Struct curve25519_dalek::ristretto::RistrettoPoint

pub struct RistrettoPoint(_);

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.

Methods

impl RistrettoPoint

pub fn compress(&self) -> CompressedRistretto

Compress this point using the Ristretto encoding.

Important traits for Vec<u8>

impl Write for Vec<u8>

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.

extern crate rand_os;
use rand_os::OsRng;

let mut rng = OsRng::new().unwrap();
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<T: RngCore + CryptoRng>(rng: T) -> Self

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

Inputs

• rng: any RNG which implements the RngCore + CryptoRng 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 = U64> + 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

extern crate sha2;
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 = U64> + 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 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 Identity for RistrettoPoint

fn identity() -> RistrettoPoint

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

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::Item: Borrow<Scalar>,
    J: IntoIterator,
    J::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 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::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::Item: Borrow<Scalar>,
    J: IntoIterator,
    J::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 Copy for RistrettoPoint

impl Clone for RistrettoPoint

fn clone(&self) -> RistrettoPoint

Returns a copy of the value.

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

Performs copy-assignment from source.

impl PartialEq<RistrettoPoint> for RistrettoPoint

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

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

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

This method tests for !=.

impl Eq for RistrettoPoint

impl Debug for RistrettoPoint

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.

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<RistrettoPoint> for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the + operator.

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

Performs the + operation.

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<RistrettoPoint> for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = RistrettoPoint

The resulting type after applying the * operator.

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

Scalar multiplication: compute scalar * self.

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

type Output = RistrettoPoint

The resulting type after applying the * operator.

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

Scalar multiplication: compute self * scalar.

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

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

Performs the += operation.

impl AddAssign<RistrettoPoint> for RistrettoPoint

fn add_assign(&mut self, rhs: RistrettoPoint)

Performs the += operation.

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

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

Performs the -= operation.

impl SubAssign<RistrettoPoint> for RistrettoPoint

fn sub_assign(&mut self, rhs: 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<T> Sum<T> for RistrettoPoint where
    T: Borrow<RistrettoPoint>, 

fn sum<I>(iter: I) -> Self where
    I: Iterator<Item = T>, 

Method which takes an iterator and generates Self from the elements by "summing up" the items.

impl Default for RistrettoPoint

fn default() -> RistrettoPoint

Returns the "default value" for a type.

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.

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.