Struct Fp5Element

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pub struct Fp5Element(pub [Goldilocks; 5]);

Expand description

Fp5 extension field element.

Represents an element of the quintic extension field GF(p^5) where p is the Goldilocks prime. Each element is represented as a polynomial of degree at most 4 over the base field.

The extension field uses the irreducible polynomial x^5 = w where w = 3.

§Example

use poseidon_hash::{Fp5Element, Goldilocks};

let a = Fp5Element::from_uint64_array([1, 2, 3, 4, 5]);
let b = Fp5Element::one();
let product = a.mul(&b);

Tuple Fields§

§0: [Goldilocks; 5]

Implementations§

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impl Fp5Element

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pub fn zero() -> Self

Returns the zero element of the extension field.

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pub fn one() -> Self

Returns the multiplicative identity (one) of the extension field.

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pub fn is_zero(&self) -> bool

Checks if this element is zero.

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pub fn add(&self, other: &Fp5Element) -> Fp5Element

Adds two extension field elements.

Addition is performed component-wise on the polynomial coefficients.

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pub fn sub(&self, other: &Fp5Element) -> Fp5Element

Subtracts two extension field elements.

Subtraction is performed component-wise on the polynomial coefficients.

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pub fn mul(&self, other: &Fp5Element) -> Fp5Element

Multiplies two extension field elements.

Uses the irreducible polynomial x^5 = w (where w = 3) to reduce the result.

§Example

use poseidon_hash::{Fp5Element, Goldilocks};

let a = Fp5Element::from_uint64_array([1, 0, 0, 0, 0]);
let b = Fp5Element::from_uint64_array([2, 0, 0, 0, 0]);
let product = a.mul(&b);

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pub fn inverse(&self) -> Fp5Element

Computes the multiplicative inverse of this element.

Returns zero if this element is zero (which has no inverse).

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pub fn inverse_or_zero(&self) -> Fp5Element

Computes the multiplicative inverse, returning zero if the element is zero.

This is a safe version of inverse() that handles zero elements gracefully.

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pub fn frobenius(&self) -> Fp5Element

Applies the Frobenius automorphism once.

The Frobenius automorphism raises each coefficient to the p-th power.

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pub fn repeated_frobenius(&self, count: usize) -> Fp5Element

Applies the Frobenius automorphism count times.

Since we’re in GF(p^5), applying it 5 times returns the original element.

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pub fn scalar_mul(&self, scalar: &Goldilocks) -> Fp5Element

Multiplies this element by a scalar (base field element).

This is more efficient than full extension field multiplication when one operand is in the base field.

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pub fn square(&self) -> Fp5Element

Computes the square of this element.

Optimized implementation that uses fewer operations than general multiplication.

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pub fn double(&self) -> Fp5Element

Doubles this element (multiplies by 2).

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pub fn from_uint64_array(arr: [u64; 5]) -> Fp5Element

Creates an Fp5Element from an array of 5 u64 values.

Each u64 value is interpreted as a Goldilocks field element.

§Example

use poseidon_hash::Fp5Element;

let elem = Fp5Element::from_uint64_array([1, 2, 3, 4, 5]);

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pub fn to_bytes_le(&self) -> [u8; 40]

Converts this element to a 40-byte little-endian representation.

Each of the 5 Goldilocks field elements contributes 8 bytes (little-endian).

§Example

use poseidon_hash::Fp5Element;

let elem = Fp5Element::one();
let bytes = elem.to_bytes_le();
assert_eq!(bytes.len(), 40);

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pub fn from_bytes_le(bytes: &[u8]) -> Result<Self, String>

Creates an Fp5Element from a 40-byte little-endian representation.

Each of the 5 Goldilocks field elements is read as 8 bytes (little-endian).

§Example

use poseidon_hash::Fp5Element;

let bytes = [0u8; 40];
let elem = Fp5Element::from_bytes_le(&bytes);

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pub fn neg(&self) -> Fp5Element

Computes the additive inverse (negation) of this element.

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pub fn exp_power_of_2(&self, n: usize) -> Fp5Element

Raises this element to the power of 2^n by repeated squaring.

Equivalent to Go’s ExpPowerOf2 function.

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pub fn sgn0(&self) -> bool

Computes the sign function Sgn0(x) for this element.

Returns true if the sign bit (LSB of the first non-zero limb) is 0. Equivalent to Go’s Sgn0 function.

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pub fn sqrt(&self) -> Option<Fp5Element>

Computes the square root of this element.

Returns Some(sqrt) if the square root exists, None otherwise. Equivalent to Go’s Sqrt function.

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pub fn canonical_sqrt(&self) -> (Fp5Element, bool)

Computes the canonical square root of this element.

Returns (canonical_sqrt, success) where success indicates if the square root exists. The canonical square root is chosen such that Sgn0(sqrt) == false. Equivalent to Go’s CanonicalSqrt function.

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