# [−][src]Struct curve25519_dalek::edwards::EdwardsBasepointTable

pub struct EdwardsBasepointTable(pub(crate) [LookupTable<AffineNielsPoint>; 32]);

A precomputed table of multiples of a basepoint, for accelerating fixed-base scalar multiplication. One table, for the Ed25519 basepoint, is provided in the constants module.

The basepoint tables are reasonably large (30KB), so they should probably be boxed.

## Methods

### impl EdwardsBasepointTable[src]

#### fn basepoint_mul(&self, scalar: &Scalar) -> EdwardsPoint[src]

The computation uses Pippeneger's algorithm, as described on page 13 of the Ed25519 paper. Write the scalar $$a$$ in radix $$16$$ with coefficients in $$[-8,8)$$, i.e., $$a = a_0 + a_1 16^1 + \cdots + a_{63} 16^{63},$$ with $$-8 \leq a_i < 8$$, $$-8 \leq a_{63} \leq 8$$. Then $$a B = a_0 B + a_1 16^1 B + \cdots + a_{63} 16^{63} B.$$ Grouping even and odd coefficients gives \begin{aligned} a B = \quad a_0 16^0 B +& a_2 16^2 B + \cdots + a_{62} 16^{62} B \\ + a_1 16^1 B +& a_3 16^3 B + \cdots + a_{63} 16^{63} B \\ = \quad(a_0 16^0 B +& a_2 16^2 B + \cdots + a_{62} 16^{62} B) \\ + 16(a_1 16^0 B +& a_3 16^2 B + \cdots + a_{63} 16^{62} B). \\ \end{aligned} For each $$i = 0 \ldots 31$$, we create a lookup table of $$[16^{2i} B, \ldots, 8\cdot16^{2i} B],$$ and use it to select $$x \cdot 16^{2i} \cdot B$$ in constant time.

The radix-$$16$$ representation requires that the scalar is bounded by $$2^{255}$$, which is always the case.

### impl EdwardsBasepointTable[src]

#### pub fn create(basepoint: &EdwardsPoint) -> EdwardsBasepointTable[src]

Create a table of precomputed multiples of basepoint.

#### pub fn basepoint(&self) -> EdwardsPoint[src]

Get the basepoint for this table as an EdwardsPoint.

## Trait Implementations

### impl<'a, 'b> Mul<&'a EdwardsBasepointTable> for &'b Scalar[src]

#### type Output = EdwardsPoint

The resulting type after applying the * operator.

#### fn mul(self, basepoint_table: &'a EdwardsBasepointTable) -> EdwardsPoint[src]

Construct an EdwardsPoint from a Scalar $$a$$ by computing the multiple $$aB$$ of this basepoint $$B$$.

### impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTable[src]

#### type Output = EdwardsPoint

The resulting type after applying the * operator.

#### fn mul(self, scalar: &'b Scalar) -> EdwardsPoint[src]

Construct an EdwardsPoint from a Scalar $$a$$ by computing the multiple $$aB$$ of this basepoint $$B$$.

## Blanket Implementations

### impl<T> Same<T> for T

#### type Output = T

Should always be Self

### impl<T> ToOwned for T where    T: Clone, [src]

#### type Owned = T

The resulting type after obtaining ownership.

### impl<T, U> TryFrom<U> for T where    U: Into<T>, [src]

#### type Error = !

The type returned in the event of a conversion error.

### impl<T, U> TryInto<U> for T where    U: TryFrom<T>, [src]

#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.