Module scuttlebutt::field

This module defines finite fields.

Modules

• fft
  Various number theoretic utility functions used in the library.
• polynomial
  This module defines polynomials (and their operations) over finite fields.

Structs

• F2
  A field element in the prime-order finite field $\textsf{GF}(2).$
• F40b
  An element of the finite field $\textsf{GF}(2^{40})$ reduced over $x^{40} + x^5 + x^4 + x^3 + 1$
• F45b
  An element of the finite field $\textsf{GF}(2^{45})$ reduced over $x^{45} + x^{28} + x^{17} + x^{11} + 1$
• F56b
  An element of the finite field $\textsf{GF}(2^{56})$ reduced over $x^{56} + x^8 + x^3 + x^2 + 1$
• F61p
  A finite field over the Mersenne Prime 2^61 - 1
• F63b
  An element of the finite field $\textsf{GF}(2^{63})$ reduced over $x^{63} + x + 1$
• F64b
  An element of the finite field $\textsf{GF}({2^{64}})$ reduced over $x^{64} + x^{19} + x^{16} + x + 1$.
• F128b
  An element of the finite field $\textsf{GF}(2^{128})$ reduced over $x^{128} + x^7 + x^2 + x + 1$

Traits

• FiniteField
  Types that implement this trait are finite fields.
• IsSubFieldOf
  Denotes that Self is a subfield of FE.
• PrimeFiniteField
  A PrimeFiniteField is a FiniteField with a prime modulus. In this case the field is isomorphic to integers modulo prime p.
• SmallBinaryField
  A GF(2) extension field such that:

Type Aliases

• Degree
  The degree, $r$ of a finite field.
• DegreeModulo
  The relative degree between two Finite Fields.