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

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`

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`fn basepoint_mul(&self, scalar: &Scalar) -> EdwardsPoint`

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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`

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`pub fn create(basepoint: &EdwardsPoint) -> EdwardsBasepointTable`

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Create a table of precomputed multiples of `basepoint`

.

`pub fn basepoint(&self) -> EdwardsPoint`

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Get the basepoint for this table as an `EdwardsPoint`

.

## Trait Implementations

`impl Clone for EdwardsBasepointTable`

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`fn clone(&self) -> EdwardsBasepointTable`

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

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Performs copy-assignment from `source`

. Read more

`impl Debug for EdwardsBasepointTable`

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`impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsBasepointTable`

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`type Output = EdwardsPoint`

The resulting type after applying the `*`

operator.

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

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Construct an `EdwardsPoint`

from a `Scalar`

\(a\) by
computing the multiple \(aB\) of this basepoint \(B\).

`impl<'a, 'b> Mul<&'a EdwardsBasepointTable> for &'b Scalar`

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`type Output = EdwardsPoint`

The resulting type after applying the `*`

operator.

`fn mul(self, basepoint_table: &'a EdwardsBasepointTable) -> EdwardsPoint`

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Construct an `EdwardsPoint`

from a `Scalar`

\(a\) by
computing the multiple \(aB\) of this basepoint \(B\).

## Auto Trait Implementations

`impl Send for EdwardsBasepointTable`

`impl Sync for EdwardsBasepointTable`

## Blanket Implementations

`impl<T> From for T`

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`impl<T, U> TryFrom for T where`

U: Into<T>,

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U: Into<T>,

`type Error = !`

`try_from`

)The type returned in the event of a conversion error.

`fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>`

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`impl<T, U> TryInto for T where`

U: TryFrom<T>,

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U: TryFrom<T>,

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

`try_from`

)The type returned in the event of a conversion error.

`fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>`

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`impl<T, U> Into for T where`

U: From<T>,

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U: From<T>,

`impl<T> Borrow for T where`

T: ?Sized,

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T: ?Sized,

`impl<T> BorrowMut for T where`

T: ?Sized,

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T: ?Sized,

`fn borrow_mut(&mut self) -> &mut T`

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`impl<T> Any for T where`

T: 'static + ?Sized,

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T: 'static + ?Sized,

`impl<T> ToOwned for T where`

T: Clone,

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T: Clone,

`impl<T> FromCast for T`

`fn from_cast(t: T) -> T`

`impl<T, U> Cast for T where`

U: FromCast<T>,

U: FromCast<T>,

`fn cast(self) -> U`

`impl<T, U> IntoBits for T where`

U: FromBits<T>,

U: FromBits<T>,

`fn into_bits(self) -> U`

`impl<T> FromBits for T`

`fn from_bits(t: T) -> T`

`impl<T> Same for T`

`type Output = T`

Should always be `Self`