Struct miden_core::crypto::dsa::rpo_falcon512::Polynomial

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

A polynomial over Z_p[x]/(phi) where phi := x^512 + 1

Implementations

impl Polynomial

pub unsafe fn new(data: [u16; 512]) -> Polynomial

Constructs a new polynomial from a list of coefficients.

Safety

This constructor validates that the coefficients are in the valid range only in debug mode.

pub fn from_pub_key(input: &[u8]) -> Result<Polynomial, FalconError>

Decodes raw bytes representing a public key into a polynomial in Z_p[x]/(phi).

Errors

Returns an error if:

• The provided input is not exactly 897 bytes long.
• The first byte of the input is not equal to log2(512) i.e., 9.
• Any of the coefficients encoded in the provided input is greater than or equal to the Falcon field modulus.

pub fn from_signature(input: &[u8]) -> Result<Polynomial, FalconError>

Decodes the signature into the coefficients of a polynomial in Z_p[x]/(phi). It assumes that the signature has been encoded using the uncompressed format.

Errors

Returns an error if:

• The signature has been encoded using a different algorithm than the reference compressed encoding algorithm.
• The encoded signature polynomial is in Z_p[x]/(phi’) where phi’ = x^N’ + 1 and N’ != 512.
• While decoding the high bits of a coefficient, the current accumulated value of its high bits is larger than 2048.
• The decoded coefficient is -0.
• The remaining unused bits in the last byte of input are non-zero.

pub fn inner(&self) -> [u16; 512]

Returns the coefficients of this polynomial as integers.

pub fn to_elements(&self) -> Vec<BaseElement>

Returns the coefficients of this polynomial as field elements.

pub fn mul_modulo_p(a: &Polynomial, b: &Polynomial) -> [u64; 1024]

Multiplies two polynomials over Z_p[x] without reducing modulo p. Given that the degrees of the input polynomials are less than 512 and their coefficients are less than the modulus q equal to 12289, the resulting product polynomial is guaranteed to have coefficients less than the Miden prime.

Note that this multiplication is not over Z_p[x]/(phi).

pub fn reduce_negacyclic(a: &[u64; 1024]) -> Polynomial

Reduces a polynomial, that is the product of two polynomials over Z_p[x], modulo the irreducible polynomial phi. This results in an element in Z_p[x]/(phi).

pub fn sq_norm(&self) -> u64

Computes the norm squared of a polynomial in Z_p[x]/(phi) after normalizing its coefficients to be in the interval (-p/2, p/2].

Trait Implementations

impl Add for Polynomial

Addition over Z_p[x]/(phi)

type Output = Polynomial

The resulting type after applying the + operator.

fn add(self, other: Polynomial) -> <Polynomial as Add>::Output

Performs the + operation.

impl Clone for Polynomial

fn clone(&self) -> Polynomial

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Polynomial

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

Formats the value using the given formatter.

impl Default for Polynomial

fn default() -> Polynomial

Returns the “default value” for a type.

impl Mul for Polynomial

Multiplication over Z_p[x]/(phi)

type Output = Polynomial

The resulting type after applying the * operator.

fn mul(self, other: Polynomial) -> <Polynomial as Mul>::Output

Performs the * operation.

impl PartialEq for Polynomial

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

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

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

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

impl Sub for Polynomial

Subtraction over Z_p[x]/(phi)

type Output = Polynomial

The resulting type after applying the - operator.

fn sub(self, other: Polynomial) -> <Polynomial as Add>::Output

Performs the - operation.

impl Copy for Polynomial

impl StructuralPartialEq for Polynomial