// // It's also possible to mix compressed and uncompressed points: /// let A3 = RistrettoPoint::optional_multiscalar_mul( /// abc.iter() /// .chain(abc.iter()), /// compressed.iter().map(|pt| pt.decompress()) /// .chain(PQR.iter().map(|&pt| Some(pt))), /// ); /// /// assert_eq!(A3, Some(A1+A1)); /// ``` fn optional_multiscalar_mul<I, J>(scalars: I, points: J) -> Option<Self::Point> where I: IntoIterator, I::Item: Borrow<Scalar>, J: IntoIterator<Item = Option<Self::Point>>; /// Given an iterator of public scalars and an iterator of /// public points, compute /// $$ /// Q = c\_1 P\_1 + \cdots + c\_n P\_n, /// $$ /// using variable-time operations. /// /// It is an error to call this function with two iterators of different lengths. /// /// # Examples /// /// The trait bound aims for maximum flexibility: the inputs must be /// convertable to iterators (`I: IntoIter`), and the iterator's items /// must be `Borrow<Scalar>` (or `Borrow<Point>`), to allow /// iterators returning either `Scalar`s or `&Scalar`s. /// /// ``` /// use curve25519_dalek::constants; /// use curve25519_dalek::traits::VartimeMultiscalarMul; /// use curve25519_dalek::ristretto::RistrettoPoint; /// use curve25519_dalek::scalar::Scalar; /// /// // Some scalars /// let a = Scalar::from(87329482u64); /// let b = Scalar::from(37264829u64); /// let c = Scalar::from(98098098u64); /// /// // Some points /// let P = constants::RISTRETTO_BASEPOINT_POINT; /// let Q = P + P; /// let R = P + Q; /// /// // A1 = a*P + b*Q + c*R /// let abc = [a,b,c]; /// let A1 = RistrettoPoint::vartime_multiscalar_mul(&abc, &[P,Q,R]); /// // Note: (&abc).into_iter(): Iterator<Item=&Scalar> /// /// // A2 = (-a)*P + (-b)*Q + (-c)*R /// let minus_abc = abc.iter().map(|x| -x); /// let A2 = RistrettoPoint::vartime_multiscalar_mul(minus_abc, &[P,Q,R]); /// // Note: minus_abc.into_iter(): Iterator<Item=Scalar> /// /// assert_eq!(A1.compress(), (-A2).compress()); /// ``` #[allow(non_snake_case)] fn vartime_multiscalar_mul<I, J>(scalars: I, points: J) -> Self::Point where I: IntoIterator, I::Item: Borrow<Scalar>, J: IntoIterator, J::Item: Borrow<Self::Point>, Self::Point: Clone, { Self::optional_multiscalar_mul( scalars, points.into_iter().map(|P| Some(P.borrow().clone())) ).unwrap() } } // ------------------------------------------------------------------------ // Private Traits // ------------------------------------------------------------------------ /// Trait for checking whether a point is on the curve. /// /// This trait is only for debugging/testing, since it should be /// impossible for a `curve25519-dalek` user to construct an invalid /// point. pub(crate) trait ValidityCheck { /// Checks whether the point is on the curve. Not CT. fn is_valid(&self) -> bool; }