Crypto.Lol.RLWE.Discrete

Functions and types for working with discretized ring-LWE samples.

Documentation

type Sample t m zq = (Cyc t m zq, Cyc t m zq)

A discrete RLWE sample \( (a,b) \in R_q \times R_q\).

type RLWECtx t m zq = (Fact m, Ring zq, Lift' zq, ToInteger (LiftOf zq), CElt t zq, CElt t (LiftOf zq))

Common constraints for working with discrete RLWE.

sample :: forall rnd v t m zq. (RLWECtx t m zq, Random zq, MonadRandom rnd, ToRational v) => v -> Cyc t m zq -> rnd (Sample t m zq)

A discrete RLWE sample with the given scaled variance and secret.

errorTerm :: RLWECtx t m zq => Cyc t m zq -> Sample t m zq -> Cyc t m (LiftOf zq)

The error term of an RLWE sample, given the purported secret.

errorGSqNorm :: (RLWECtx t m zq, Ring (LiftOf zq)) => Cyc t m zq -> Sample t m zq -> LiftOf zq

The gSqNorm of the error term of an RLWE sample, given the purported secret.

errorBound

Arguments

:: (RealRing v, Transcendental v, Fact m)

=> v

the scaled variance

-> v

\(\epsilon\)

-> Tagged m Int64

A bound such that the gSqNorm of a discretized error term generated by errorRounded with scaled variance \(v\) (over the \(m\)th cyclotomic field) is less than the bound except with probability approximately \(\epsilon\).