Module scuttlebutt::field

source · [−]

Expand description

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 $\textsf{GF}(2).$

F2e19x3e26

The finite field over the prime $M = 2^{19} 3^{26} + 1$. Hence, $\phi(M)$ is divisible by $2^{19}$ and $3^{26}$ and thus supports a large number of FFT<2> and FFT<3> sizes for threshold secret sharing.

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 $x^{128} + x^7 + x^2 + x + 1$

F128p

The finite field over the prime $P = 2^{128} - 159$.

F256p

The finite field over the prime $

P = 2^{256} - 2^{224} + 2^{192} + 2^{96} - 1 = 115792089210356248762697446949407573530086143415290314195533631308867097853951

$.

F384p

The finite field over the prime $

P = 2^{384} - 2^{128} - 2^{96} + 2^{32} - 1 = 39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319

$.

F384q

The finite field over the prime $Q = 39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942643$.

F400p

The finite field over the prime $2^{400} - 593$.

Fbls12381

The BLS12-381 finite field.

Fbn254

The BN-254 finite field.