Copyright	(c) Eric Crockett 2011-2017 Chris Peikert 2011-2017
License	GPL-3
Maintainer	ecrockett0@email.com
Stability	experimental
Portability	POSIX \( \def\Z{\mathbb{Z}} \)
Safe Haskell	None
Language	Haskell2010

Crypto.Lol.Types.ZmStar

Description

A collection of helper functions for working with \(\Z_m^*\).

Synopsis

order :: forall m. Reflects m Int => Int -> Int
partitionCosets :: forall m m'. m `Divides` m' => Int -> [[Int]]

Documentation

order :: forall m. Reflects m Int => Int -> Int Source #

The multiplicative order of \(p\) (the argument) modulo \(m\). Requires \(\gcd(p,m)=1\).

partitionCosets :: forall m m'. m `Divides` m' => Int -> [[Int]] Source #

Given \(p\), returns a partition of the cosets of \(\Z_{m'}^* / <p>\) (specified by representatives), where the cosets in each component are in bijective correspondence with the cosets of \(\Z_m^* / <p>\) under the natural ((bmod m)) homomorphism.