Struct RistrettoPoint

pub struct RistrettoPoint(/* private fields */);

A RistrettoPoint represents a point in the Ristretto group for Curve25519. Ristretto, a variant of Decaf, constructs a prime-order group as a quotient group of a subgroup of (the Edwards form of) Curve25519.

Internally, a RistrettoPoint is implemented as a wrapper type around EdwardsPoint, with custom equality, compression, and decompression routines to account for the quotient. This means that operations on RistrettoPoints are exactly as fast as operations on EdwardsPoints.

Implementations

impl RistrettoPoint

pub fn compress(&self) -> CompressedRistretto

Compress this point using the Ristretto encoding.

pub fn double_and_compress_batch<'a, I>(points: I) -> Vec<CompressedRistretto>

where I: IntoIterator<Item = &'a RistrettoPoint>,

Double-and-compress a batch of points. The Ristretto encoding is not batchable, since it requires an inverse square root.

However, given input points \( P_1, \ldots, P_n, \) it is possible to compute the encodings of their doubles \( \mathrm{enc}( [2]P_1), \ldots, \mathrm{enc}( [2]P_n ) \) in a batch.

use rand_core::OsRng;

let mut rng = OsRng;

let points: Vec<RistrettoPoint> =
    (0..32).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());
}

pub fn random<R>(rng: &mut R) -> RistrettoPoint

where R: CryptoRngCore + ?Sized,

Return a RistrettoPoint chosen uniformly at random using a user-provided RNG.

Inputs

• rng: any RNG which implements CryptoRngCore (i.e. CryptoRng + RngCore) 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.

pub fn hash_from_bytes<D>(input: &[u8]) -> RistrettoPoint

where D: Digest<OutputSize = UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>> + Default,

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

use sha2::Sha512;

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 from_hash<D>(hash: D) -> RistrettoPoint

where D: Digest<OutputSize = UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>> + Default,

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_uniform_bytes(bytes: &[u8; 64]) -> RistrettoPoint

Construct a RistrettoPoint from 64 bytes of data.

If the input bytes are uniformly distributed, the resulting point will be uniformly distributed over the group, and its discrete log with respect to other points should be unknown.

Implementation

This function splits the input array into two 32-byte halves, takes the low 255 bits of each half mod p, applies the Ristretto-flavored Elligator map to each, and adds the results.

impl RistrettoPoint

pub fn mul_base(scalar: &Scalar) -> RistrettoPoint

Fixed-base scalar multiplication by the Ristretto base point.

Uses precomputed basepoint tables when the precomputed-tables feature is enabled, trading off increased code size for ~4x better performance.

impl RistrettoPoint

pub fn vartime_double_scalar_mul_basepoint( a: &Scalar, A: &RistrettoPoint, b: &Scalar, ) -> RistrettoPoint

Compute \(aA + bB\) in variable time, where \(B\) is the Ristretto basepoint.

Trait Implementations

impl<'a, 'b> Add<&'b RistrettoPoint> for &'a RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the + operator.

fn add(self, other: &'b RistrettoPoint) -> RistrettoPoint

Performs the + operation.

impl<'b> Add<&'b RistrettoPoint> for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the + operator.

fn add(self, rhs: &'b RistrettoPoint) -> RistrettoPoint

Performs the + operation.

impl<'a> Add<RistrettoPoint> for &'a RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the + operator.

fn add(self, rhs: RistrettoPoint) -> RistrettoPoint

Performs the + operation.

impl Add for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the + operator.

fn add(self, rhs: RistrettoPoint) -> RistrettoPoint

Performs the + operation.

impl<'b> AddAssign<&'b RistrettoPoint> for RistrettoPoint

fn add_assign(&mut self, _rhs: &RistrettoPoint)

Performs the += operation.

impl AddAssign for RistrettoPoint

fn add_assign(&mut self, rhs: RistrettoPoint)

Performs the += operation.

impl Clone for RistrettoPoint

fn clone(&self) -> RistrettoPoint

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl CofactorGroup for RistrettoPoint

Ristretto has a cofactor of 1.

type Subgroup = RistrettoPoint

The large prime-order subgroup in which cryptographic operations are performed. If Self implements PrimeGroup, then Self::Subgroup may be Self.

fn clear_cofactor(&self) -> <RistrettoPoint as CofactorGroup>::Subgroup

Maps self to the prime-order subgroup by multiplying this element by some k-multiple of the cofactor.

fn into_subgroup(self) -> CtOption<<RistrettoPoint as CofactorGroup>::Subgroup>

Returns self if it is contained in the prime-order subgroup.

fn is_torsion_free(&self) -> Choice

Determines if this element is “torsion free”, i.e., is contained in the prime-order subgroup.

fn is_small_order(&self) -> Choice

Determines if this element is of small order.

impl ConditionallySelectable for RistrettoPoint

fn conditional_select( a: &RistrettoPoint, b: &RistrettoPoint, choice: Choice, ) -> RistrettoPoint

Conditionally select between self and other.

Example

use subtle::ConditionallySelectable;
use subtle::Choice;

let A = RistrettoPoint::identity();
let B = constants::RISTRETTO_BASEPOINT_POINT;

let mut P = A;

P = RistrettoPoint::conditional_select(&A, &B, Choice::from(0));
assert_eq!(P, A);
P = RistrettoPoint::conditional_select(&A, &B, Choice::from(1));
assert_eq!(P, B);

fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice.

fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves.

impl ConstantTimeEq for RistrettoPoint

fn ct_eq(&self, other: &RistrettoPoint) -> Choice

Test equality between two RistrettoPoints.

Returns

• Choice(1) if the two RistrettoPoints are equal;
• Choice(0) otherwise.

fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal.

impl Debug for RistrettoPoint

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl Default for RistrettoPoint

fn default() -> RistrettoPoint

Returns the “default value” for a type.

impl Group for RistrettoPoint

type Scalar = Scalar

Scalars modulo the order of this group’s scalar field.

fn random(rng: impl RngCore) -> RistrettoPoint

Returns an element chosen uniformly at random from the non-identity elements of this group.

fn identity() -> RistrettoPoint

Returns the additive identity, also known as the “neutral element”.

fn generator() -> RistrettoPoint

Returns a fixed generator of the prime-order subgroup.

fn is_identity(&self) -> Choice

Determines if this point is the identity.

fn double(&self) -> RistrettoPoint

Doubles this element.

impl GroupEncoding for RistrettoPoint

type Repr = [u8; 32]

The encoding of group elements.

fn from_bytes( bytes: &<RistrettoPoint as GroupEncoding>::Repr, ) -> CtOption<RistrettoPoint>

Attempts to deserialize a group element from its encoding.

fn from_bytes_unchecked( bytes: &<RistrettoPoint as GroupEncoding>::Repr, ) -> CtOption<RistrettoPoint>

Attempts to deserialize a group element, not checking if the element is valid.

fn to_bytes(&self) -> <RistrettoPoint as GroupEncoding>::Repr

Converts this element into its byte encoding. This may or may not support encoding the identity.

impl Identity for RistrettoPoint

fn identity() -> RistrettoPoint

Returns the identity element of the curve. Can be used as a constructor.

impl<'a, 'b> Mul<&'b RistrettoPoint> for &'a Scalar

fn mul(self, point: &'b RistrettoPoint) -> RistrettoPoint

Scalar multiplication: compute self * scalar.

type Output = RistrettoPoint

The resulting type after applying the * operator.

impl<'b> Mul<&'b RistrettoPoint> for Scalar

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: &'b RistrettoPoint) -> RistrettoPoint

Performs the * operation.

impl<'a, 'b> Mul<&'b Scalar> for &'a RistrettoPoint

fn mul(self, scalar: &'b Scalar) -> RistrettoPoint

Scalar multiplication: compute scalar * self.

type Output = RistrettoPoint

The resulting type after applying the * operator.

impl<'b> Mul<&'b Scalar> for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Scalar) -> RistrettoPoint

Performs the * operation.

impl<'a> Mul<RistrettoPoint> for &'a Scalar

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: RistrettoPoint) -> RistrettoPoint

Performs the * operation.

impl Mul<RistrettoPoint> for Scalar

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: RistrettoPoint) -> RistrettoPoint

Performs the * operation.

impl<'a> Mul<Scalar> for &'a RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> RistrettoPoint

Performs the * operation.

impl Mul<Scalar> for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> RistrettoPoint

Performs the * operation.

impl<'b> MulAssign<&'b Scalar> for RistrettoPoint

fn mul_assign(&mut self, scalar: &'b Scalar)

Performs the *= operation.

impl MulAssign<Scalar> for RistrettoPoint

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl MultiscalarMul for RistrettoPoint

type Point = RistrettoPoint

The type of point being multiplied, e.g., RistrettoPoint.

fn multiscalar_mul<I, J>(scalars: I, points: J) -> RistrettoPoint

where I: IntoIterator, <I as IntoIterator>::Item: Borrow<Scalar>, J: IntoIterator, <J as IntoIterator>::Item: Borrow<RistrettoPoint>,

Given an iterator of (possibly secret) scalars and an iterator of public points, compute $$ Q = c_1 P_1 + \cdots + c_n P_n. $$

impl<'a> Neg for &'a RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the - operator.

fn neg(self) -> RistrettoPoint

Performs the unary - operation.

impl Neg for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the - operator.

fn neg(self) -> RistrettoPoint

Performs the unary - operation.

impl PartialEq for RistrettoPoint

fn eq(&self, other: &RistrettoPoint) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<'a, 'b> Sub<&'b RistrettoPoint> for &'a RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the - operator.

fn sub(self, other: &'b RistrettoPoint) -> RistrettoPoint

Performs the - operation.

impl<'b> Sub<&'b RistrettoPoint> for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the - operator.

fn sub(self, rhs: &'b RistrettoPoint) -> RistrettoPoint

Performs the - operation.

impl<'a> Sub<RistrettoPoint> for &'a RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the - operator.

fn sub(self, rhs: RistrettoPoint) -> RistrettoPoint

Performs the - operation.

impl Sub for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the - operator.

fn sub(self, rhs: RistrettoPoint) -> RistrettoPoint

Performs the - operation.

impl<'b> SubAssign<&'b RistrettoPoint> for RistrettoPoint

fn sub_assign(&mut self, _rhs: &RistrettoPoint)

Performs the -= operation.

impl SubAssign for RistrettoPoint

fn sub_assign(&mut self, rhs: RistrettoPoint)

Performs the -= operation.

impl<T> Sum<T> for RistrettoPoint

where T: Borrow<RistrettoPoint>,

fn sum<I>(iter: I) -> RistrettoPoint

where I: Iterator<Item = T>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl VartimeMultiscalarMul for RistrettoPoint

type Point = RistrettoPoint

The type of point being multiplied, e.g., RistrettoPoint.

fn optional_multiscalar_mul<I, J>( scalars: I, points: J, ) -> Option<RistrettoPoint>

where I: IntoIterator, <I as IntoIterator>::Item: Borrow<Scalar>, J: IntoIterator<Item = Option<RistrettoPoint>>,

Given an iterator of public scalars and an iterator of Options 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.

fn vartime_multiscalar_mul<I, J>(scalars: I, points: J) -> Self::Point

where I: IntoIterator, <I as IntoIterator>::Item: Borrow<Scalar>, J: IntoIterator, <J as IntoIterator>::Item: Borrow<Self::Point>, Self::Point: Clone,

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.

impl Zeroize for RistrettoPoint

fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.

impl Copy for RistrettoPoint

impl Eq for RistrettoPoint

impl PrimeGroup for RistrettoPoint