mirror of
https://github.com/saymrwulf/curve25519-dalek-source.git
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e3bf9b0213
These traits have the same interface, but with different names, so that it's not possible to use them interchangeably. (Constant-time and variable-time routines should not be used interchangeably). This commit changes the external API to use these traits, replacing ``` edwards::multiscalar_mul edwards::vartime::multiscalar_mul ``` with ``` EdwardsPoint::multiscalar_mul (as an impl) EdwardsPoint::vartime_multiscalar_mul (as an impl) ``` and similarly for Ristretto. Refactoring the backend is for a later commit. Multiscalar multiplication with precomputation is for a later commit. The `edwards::vartime` module is retained since it's used for `vartime_double_base_scalar_mul`. It should be subsumed into the precomputation API in a later commit.
1176 lines
46 KiB
Rust
1176 lines
46 KiB
Rust
// -*- mode: rust; -*-
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//
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// This file is part of curve25519-dalek.
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// Copyright (c) 2016-2017 Isis Lovecruft, Henry de Valence
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// See LICENSE for licensing information.
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//
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// Authors:
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// - Isis Agora Lovecruft <isis@patternsinthevoid.net>
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// - Henry de Valence <hdevalence@hdevalence.ca>
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// We allow non snake_case names because coordinates in projective space are
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// traditionally denoted by the capitalisation of their respective
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// counterparts in affine space. Yeah, you heard me, rustc, I'm gonna have my
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// affine and projective cakes and eat both of them too.
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#![allow(non_snake_case)]
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//! An implementation of Ristretto, which provides a prime-order group.
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//!
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//! # The Ristretto Group
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//!
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//! Ristretto is a modification of Mike Hamburg's Decaf scheme to work
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//! with cofactor-\\(8\\) curves, such as Curve25519.
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//!
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//! The introduction of the Decaf paper, [_Decaf:
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//! Eliminating cofactors through point
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//! compression_](https://eprint.iacr.org/2015/673.pdf), notes that while
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//! most cryptographic systems require a group of prime order, most
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//! concrete implementations using elliptic curve groups fall short –
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//! they either provide a group of prime order, but with incomplete or
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//! variable-time addition formulae (for instance, most Weierstrass
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//! models), or else they provide a fast and safe implementation of a
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//! group whose order is not quite a prime \\(q\\), but \\(hq\\) for a
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//! small cofactor \\(h\\) (for instance, Edwards curves, which have
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//! cofactor at least \\(4\\)).
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//!
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//! This abstraction mismatch is commonly “handled” by pushing the
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//! complexity upwards, adding ad-hoc protocol modifications. But
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//! these modifications require careful analysis and are a recurring
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//! source of [vulnerabilities][cryptonote] and [design
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//! complications][ed25519_hkd].
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//!
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//! Instead, Decaf (and Ristretto) use a quotient group to implement a
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//! prime-order group using a non-prime-order curve. This provides
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//! the correct abstraction for cryptographic systems, while retaining
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//! the speed and safety benefits of an Edwards curve.
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//!
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//! Decaf is named “after the procedure which divides the effect of
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//! coffee by \\(4\\)”. However, Curve25519 has a cofactor of
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//! \\(8\\). To eliminate its cofactor, Ristretto restricts further;
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//! this [additional restriction][ristretto_coffee] gives the
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//! _Ristretto_ encoding.
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//!
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//! More details
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//! are described in the *Implementation* section below. Ristretto
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//! points are provided in `curve25519-dalek` by the `RistrettoPoint`
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//! struct.
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//!
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//! ## Encoding and Decoding
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//!
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//! Encoding is done by converting to and from a `CompressedRistretto`
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//! struct, which is a typed wrapper around `[u8; 32]`.
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//!
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//! The encoding is not batchable, but it is possible to
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//! double-and-encode in a batch using
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//! `RistrettoPoint::double_and_compress_batch`.
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//!
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//! ## Equality Testing
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//!
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//! Testing equality of points on an Edwards curve in projective
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//! coordinates requires an expensive inversion. By contrast, equality
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//! checking in the Ristretto group can be done in projective
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//! coordinates without requiring an inversion, so it is much faster.
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//!
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//! The `RistrettoPoint` struct implements the
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//! `subtle::ConstantTimeEq` trait for constant-time equality
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//! checking, and the Rust `Eq` trait for variable-time equality
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//! checking.
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//!
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//! ## Scalars
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//!
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//! Scalars are represented by the `Scalar` struct. Each scalar has a
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//! canonical representative mod the group order. To attempt to load
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//! a supposedly-canonical scalar, use
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//! `Scalar::from_canonical_bytes()`. To check whether a
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//! representative is canonical, use `Scalar::is_canonical()`.
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//!
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//! ## Scalar Multiplication
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//!
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//! Scalar multiplication on Ristretto points is provided by:
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//!
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//! * the `*` operator between a `Scalar` and a `RistrettoPoint`, which
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//! performs constant-time variable-base scalar multiplication;
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//!
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//! * the `*` operator between a `Scalar` and a
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//! `RistrettoBasepointTable`, which performs constant-time fixed-base
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//! scalar multiplication;
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//!
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//! * the `ristretto::multiscalar_mul` function, which performs
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//! constant-time variable-base multiscalar multiplication;
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//!
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//! * the `ristretto::vartime::multiscalar_mul` function, which
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//! performs variable-time variable-base multiscalar multiplication.
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//!
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//! ## Random Points and Hashing to Ristretto
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//!
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//! The Ristretto group comes equipped with an Elligator map. This is
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//! used to implement
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//!
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//! * `RistrettoPoint::random()`, which generates random points from an
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//! RNG;
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//!
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//! * `RistrettoPoint::from_hash()` and
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//! `RistrettoPoint::hash_from_bytes()`, which perform hashing to the
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//! group.
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//!
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//! The Elligator map itself is not currently exposed.
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//!
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//! ## Implementation
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//!
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//! The Decaf suggestion is to use a quotient group, such as \\(\mathcal
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//! E / \mathcal E[4]\\) or \\(2 \mathcal E / \mathcal E[2] \\), to
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//! implement a prime-order group using a non-prime-order curve.
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//!
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//! This requires only changing
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//!
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//! 1. the function for equality checking (so that two representatives
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//! of the same coset are considered equal);
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//! 2. the function for encoding (so that two representatives of the
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//! same coset are encoded as identical bitstrings);
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//! 3. the function for decoding (so that only the canonical encoding of
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//! a coset is accepted).
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//!
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//! Internally, each coset is represented by a curve point; two points
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//! \\( P, Q \\) may represent the same coset in the same way that two
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//! points with different \\(X,Y,Z\\) coordinates may represent the
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//! same point. The group operations are carried out with no overhead
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//! using Edwards formulas.
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//!
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//! Notes on the details of the encoding can be found in the
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//! [`ristretto::notes`][ristretto_notes] submodule of the internal `curve25519-dalek`
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//! documentation.
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//!
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//! [cryptonote]:
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//! https://moderncrypto.org/mail-archive/curves/2017/000898.html
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//! [ed25519_hkd]:
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//! https://moderncrypto.org/mail-archive/curves/2017/000858.html
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//! [ristretto_coffee]:
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//! https://en.wikipedia.org/wiki/Ristretto
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//! [ristretto_notes]:
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//! https://doc-internal.dalek.rs/curve25519_dalek/ristretto/notes/index.html
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// Conditionally include the Ristretto notes if:
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// - we're on nightly (so we can include docs at all)
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// - we're in stage 2 of the build.
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// The latter point prevents a really silly and annoying problem,
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// where the location of ".." is different depending on whether we're
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// building the crate for real, or whether we're in build.rs
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// generating the lookup tables (in which case we're relative to the
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// location of build.rs, not lib.rs, so the markdown file appears
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// missing).
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//
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// This hack is also used in the avx2 notes.
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#[cfg_attr(all(feature = "nightly", feature = "stage2_build"), doc(include = "../docs/ristretto-notes.md"))]
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mod notes {
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}
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use core::fmt::Debug;
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use core::ops::{Add, Sub, Neg};
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use core::ops::{AddAssign, SubAssign};
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use core::ops::{Mul, MulAssign};
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use core::iter::Sum;
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use core::borrow::Borrow;
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#[cfg(feature = "std")]
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use rand::Rng;
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use digest::Digest;
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use generic_array::typenum::U64;
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use constants;
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use field::FieldElement;
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use subtle::ConditionallyAssignable;
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use subtle::ConditionallyNegatable;
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use subtle::ConstantTimeEq;
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use subtle::Choice;
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use edwards::EdwardsPoint;
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use edwards::EdwardsBasepointTable;
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use scalar::Scalar;
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use curve_models::CompletedPoint;
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use traits::{Identity, MultiscalarMul, VartimeMultiscalarMul};
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// ------------------------------------------------------------------------
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// Compressed points
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// ------------------------------------------------------------------------
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/// A Ristretto point, in compressed wire format.
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///
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/// The Ristretto encoding is canonical, so two points are equal if and
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/// only if their encodings are equal.
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#[derive(Copy, Clone, Eq, PartialEq)]
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pub struct CompressedRistretto(pub [u8; 32]);
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impl CompressedRistretto {
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/// Copy the bytes of this `CompressedRistretto`.
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pub fn to_bytes(&self) -> [u8; 32] {
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self.0
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}
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/// View this `CompressedRistretto` as an array of bytes.
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pub fn as_bytes(&self) -> &[u8; 32] {
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&self.0
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}
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/// Attempt to decompress to an `RistrettoPoint`.
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///
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/// # Return
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///
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/// - `Some(RistrettoPoint)` if `self` was the canonical encoding of a point;
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///
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/// - `None` if `self` was not the canonical encoding of a point.
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pub fn decompress(&self) -> Option<RistrettoPoint> {
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// Step 1. Check s for validity:
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// 1.a) s must be 32 bytes (we get this from the type system)
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// 1.b) s < p
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// 1.c) s is nonnegative
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//
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// Our decoding routine ignores the high bit, so the only
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// possible failure for 1.b) is if someone encodes s in 0..18
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// as s+p in 2^255-19..2^255-1. We can check this by
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// converting back to bytes, and checking that we get the
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// original input, since our encoding routine is canonical.
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let s = FieldElement::from_bytes(self.as_bytes());
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let s_bytes_check = s.to_bytes();
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let s_encoding_is_canonical =
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&s_bytes_check[..].ct_eq(self.as_bytes());
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let s_is_negative = s.is_negative();
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if s_encoding_is_canonical.unwrap_u8() == 0u8 || s_is_negative.unwrap_u8() == 1u8 {
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return None;
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}
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// Step 2. The rest. (XXX write comments)
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let one = FieldElement::one();
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let ss = s.square();
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let yden = &one + &ss; // 1 - a*s^2
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let ynum = &one - &ss; // 1 + a*s^2
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let yden_sqr = yden.square();
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let xden_sqr = &(&(-&constants::EDWARDS_D) * &ynum.square()) - &yden_sqr;
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let (ok, invsqrt) = (&xden_sqr * &yden_sqr).invsqrt();
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let xden_inv = &invsqrt * &yden;
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let yden_inv = &invsqrt * &(&xden_inv * &xden_sqr);
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let mut x = &(&s + &s) * &xden_inv; // 2*s*xden_inv
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let x_is_negative = x.is_negative();
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x.conditional_negate(x_is_negative);
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let y = &ynum * &yden_inv;
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let t = &x * &y;
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if ok.unwrap_u8() == 0u8 || t.is_negative().unwrap_u8() == 1u8 || y.is_zero().unwrap_u8() == 1u8 {
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return None;
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} else {
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return Some(RistrettoPoint(EdwardsPoint{X: x, Y: y, Z: one, T: t}));
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}
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}
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}
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impl Identity for CompressedRistretto {
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fn identity() -> CompressedRistretto {
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CompressedRistretto([0u8; 32])
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}
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}
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// ------------------------------------------------------------------------
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// Serde support
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// ------------------------------------------------------------------------
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// Serializes to and from `RistrettoPoint` directly, doing compression
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// and decompression internally. This means that users can create
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// structs containing `RistrettoPoint`s and use Serde's derived
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// serializers to serialize those structures.
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#[cfg(feature = "serde")]
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use serde::{self, Serialize, Deserialize, Serializer, Deserializer};
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#[cfg(feature = "serde")]
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use serde::de::Visitor;
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#[cfg(feature = "serde")]
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impl Serialize for RistrettoPoint {
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fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
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where S: Serializer
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{
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serializer.serialize_bytes(self.compress().as_bytes())
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}
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}
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#[cfg(feature = "serde")]
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impl<'de> Deserialize<'de> for RistrettoPoint {
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fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
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where D: Deserializer<'de>
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{
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struct RistrettoPointVisitor;
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impl<'de> Visitor<'de> for RistrettoPointVisitor {
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type Value = RistrettoPoint;
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fn expecting(&self, formatter: &mut ::core::fmt::Formatter) -> ::core::fmt::Result {
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formatter.write_str("a valid point in Ristretto format")
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}
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fn visit_bytes<E>(self, v: &[u8]) -> Result<RistrettoPoint, E>
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where E: serde::de::Error
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{
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if v.len() == 32 {
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let mut arr32 = [0u8; 32];
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arr32[0..32].copy_from_slice(v);
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CompressedRistretto(arr32)
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.decompress()
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.ok_or(serde::de::Error::custom("decompression failed"))
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} else {
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Err(serde::de::Error::invalid_length(v.len(), &self))
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}
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}
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}
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deserializer.deserialize_bytes(RistrettoPointVisitor)
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}
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}
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// ------------------------------------------------------------------------
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// Internal point representations
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// ------------------------------------------------------------------------
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/// A `RistrettoPoint` represents a point in the Ristretto group for
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/// Curve25519. Ristretto, a variant of Decaf, constructs a
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/// prime-order group as a quotient group of a subgroup of (the
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/// Edwards form of) Curve25519.
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///
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/// Internally, a `RistrettoPoint` is implemented as a wrapper type
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/// around `EdwardsPoint`, with custom equality, compression, and
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/// decompression routines to account for the quotient. This means that
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/// operations on `RistrettoPoint`s are exactly as fast as operations on
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/// `EdwardsPoint`s.
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///
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#[derive(Copy, Clone)]
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pub struct RistrettoPoint(pub(crate) EdwardsPoint);
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impl RistrettoPoint {
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/// Compress this point using the Ristretto encoding.
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pub fn compress(&self) -> CompressedRistretto {
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let mut X = self.0.X;
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let mut Y = self.0.Y;
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let Z = &self.0.Z;
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let T = &self.0.T;
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let u1 = &(Z + &Y) * &(Z - &Y);
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let u2 = &X * &Y;
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// Ignore return value since this is always square
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let (_, invsqrt) = (&u1 * &u2.square()).invsqrt();
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let i1 = &invsqrt * &u1;
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let i2 = &invsqrt * &u2;
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let z_inv = &i1 * &(&i2 * T);
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let mut den_inv = i2;
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let iX = &X * &constants::SQRT_M1;
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let iY = &Y * &constants::SQRT_M1;
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let ristretto_magic = &constants::INVSQRT_A_MINUS_D;
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let enchanted_denominator = &i1 * ristretto_magic;
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let rotate = (T * &z_inv).is_negative();
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X.conditional_assign(&iY, rotate);
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Y.conditional_assign(&iX, rotate);
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den_inv.conditional_assign(&enchanted_denominator, rotate);
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Y.conditional_negate((&X * &z_inv).is_negative());
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let mut s = &den_inv * &(Z - &Y);
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let s_is_negative = s.is_negative();
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s.conditional_negate(s_is_negative);
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CompressedRistretto(s.to_bytes())
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}
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/// Double-and-compress a batch of points. The Ristretto encoding
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/// is not batchable, since it requires an inverse square root.
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///
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/// However, given input points \\( P\_1, \ldots, P\_n, \\)
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/// it is possible to compute the encodings of their doubles \\(
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/// \mathrm{enc}( [2]P\_1), \ldots, \mathrm{enc}( [2]P\_n ) \\)
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/// in a batch.
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///
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/// This function has optimal performance when the batch size is a
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/// power of two, but this is not a requirement.
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///
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/// ```
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/// # extern crate curve25519_dalek;
|
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/// # use curve25519_dalek::ristretto::RistrettoPoint;
|
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/// extern crate rand;
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/// use rand::OsRng;
|
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///
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/// # // Need fn main() here in comment so the doctest compiles
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/// # // See https://doc.rust-lang.org/book/documentation.html#documentation-as-tests
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/// # fn main() {
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/// let mut rng = OsRng::new().unwrap();
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/// let points: Vec<RistrettoPoint> =
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/// (0..32).map(|_| RistrettoPoint::random(&mut rng)).collect();
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///
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/// let compressed = RistrettoPoint::double_and_compress_batch(&points);
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///
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/// for (P, P2_compressed) in points.iter().zip(compressed.iter()) {
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/// assert_eq!(*P2_compressed, (P + P).compress());
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/// }
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/// # }
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/// ```
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#[cfg(any(feature = "alloc", feature = "std"))]
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pub fn double_and_compress_batch<'a, I>(points: I) -> Vec<CompressedRistretto>
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where I: IntoIterator<Item = &'a RistrettoPoint>
|
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{
|
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#[derive(Copy, Clone, Debug)]
|
||
struct BatchCompressState {
|
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e: FieldElement,
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f: FieldElement,
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g: FieldElement,
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h: FieldElement,
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eg: FieldElement,
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fh: FieldElement,
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}
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impl BatchCompressState {
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fn efgh(&self) -> FieldElement {
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&self.eg * &self.fh
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}
|
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}
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impl<'a> From<&'a RistrettoPoint> for BatchCompressState {
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fn from(P: &'a RistrettoPoint) -> BatchCompressState {
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let XX = P.0.X.square();
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let YY = P.0.Y.square();
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let ZZ = P.0.Z.square();
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let dTT = &P.0.T.square() * &constants::EDWARDS_D;
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let e = &P.0.X * &(&P.0.Y + &P.0.Y); // = 2*X*Y
|
||
let f = &ZZ + &dTT; // = Z^2 + d*T^2
|
||
let g = &YY + &XX; // = Y^2 - a*X^2
|
||
let h = &ZZ - &dTT; // = Z^2 - d*T^2
|
||
|
||
let eg = &e * &g;
|
||
let fh = &f * &h;
|
||
|
||
BatchCompressState{ e: e, f: f, g: g, h: h, eg: eg, fh: fh }
|
||
}
|
||
}
|
||
|
||
let states: Vec<BatchCompressState> = points.into_iter().map(|P| BatchCompressState::from(P)).collect();
|
||
|
||
let mut invs: Vec<FieldElement> = states.iter().map(|state| state.efgh()).collect();
|
||
|
||
FieldElement::batch_invert(&mut invs[..]);
|
||
|
||
states.iter().zip(invs.iter()).map(|(state, inv): (&BatchCompressState, &FieldElement)| {
|
||
let Zinv = &state.eg * &inv;
|
||
let Tinv = &state.fh * &inv;
|
||
|
||
let mut magic = constants::INVSQRT_A_MINUS_D;
|
||
|
||
let negcheck1 = (&state.eg * &Zinv).is_negative();
|
||
|
||
let mut e = state.e;
|
||
let mut g = state.g;
|
||
let mut h = state.h;
|
||
|
||
let minus_e = -&e;
|
||
let f_times_sqrta = &state.f * &constants::SQRT_M1;
|
||
|
||
e.conditional_assign(&state.g, negcheck1);
|
||
g.conditional_assign(&minus_e, negcheck1);
|
||
h.conditional_assign(&f_times_sqrta, negcheck1);
|
||
|
||
magic.conditional_assign(&constants::SQRT_M1, negcheck1);
|
||
|
||
let negcheck2 = (&(&h * &e) * &Zinv).is_negative();
|
||
|
||
g.conditional_negate(negcheck2);
|
||
|
||
let mut s = &(&h - &g) * &(&magic * &(&g * &Tinv));
|
||
|
||
let s_is_negative = s.is_negative();
|
||
s.conditional_negate(s_is_negative);
|
||
|
||
CompressedRistretto(s.to_bytes())
|
||
}).collect()
|
||
}
|
||
|
||
|
||
/// Return the coset self + E[4], for debugging.
|
||
fn coset4(&self) -> [EdwardsPoint; 4] {
|
||
[ self.0
|
||
, &self.0 + &constants::EIGHT_TORSION[2]
|
||
, &self.0 + &constants::EIGHT_TORSION[4]
|
||
, &self.0 + &constants::EIGHT_TORSION[6]
|
||
]
|
||
}
|
||
|
||
/// Computes the Ristretto Elligator map.
|
||
///
|
||
/// # Note
|
||
///
|
||
/// This method is not public because it's just used for hashing
|
||
/// to a point -- proper elligator support is deferred for now.
|
||
pub(crate) fn elligator_ristretto_flavor(r_0: &FieldElement) -> RistrettoPoint {
|
||
let (i, d) = (&constants::SQRT_M1, &constants::EDWARDS_D);
|
||
let one = FieldElement::one();
|
||
|
||
let r = i * &r_0.square();
|
||
|
||
// D = (dr -a)(ar-d) = -(dr+1)(r+d)
|
||
let D = -&( &(&(d * &r) + &one) * &(&r + d) );
|
||
// N = a(d-a)(d+a)(r+1) = -(r+1)(d^2 -1)
|
||
let d_sq = d.square();
|
||
let N = -&( &(&d_sq - &one) * &(&r + &one) );
|
||
|
||
let mut s = FieldElement::zero();
|
||
let mut c = -&one;
|
||
|
||
let (N_over_D_is_square, maybe_s) = FieldElement::sqrt_ratio(&N, &D);
|
||
// s = sqrt(N/D) if N/D is square
|
||
s.conditional_assign(&maybe_s, N_over_D_is_square);
|
||
|
||
// XXX how exactly do we reuse the computation of sqrt(N/D) to find sqrt(rN/D) ?
|
||
let (rN_over_D_is_square, mut maybe_s) = FieldElement::sqrt_ratio(&(&r*&N), &D);
|
||
maybe_s.negate();
|
||
|
||
// s = -sqrt(rN/D) if rN/D is square (should happen exactly when N/D is nonsquare)
|
||
debug_assert_eq!((N_over_D_is_square ^ rN_over_D_is_square).unwrap_u8(), 1u8);
|
||
s.conditional_assign(&maybe_s, rN_over_D_is_square);
|
||
c.conditional_assign(&r, rN_over_D_is_square);
|
||
|
||
// T = (c * (r - one) * (d-one).square()) - D;
|
||
let T = &(&c * &(&(&r - &one) * &((d - &one).square()))) - &D;
|
||
|
||
let s_sq = s.square();
|
||
let P = CompletedPoint{
|
||
X: &(&s + &s) * &D,
|
||
Z: &T * &constants::SQRT_AD_MINUS_ONE,
|
||
Y: &FieldElement::one() - &s_sq,
|
||
T: &FieldElement::one() + &s_sq,
|
||
};
|
||
|
||
// Convert to extended and return.
|
||
RistrettoPoint(P.to_extended())
|
||
}
|
||
|
||
/// Return a `RistrettoPoint` chosen uniformly at random using a user-provided RNG.
|
||
///
|
||
/// # Inputs
|
||
///
|
||
/// * `rng`: any RNG which implements the `rand::Rng` interface.
|
||
///
|
||
/// # Returns
|
||
///
|
||
/// A random element of the Ristretto group.
|
||
///
|
||
/// # Implementation
|
||
///
|
||
/// Uses the Ristretto-flavoured Elligator 2 map, so that the
|
||
/// discrete log of the output point with respect to any other
|
||
/// point should be unknown. The map is applied twice and the
|
||
/// results are added, to ensure a uniform distribution.
|
||
#[cfg(feature = "std")]
|
||
pub fn random<T: Rng>(rng: &mut T) -> Self {
|
||
let mut field_bytes = [0u8; 32];
|
||
|
||
rng.fill_bytes(&mut field_bytes);
|
||
let r_1 = FieldElement::from_bytes(&field_bytes);
|
||
let R_1 = RistrettoPoint::elligator_ristretto_flavor(&r_1);
|
||
|
||
rng.fill_bytes(&mut field_bytes);
|
||
let r_2 = FieldElement::from_bytes(&field_bytes);
|
||
let R_2 = RistrettoPoint::elligator_ristretto_flavor(&r_2);
|
||
|
||
// Applying Elligator twice and adding the results ensures a
|
||
// uniform distribution.
|
||
&R_1 + &R_2
|
||
}
|
||
|
||
/// Hash a slice of bytes into a `RistrettoPoint`.
|
||
///
|
||
/// Takes a type parameter `D`, which is any `Digest` producing 64
|
||
/// bytes of output.
|
||
///
|
||
/// Convenience wrapper around `from_hash`.
|
||
///
|
||
/// # Implementation
|
||
///
|
||
/// Uses the Ristretto-flavoured Elligator 2 map, so that the
|
||
/// discrete log of the output point with respect to any other
|
||
/// point should be unknown. The map is applied twice and the
|
||
/// results are added, to ensure a uniform distribution.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # extern crate curve25519_dalek;
|
||
/// # use curve25519_dalek::ristretto::RistrettoPoint;
|
||
/// extern crate sha2;
|
||
/// use sha2::Sha512;
|
||
///
|
||
/// # // Need fn main() here in comment so the doctest compiles
|
||
/// # // See https://doc.rust-lang.org/book/documentation.html#documentation-as-tests
|
||
/// # fn main() {
|
||
/// let msg = "To really appreciate architecture, you may even need to commit a murder";
|
||
/// let P = RistrettoPoint::hash_from_bytes::<Sha512>(msg.as_bytes());
|
||
/// # }
|
||
/// ```
|
||
///
|
||
pub fn hash_from_bytes<D>(input: &[u8]) -> RistrettoPoint
|
||
where D: Digest<OutputSize = U64> + Default
|
||
{
|
||
let mut hash = D::default();
|
||
hash.input(input);
|
||
RistrettoPoint::from_hash(hash)
|
||
}
|
||
|
||
/// Construct a `RistrettoPoint` from an existing `Digest` instance.
|
||
///
|
||
/// Use this instead of `hash_from_bytes` if it is more convenient
|
||
/// to stream data into the `Digest` than to pass a single byte
|
||
/// slice.
|
||
pub fn from_hash<D>(hash: D) -> RistrettoPoint
|
||
where D: Digest<OutputSize = U64> + Default
|
||
{
|
||
// dealing with generic arrays is clumsy, until const generics land
|
||
let output = hash.result();
|
||
|
||
let mut r_1_bytes = [0u8; 32];
|
||
r_1_bytes.copy_from_slice(&output.as_slice()[0..32]);
|
||
let r_1 = FieldElement::from_bytes(&r_1_bytes);
|
||
let R_1 = RistrettoPoint::elligator_ristretto_flavor(&r_1);
|
||
|
||
let mut r_2_bytes = [0u8; 32];
|
||
r_2_bytes.copy_from_slice(&output.as_slice()[0..32]);
|
||
let r_2 = FieldElement::from_bytes(&r_2_bytes);
|
||
let R_2 = RistrettoPoint::elligator_ristretto_flavor(&r_2);
|
||
|
||
// Applying Elligator twice and adding the results ensures a
|
||
// uniform distribution.
|
||
&R_1 + &R_2
|
||
}
|
||
}
|
||
|
||
impl Identity for RistrettoPoint {
|
||
fn identity() -> RistrettoPoint {
|
||
RistrettoPoint(EdwardsPoint::identity())
|
||
}
|
||
}
|
||
|
||
// ------------------------------------------------------------------------
|
||
// Equality
|
||
// ------------------------------------------------------------------------
|
||
|
||
impl PartialEq for RistrettoPoint {
|
||
fn eq(&self, other: &RistrettoPoint) -> bool {
|
||
self.ct_eq(other).unwrap_u8() == 1u8
|
||
}
|
||
}
|
||
|
||
impl ConstantTimeEq for RistrettoPoint {
|
||
/// Test equality between two `RistrettoPoint`s.
|
||
///
|
||
/// # Returns
|
||
///
|
||
/// * `Choice(1)` if the two `RistrettoPoint`s are equal;
|
||
/// * `Choice(0)` otherwise.
|
||
fn ct_eq(&self, other: &RistrettoPoint) -> Choice {
|
||
let X1Y2 = &self.0.X * &other.0.Y;
|
||
let Y1X2 = &self.0.Y * &other.0.X;
|
||
let X1X2 = &self.0.X * &other.0.X;
|
||
let Y1Y2 = &self.0.Y * &other.0.Y;
|
||
|
||
X1Y2.ct_eq(&Y1X2) | X1X2.ct_eq(&Y1Y2)
|
||
}
|
||
}
|
||
|
||
impl Eq for RistrettoPoint {}
|
||
|
||
// ------------------------------------------------------------------------
|
||
// Arithmetic
|
||
// ------------------------------------------------------------------------
|
||
|
||
impl<'a, 'b> Add<&'b RistrettoPoint> for &'a RistrettoPoint {
|
||
type Output = RistrettoPoint;
|
||
|
||
fn add(self, other: &'b RistrettoPoint) -> RistrettoPoint {
|
||
RistrettoPoint(&self.0 + &other.0)
|
||
}
|
||
}
|
||
|
||
define_add_variants!(LHS = RistrettoPoint, RHS = RistrettoPoint, Output = RistrettoPoint);
|
||
|
||
impl<'b> AddAssign<&'b RistrettoPoint> for RistrettoPoint {
|
||
fn add_assign(&mut self, _rhs: &RistrettoPoint) {
|
||
*self = (self as &RistrettoPoint) + _rhs;
|
||
}
|
||
}
|
||
|
||
define_add_assign_variants!(LHS = RistrettoPoint, RHS = RistrettoPoint);
|
||
|
||
impl<'a, 'b> Sub<&'b RistrettoPoint> for &'a RistrettoPoint {
|
||
type Output = RistrettoPoint;
|
||
|
||
fn sub(self, other: &'b RistrettoPoint) -> RistrettoPoint {
|
||
RistrettoPoint(&self.0 - &other.0)
|
||
}
|
||
}
|
||
|
||
define_sub_variants!(LHS = RistrettoPoint, RHS = RistrettoPoint, Output = RistrettoPoint);
|
||
|
||
impl<'b> SubAssign<&'b RistrettoPoint> for RistrettoPoint {
|
||
fn sub_assign(&mut self, _rhs: &RistrettoPoint) {
|
||
*self = (self as &RistrettoPoint) - _rhs;
|
||
}
|
||
}
|
||
|
||
define_sub_assign_variants!(LHS = RistrettoPoint, RHS = RistrettoPoint);
|
||
|
||
impl<T> Sum<T> for RistrettoPoint
|
||
where
|
||
T: Borrow<RistrettoPoint>
|
||
{
|
||
fn sum<I>(iter: I) -> Self
|
||
where
|
||
I: Iterator<Item = T>
|
||
{
|
||
iter.fold(RistrettoPoint::identity(), |acc, item| acc + item.borrow())
|
||
}
|
||
}
|
||
|
||
impl<'a> Neg for &'a RistrettoPoint {
|
||
type Output = RistrettoPoint;
|
||
|
||
fn neg(self) -> RistrettoPoint {
|
||
RistrettoPoint(-&self.0)
|
||
}
|
||
}
|
||
|
||
impl Neg for RistrettoPoint {
|
||
type Output = RistrettoPoint;
|
||
|
||
fn neg(self) -> RistrettoPoint {
|
||
-&self
|
||
}
|
||
}
|
||
|
||
impl<'b> MulAssign<&'b Scalar> for RistrettoPoint {
|
||
fn mul_assign(&mut self, scalar: &'b Scalar) {
|
||
let result = (self as &RistrettoPoint) * scalar;
|
||
*self = result;
|
||
}
|
||
}
|
||
|
||
impl<'a, 'b> Mul<&'b Scalar> for &'a RistrettoPoint {
|
||
type Output = RistrettoPoint;
|
||
/// Scalar multiplication: compute `scalar * self`.
|
||
fn mul(self, scalar: &'b Scalar) -> RistrettoPoint {
|
||
RistrettoPoint(&self.0 * scalar)
|
||
}
|
||
}
|
||
|
||
impl<'a, 'b> Mul<&'b RistrettoPoint> for &'a Scalar {
|
||
type Output = RistrettoPoint;
|
||
|
||
/// Scalar multiplication: compute `self * scalar`.
|
||
fn mul(self, point: &'b RistrettoPoint) -> RistrettoPoint {
|
||
RistrettoPoint(self * &point.0)
|
||
}
|
||
}
|
||
|
||
define_mul_assign_variants!(LHS = RistrettoPoint, RHS = Scalar);
|
||
|
||
define_mul_variants!(LHS = RistrettoPoint, RHS = Scalar, Output = RistrettoPoint);
|
||
define_mul_variants!(LHS = Scalar, RHS = RistrettoPoint, Output = RistrettoPoint);
|
||
|
||
// ------------------------------------------------------------------------
|
||
// Multiscalar Multiplication impls
|
||
// ------------------------------------------------------------------------
|
||
|
||
// These use iterator combinators to unwrap the underlying points and
|
||
// forward to the EdwardsPoint implementations.
|
||
|
||
#[cfg(any(feature = "alloc", feature = "std"))]
|
||
impl MultiscalarMul for RistrettoPoint {
|
||
type Point = RistrettoPoint;
|
||
|
||
fn multiscalar_mul<I, J>(scalars: I, points: J) -> RistrettoPoint
|
||
where
|
||
I: IntoIterator,
|
||
I::Item: Borrow<Scalar>,
|
||
J: IntoIterator,
|
||
J::Item: Borrow<RistrettoPoint>,
|
||
{
|
||
let extended_points = points.into_iter().map(|P| P.borrow().0);
|
||
RistrettoPoint(
|
||
EdwardsPoint::multiscalar_mul(scalars, extended_points)
|
||
)
|
||
}
|
||
}
|
||
|
||
#[cfg(any(feature = "alloc", feature = "std"))]
|
||
impl VartimeMultiscalarMul for RistrettoPoint {
|
||
type Point = RistrettoPoint;
|
||
|
||
fn vartime_multiscalar_mul<I, J>(scalars: I, points: J) -> RistrettoPoint
|
||
where
|
||
I: IntoIterator,
|
||
I::Item: Borrow<Scalar>,
|
||
J: IntoIterator,
|
||
J::Item: Borrow<RistrettoPoint>,
|
||
{
|
||
let extended_points = points.into_iter().map(|P| P.borrow().0);
|
||
RistrettoPoint(
|
||
EdwardsPoint::vartime_multiscalar_mul(scalars, extended_points)
|
||
)
|
||
}
|
||
}
|
||
|
||
/// A precomputed table of multiples of a basepoint, used to accelerate
|
||
/// scalar multiplication.
|
||
///
|
||
/// A precomputed table of multiples of the Ristretto basepoint is
|
||
/// available in the `constants` module:
|
||
/// ```
|
||
/// use curve25519_dalek::constants;
|
||
/// use curve25519_dalek::scalar::Scalar;
|
||
///
|
||
/// let a = Scalar::from_u64(87329482);
|
||
/// let P = &a * &constants::RISTRETTO_BASEPOINT_TABLE;
|
||
/// ```
|
||
#[derive(Clone)]
|
||
pub struct RistrettoBasepointTable(pub(crate) EdwardsBasepointTable);
|
||
|
||
impl<'a, 'b> Mul<&'b Scalar> for &'a RistrettoBasepointTable {
|
||
type Output = RistrettoPoint;
|
||
|
||
fn mul(self, scalar: &'b Scalar) -> RistrettoPoint {
|
||
RistrettoPoint(&self.0 * scalar)
|
||
}
|
||
}
|
||
|
||
impl<'a, 'b> Mul<&'a RistrettoBasepointTable> for &'b Scalar {
|
||
type Output = RistrettoPoint;
|
||
|
||
fn mul(self, basepoint_table: &'a RistrettoBasepointTable) -> RistrettoPoint {
|
||
RistrettoPoint(self * &basepoint_table.0)
|
||
}
|
||
}
|
||
|
||
impl RistrettoBasepointTable {
|
||
/// Create a precomputed table of multiples of the given `basepoint`.
|
||
pub fn create(basepoint: &RistrettoPoint) -> RistrettoBasepointTable {
|
||
RistrettoBasepointTable(EdwardsBasepointTable::create(&basepoint.0))
|
||
}
|
||
|
||
/// Get the basepoint for this table as a `RistrettoPoint`.
|
||
pub fn basepoint(&self) -> RistrettoPoint {
|
||
RistrettoPoint(self.0.basepoint())
|
||
}
|
||
}
|
||
|
||
// ------------------------------------------------------------------------
|
||
// Constant-time conditional assignment
|
||
// ------------------------------------------------------------------------
|
||
|
||
impl ConditionallyAssignable for RistrettoPoint {
|
||
/// Conditionally assign `other` to `self`, if `choice == Choice(1)`.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # extern crate subtle;
|
||
/// # extern crate curve25519_dalek;
|
||
/// #
|
||
/// use subtle::ConditionallyAssignable;
|
||
/// use subtle::Choice;
|
||
/// #
|
||
/// # use curve25519_dalek::traits::Identity;
|
||
/// # use curve25519_dalek::ristretto::RistrettoPoint;
|
||
/// # use curve25519_dalek::constants;
|
||
/// # fn main() {
|
||
///
|
||
/// let A = RistrettoPoint::identity();
|
||
/// let B = constants::RISTRETTO_BASEPOINT_POINT;
|
||
///
|
||
/// let mut P = A;
|
||
///
|
||
/// P.conditional_assign(&B, Choice::from(0));
|
||
/// assert_eq!(P, A);
|
||
/// P.conditional_assign(&B, Choice::from(1));
|
||
/// assert_eq!(P, B);
|
||
/// # }
|
||
/// ```
|
||
fn conditional_assign(&mut self, other: &RistrettoPoint, choice: Choice) {
|
||
self.0.X.conditional_assign(&other.0.X, choice);
|
||
self.0.Y.conditional_assign(&other.0.Y, choice);
|
||
self.0.Z.conditional_assign(&other.0.Z, choice);
|
||
self.0.T.conditional_assign(&other.0.T, choice);
|
||
}
|
||
}
|
||
|
||
// ------------------------------------------------------------------------
|
||
// Debug traits
|
||
// ------------------------------------------------------------------------
|
||
|
||
impl Debug for CompressedRistretto {
|
||
fn fmt(&self, f: &mut ::core::fmt::Formatter) -> ::core::fmt::Result {
|
||
write!(f, "CompressedRistretto: {:?}", self.as_bytes())
|
||
}
|
||
}
|
||
|
||
impl Debug for RistrettoPoint {
|
||
fn fmt(&self, f: &mut ::core::fmt::Formatter) -> ::core::fmt::Result {
|
||
let coset = self.coset4();
|
||
write!(f, "RistrettoPoint: coset \n{:?}\n{:?}\n{:?}\n{:?}",
|
||
coset[0], coset[1], coset[2], coset[3])
|
||
}
|
||
}
|
||
|
||
// ------------------------------------------------------------------------
|
||
// Tests
|
||
// ------------------------------------------------------------------------
|
||
|
||
#[cfg(all(test, feature = "stage2_build"))]
|
||
mod test {
|
||
use rand::OsRng;
|
||
|
||
use scalar::Scalar;
|
||
use constants;
|
||
use edwards::CompressedEdwardsY;
|
||
use traits::{Identity, ValidityCheck};
|
||
use super::*;
|
||
|
||
#[cfg(feature = "serde")]
|
||
use serde_cbor;
|
||
|
||
#[test]
|
||
#[cfg(feature = "serde")]
|
||
fn serde_cbor_basepoint_roundtrip() {
|
||
let output = serde_cbor::to_vec(&constants::RISTRETTO_BASEPOINT_POINT).unwrap();
|
||
let parsed: RistrettoPoint = serde_cbor::from_slice(&output).unwrap();
|
||
assert_eq!(parsed, constants::RISTRETTO_BASEPOINT_POINT);
|
||
}
|
||
|
||
#[test]
|
||
fn scalarmult_ristrettopoint_works_both_ways() {
|
||
let P = constants::RISTRETTO_BASEPOINT_POINT;
|
||
let s = Scalar::from_u64(999);
|
||
|
||
let P1 = &P * &s;
|
||
let P2 = &s * &P;
|
||
|
||
assert!(P1.compress().as_bytes() == P2.compress().as_bytes());
|
||
}
|
||
|
||
#[test]
|
||
fn impl_sum() {
|
||
|
||
// Test that sum works for non-empty iterators
|
||
let BASE = constants::RISTRETTO_BASEPOINT_POINT;
|
||
|
||
let s1 = Scalar::from_u64(999);
|
||
let P1 = &BASE * &s1;
|
||
|
||
let s2 = Scalar::from_u64(333);
|
||
let P2 = &BASE * &s2;
|
||
|
||
let vec = vec![P1.clone(), P2.clone()];
|
||
let sum: RistrettoPoint = vec.iter().sum();
|
||
|
||
assert_eq!(sum, P1 + P2);
|
||
|
||
// Test that sum works for the empty iterator
|
||
let empty_vector: Vec<RistrettoPoint> = vec![];
|
||
let sum: RistrettoPoint = empty_vector.iter().sum();
|
||
|
||
assert_eq!(sum, RistrettoPoint::identity());
|
||
|
||
// Test that sum works on owning iterators
|
||
let s = Scalar::from_u64(2);
|
||
let mapped = vec.iter().map(|x| x * &s);
|
||
let sum: RistrettoPoint = mapped.sum();
|
||
|
||
assert_eq!(sum, &P1 * &s + &P2 * &s);
|
||
}
|
||
|
||
#[test]
|
||
fn decompress_negative_s_fails() {
|
||
// constants::d is neg, so decompression should fail as |d| != d.
|
||
let bad_compressed = CompressedRistretto(constants::EDWARDS_D.to_bytes());
|
||
assert!(bad_compressed.decompress().is_none());
|
||
}
|
||
|
||
#[test]
|
||
fn decompress_id() {
|
||
let compressed_id = CompressedRistretto::identity();
|
||
let id = compressed_id.decompress().unwrap();
|
||
let mut identity_in_coset = false;
|
||
for P in &id.coset4() {
|
||
if P.compress() == CompressedEdwardsY::identity() {
|
||
identity_in_coset = true;
|
||
}
|
||
}
|
||
assert!(identity_in_coset);
|
||
}
|
||
|
||
#[test]
|
||
fn compress_id() {
|
||
let id = RistrettoPoint::identity();
|
||
assert_eq!(id.compress(), CompressedRistretto::identity());
|
||
}
|
||
|
||
#[test]
|
||
fn basepoint_roundtrip() {
|
||
let bp_compressed_ristretto = constants::RISTRETTO_BASEPOINT_POINT.compress();
|
||
let bp_recaf = bp_compressed_ristretto.decompress().unwrap().0;
|
||
// Check that bp_recaf differs from bp by a point of order 4
|
||
let diff = &constants::RISTRETTO_BASEPOINT_POINT.0 - &bp_recaf;
|
||
let diff4 = diff.mul_by_pow_2(2);
|
||
assert_eq!(diff4.compress(), CompressedEdwardsY::identity());
|
||
}
|
||
|
||
#[test]
|
||
fn encodings_of_small_multiples_of_basepoint() {
|
||
// Table of encodings of i*basepoint
|
||
// Generated using ristretto.sage
|
||
let compressed = [
|
||
CompressedRistretto([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
|
||
CompressedRistretto([226, 242, 174, 10, 106, 188, 78, 113, 168, 132, 169, 97, 197, 0, 81, 95, 88, 227, 11, 106, 165, 130, 221, 141, 182, 166, 89, 69, 224, 141, 45, 118]),
|
||
CompressedRistretto([106, 73, 50, 16, 247, 73, 156, 209, 127, 236, 181, 16, 174, 12, 234, 35, 161, 16, 232, 213, 185, 1, 248, 172, 173, 211, 9, 92, 115, 163, 185, 25]),
|
||
CompressedRistretto([148, 116, 31, 93, 93, 82, 117, 94, 206, 79, 35, 240, 68, 238, 39, 213, 209, 234, 30, 43, 209, 150, 180, 98, 22, 107, 22, 21, 42, 157, 2, 89]),
|
||
CompressedRistretto([218, 128, 134, 39, 115, 53, 139, 70, 111, 250, 223, 224, 179, 41, 58, 179, 217, 253, 83, 197, 234, 108, 149, 83, 88, 245, 104, 50, 45, 175, 106, 87]),
|
||
CompressedRistretto([232, 130, 177, 49, 1, 107, 82, 193, 211, 51, 112, 128, 24, 124, 247, 104, 66, 62, 252, 203, 181, 23, 187, 73, 90, 184, 18, 196, 22, 15, 244, 78]),
|
||
CompressedRistretto([246, 71, 70, 211, 201, 43, 19, 5, 14, 216, 216, 2, 54, 167, 240, 0, 124, 59, 63, 150, 47, 91, 167, 147, 209, 154, 96, 30, 187, 29, 244, 3]),
|
||
CompressedRistretto([68, 245, 53, 32, 146, 110, 200, 31, 189, 90, 56, 120, 69, 190, 183, 223, 133, 169, 106, 36, 236, 225, 135, 56, 189, 207, 166, 167, 130, 42, 23, 109]),
|
||
CompressedRistretto([144, 50, 147, 216, 242, 40, 126, 190, 16, 226, 55, 77, 193, 165, 62, 11, 200, 135, 229, 146, 105, 159, 2, 208, 119, 213, 38, 60, 221, 85, 96, 28]),
|
||
CompressedRistretto([2, 98, 42, 206, 143, 115, 3, 163, 28, 175, 198, 63, 143, 196, 143, 220, 22, 225, 200, 200, 210, 52, 178, 240, 214, 104, 82, 130, 169, 7, 96, 49]),
|
||
CompressedRistretto([32, 112, 111, 215, 136, 178, 114, 10, 30, 210, 165, 218, 212, 149, 43, 1, 244, 19, 188, 240, 231, 86, 77, 232, 205, 200, 22, 104, 158, 45, 185, 95]),
|
||
CompressedRistretto([188, 232, 63, 139, 165, 221, 47, 165, 114, 134, 76, 36, 186, 24, 16, 249, 82, 43, 198, 0, 74, 254, 149, 135, 122, 199, 50, 65, 202, 253, 171, 66]),
|
||
CompressedRistretto([228, 84, 158, 225, 107, 154, 160, 48, 153, 202, 32, 140, 103, 173, 175, 202, 250, 76, 63, 62, 78, 83, 3, 222, 96, 38, 227, 202, 143, 248, 68, 96]),
|
||
CompressedRistretto([170, 82, 224, 0, 223, 46, 22, 245, 95, 177, 3, 47, 195, 59, 196, 39, 66, 218, 214, 189, 90, 143, 192, 190, 1, 103, 67, 108, 89, 72, 80, 31]),
|
||
CompressedRistretto([70, 55, 107, 128, 244, 9, 178, 157, 194, 181, 246, 240, 197, 37, 145, 153, 8, 150, 229, 113, 111, 65, 71, 124, 211, 0, 133, 171, 127, 16, 48, 30]),
|
||
CompressedRistretto([224, 196, 24, 247, 200, 217, 196, 205, 215, 57, 91, 147, 234, 18, 79, 58, 217, 144, 33, 187, 104, 29, 252, 51, 2, 169, 217, 154, 46, 83, 230, 78]),
|
||
];
|
||
let mut bp = RistrettoPoint::identity();
|
||
for i in 0..16 {
|
||
assert_eq!(bp.compress(), compressed[i]);
|
||
bp = &bp + &constants::RISTRETTO_BASEPOINT_POINT;
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn four_torsion_basepoint() {
|
||
let bp = constants::RISTRETTO_BASEPOINT_POINT;
|
||
let bp_coset = bp.coset4();
|
||
for i in 0..4 {
|
||
assert_eq!(bp, RistrettoPoint(bp_coset[i]));
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn four_torsion_random() {
|
||
let mut rng = OsRng::new().unwrap();
|
||
let B = &constants::RISTRETTO_BASEPOINT_TABLE;
|
||
let P = B * &Scalar::random(&mut rng);
|
||
let P_coset = P.coset4();
|
||
for i in 0..4 {
|
||
assert_eq!(P, RistrettoPoint(P_coset[i]));
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn elligator_vs_ristretto_sage() {
|
||
// Test vectors extracted from ristretto.sage.
|
||
//
|
||
// Notice that all of the byte sequences have bit 255 set to 0; this is because
|
||
// ristretto.sage does not mask the high bit of a field element. When the high bit is set,
|
||
// the ristretto.sage elligator implementation gives different results, since it takes a
|
||
// different field element as input.
|
||
let bytes: [[u8;32]; 16] = [
|
||
[184, 249, 135, 49, 253, 123, 89, 113, 67, 160, 6, 239, 7, 105, 211, 41, 192, 249, 185, 57, 9, 102, 70, 198, 15, 127, 7, 26, 160, 102, 134, 71],
|
||
[229, 14, 241, 227, 75, 9, 118, 60, 128, 153, 226, 21, 183, 217, 91, 136, 98, 0, 231, 156, 124, 77, 82, 139, 142, 134, 164, 169, 169, 62, 250, 52],
|
||
[115, 109, 36, 220, 180, 223, 99, 6, 204, 169, 19, 29, 169, 68, 84, 23, 21, 109, 189, 149, 127, 205, 91, 102, 172, 35, 112, 35, 134, 69, 186, 34],
|
||
[16, 49, 96, 107, 171, 199, 164, 9, 129, 16, 64, 62, 241, 63, 132, 173, 209, 160, 112, 215, 105, 50, 157, 81, 253, 105, 1, 154, 229, 25, 120, 83],
|
||
[156, 131, 161, 162, 236, 251, 5, 187, 167, 171, 17, 178, 148, 210, 90, 207, 86, 21, 79, 161, 167, 215, 234, 1, 136, 242, 182, 248, 38, 85, 79, 86],
|
||
[251, 177, 124, 54, 18, 101, 75, 235, 245, 186, 19, 46, 133, 157, 229, 64, 10, 136, 181, 185, 78, 144, 254, 167, 137, 49, 107, 10, 61, 10, 21, 25],
|
||
[232, 193, 20, 68, 240, 77, 186, 77, 183, 40, 44, 86, 150, 31, 198, 212, 76, 81, 3, 217, 197, 8, 126, 128, 126, 152, 164, 208, 153, 44, 189, 77],
|
||
[173, 229, 149, 177, 37, 230, 30, 69, 61, 56, 172, 190, 219, 115, 167, 194, 71, 134, 59, 75, 28, 244, 118, 26, 162, 97, 64, 16, 15, 189, 30, 64],
|
||
[106, 71, 61, 107, 250, 117, 42, 151, 91, 202, 212, 100, 52, 188, 190, 21, 125, 218, 31, 18, 253, 241, 160, 133, 57, 242, 3, 164, 189, 68, 111, 75],
|
||
[112, 204, 182, 90, 220, 198, 120, 73, 173, 107, 193, 17, 227, 40, 162, 36, 150, 141, 235, 55, 172, 183, 12, 39, 194, 136, 43, 153, 244, 118, 91, 89],
|
||
[111, 24, 203, 123, 254, 189, 11, 162, 51, 196, 163, 136, 204, 143, 10, 222, 33, 112, 81, 205, 34, 35, 8, 66, 90, 6, 164, 58, 170, 177, 34, 25],
|
||
[225, 183, 30, 52, 236, 82, 6, 183, 109, 25, 227, 181, 25, 82, 41, 193, 80, 77, 161, 80, 242, 203, 79, 204, 136, 245, 131, 110, 237, 106, 3, 58],
|
||
[207, 246, 38, 56, 30, 86, 176, 90, 27, 200, 61, 42, 221, 27, 56, 210, 79, 178, 189, 120, 68, 193, 120, 167, 77, 185, 53, 197, 124, 128, 191, 126],
|
||
[1, 136, 215, 80, 240, 46, 63, 147, 16, 244, 230, 207, 82, 189, 74, 50, 106, 169, 138, 86, 30, 131, 214, 202, 166, 125, 251, 228, 98, 24, 36, 21],
|
||
[210, 207, 228, 56, 155, 116, 207, 54, 84, 195, 251, 215, 249, 199, 116, 75, 109, 239, 196, 251, 194, 246, 252, 228, 70, 146, 156, 35, 25, 39, 241, 4],
|
||
[34, 116, 123, 9, 8, 40, 93, 189, 9, 103, 57, 103, 66, 227, 3, 2, 157, 107, 134, 219, 202, 74, 230, 154, 78, 107, 219, 195, 214, 14, 84, 80],
|
||
];
|
||
let encoded_images: [CompressedRistretto; 16] = [
|
||
CompressedRistretto([176, 157, 237, 97, 66, 29, 140, 166, 168, 94, 26, 157, 212, 216, 229, 160, 195, 246, 232, 239, 169, 112, 63, 193, 64, 32, 152, 69, 11, 190, 246, 86]),
|
||
CompressedRistretto([234, 141, 77, 203, 181, 225, 250, 74, 171, 62, 15, 118, 78, 212, 150, 19, 131, 14, 188, 238, 194, 244, 141, 138, 166, 162, 83, 122, 228, 201, 19, 26]),
|
||
CompressedRistretto([232, 231, 51, 92, 5, 168, 80, 36, 173, 179, 104, 68, 186, 149, 68, 40, 140, 170, 27, 103, 99, 140, 21, 242, 43, 62, 250, 134, 208, 255, 61, 89]),
|
||
CompressedRistretto([208, 120, 140, 129, 177, 179, 237, 159, 252, 160, 28, 13, 206, 5, 211, 241, 192, 218, 1, 97, 130, 241, 20, 169, 119, 46, 246, 29, 79, 80, 77, 84]),
|
||
CompressedRistretto([202, 11, 236, 145, 58, 12, 181, 157, 209, 6, 213, 88, 75, 147, 11, 119, 191, 139, 47, 142, 33, 36, 153, 193, 223, 183, 178, 8, 205, 120, 248, 110]),
|
||
CompressedRistretto([26, 66, 231, 67, 203, 175, 116, 130, 32, 136, 62, 253, 215, 46, 5, 214, 166, 248, 108, 237, 216, 71, 244, 173, 72, 133, 82, 6, 143, 240, 104, 41]),
|
||
CompressedRistretto([40, 157, 102, 96, 201, 223, 200, 197, 150, 181, 106, 83, 103, 126, 143, 33, 145, 230, 78, 6, 171, 146, 210, 143, 112, 5, 245, 23, 183, 138, 18, 120]),
|
||
CompressedRistretto([220, 37, 27, 203, 239, 196, 176, 131, 37, 66, 188, 243, 185, 250, 113, 23, 167, 211, 154, 243, 168, 215, 54, 171, 159, 36, 195, 81, 13, 150, 43, 43]),
|
||
CompressedRistretto([232, 121, 176, 222, 183, 196, 159, 90, 238, 193, 105, 52, 101, 167, 244, 170, 121, 114, 196, 6, 67, 152, 80, 185, 221, 7, 83, 105, 176, 208, 224, 121]),
|
||
CompressedRistretto([226, 181, 183, 52, 241, 163, 61, 179, 221, 207, 220, 73, 245, 242, 25, 236, 67, 84, 179, 222, 167, 62, 167, 182, 32, 9, 92, 30, 165, 127, 204, 68]),
|
||
CompressedRistretto([226, 119, 16, 242, 200, 139, 240, 87, 11, 222, 92, 146, 156, 243, 46, 119, 65, 59, 1, 248, 92, 183, 50, 175, 87, 40, 206, 53, 208, 220, 148, 13]),
|
||
CompressedRistretto([70, 240, 79, 112, 54, 157, 228, 146, 74, 122, 216, 88, 232, 62, 158, 13, 14, 146, 115, 117, 176, 222, 90, 225, 244, 23, 94, 190, 150, 7, 136, 96]),
|
||
CompressedRistretto([22, 71, 241, 103, 45, 193, 195, 144, 183, 101, 154, 50, 39, 68, 49, 110, 51, 44, 62, 0, 229, 113, 72, 81, 168, 29, 73, 106, 102, 40, 132, 24]),
|
||
CompressedRistretto([196, 133, 107, 11, 130, 105, 74, 33, 204, 171, 133, 221, 174, 193, 241, 36, 38, 179, 196, 107, 219, 185, 181, 253, 228, 47, 155, 42, 231, 73, 41, 78]),
|
||
CompressedRistretto([58, 255, 225, 197, 115, 208, 160, 143, 39, 197, 82, 69, 143, 235, 92, 170, 74, 40, 57, 11, 171, 227, 26, 185, 217, 207, 90, 185, 197, 190, 35, 60]),
|
||
CompressedRistretto([88, 43, 92, 118, 223, 136, 105, 145, 238, 186, 115, 8, 214, 112, 153, 253, 38, 108, 205, 230, 157, 130, 11, 66, 101, 85, 253, 110, 110, 14, 148, 112]),
|
||
];
|
||
for i in 0..16 {
|
||
let r_0 = FieldElement::from_bytes(&bytes[i]);
|
||
let Q = RistrettoPoint::elligator_ristretto_flavor(&r_0);
|
||
assert_eq!(Q.compress(), encoded_images[i]);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn random_roundtrip() {
|
||
let mut rng = OsRng::new().unwrap();
|
||
let B = &constants::RISTRETTO_BASEPOINT_TABLE;
|
||
for _ in 0..100 {
|
||
let P = B * &Scalar::random(&mut rng);
|
||
let compressed_P = P.compress();
|
||
let Q = compressed_P.decompress().unwrap();
|
||
assert_eq!(P, Q);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn double_and_compress_1024_random_points() {
|
||
let mut rng = OsRng::new().unwrap();
|
||
|
||
let points: Vec<RistrettoPoint> =
|
||
(0..1024).map(|_| RistrettoPoint::random(&mut rng)).collect();
|
||
|
||
let compressed = RistrettoPoint::double_and_compress_batch(&points);
|
||
|
||
for (P, P2_compressed) in points.iter().zip(compressed.iter()) {
|
||
assert_eq!(*P2_compressed, (P + P).compress());
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn random_is_valid() {
|
||
let mut rng = OsRng::new().unwrap();
|
||
for _ in 0..100 {
|
||
let P = RistrettoPoint::random(&mut rng);
|
||
// Check that P is on the curve
|
||
assert!(P.0.is_valid());
|
||
// Check that P is in the image of the ristretto map
|
||
P.compress();
|
||
}
|
||
}
|
||
}
|