Enum FieldOperation 

pub enum FieldOperation {
    BasicArithmetic,
    Inversion,
    SquareRoot,
    BatchOperations,
    MultiExponentiation,
    LegendreSymbol,
}

Operations that may or may not be supported by different field implementations.

This enum defines the various mathematical operations that field implementations can support. Some operations may not be available for certain moduli (e.g., square root may not exist for all elements in some fields), while others may be computationally expensive or have specialized implementations.

Variants

BasicArithmetic

Basic arithmetic operations: addition, subtraction, and multiplication.

These are the fundamental operations that all field implementations should support. They include modular addition, subtraction, and multiplication with proper reduction modulo the field prime.

Inversion

Modular inversion: finding x such that (a * x) ≡ 1 mod p.

Not all elements have multiplicative inverses (specifically, zero does not). This operation typically uses the extended Euclidean algorithm.

SquareRoot

Square root computation in the field.

Computes x such that x² ≡ a mod p. This may not exist for all elements depending on the field properties (Tonelli-Shanks algorithm is commonly used).

BatchOperations

Batch operations: performing the same operation on multiple field elements.

This enables optimizations like Montgomery batch processing or SIMD operations when multiple field elements need the same operation applied.

MultiExponentiation

Multi-exponentiation: computing ∑ bᵢ * xᵢ^yᵢ for multiple bases and exponents.

This is a fundamental operation in cryptographic protocols and pairing-based cryptography. Efficient implementations use techniques like the Pippenger algorithm.

LegendreSymbol

Legendre symbol computation: determining if an element is a quadratic residue.

Computes the Legendre symbol (a/p) which indicates whether a has a square root modulo p. Returns 1 (quadratic residue), -1 (non-residue), or 0 (zero).

Trait Implementations

impl Clone for FieldOperation

fn clone(&self) -> FieldOperation

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for FieldOperation

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

Formats the value using the given formatter.

impl PartialEq for FieldOperation

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl Copy for FieldOperation

impl Eq for FieldOperation

impl StructuralPartialEq for FieldOperation