Crypto.Number.Nat

crypton-1.0.1: Cryptography Primitives sink

License | BSD-style
Maintainer | Vincent Hanquez <vincent@snarc.org>
Stability | experimental
Portability | Good
Safe Haskell | None
Language | Haskell2010

Crypto.Number.Nat

Description

Numbers at type level.

This module provides extensions to GHC.TypeLits and GHC.TypeNats useful to work with cryptographic algorithms parameterized with a variable bit length. Constraints like ``IsDivisibleBy8` n` ensure that the type-level parameter is applicable to the algorithm.

Functions are also provided to test whether constraints are satisfied from values known at runtime. The following example shows how to discharge `IsDivisibleBy8` in a computation `fn` requiring this constraint:

    withDivisibleBy8 :: Integer
                     -> (forall proxy n . (KnownNat n, IsDivisibleBy8 n) => proxy n -> a)
                     -> Maybe a
    withDivisibleBy8 len fn = do
        SomeNat p <- someNatVal len
        Refl <- isDivisibleBy8 p
        pure (fn p)

Function `withDivisibleBy8` above returns `Nothing` when the argument `len` is negative or not divisible by 8.

Synopsis

- type IsDivisibleBy8 (bitLen :: Nat) = IsDiv8 bitLen bitLen ~ 'True
- type IsAtMost (bitlen :: Nat) (n :: Nat) = IsLE bitlen n (bitlen <=? n) ~ 'True
- type IsAtLeast (bitlen :: Nat) (n :: Nat) = IsGE bitlen n (n <=? bitlen) ~ 'True
- isDivisibleBy8 :: forall (n :: Nat) proxy. KnownNat n => proxy n -> Maybe (IsDiv8 n n :~: 'True)
- isAtMost :: forall (value :: Nat) (bound :: Nat) proxy proxy'. (KnownNat value, KnownNat bound) => proxy value -> proxy' bound -> Maybe ((value <=? bound) :~: 'True)
- isAtLeast :: forall (value :: Nat) (bound :: Nat) proxy proxy'. (KnownNat value, KnownNat bound) => proxy value -> proxy' bound -> Maybe ((bound <=? value) :~: 'True)

# Documentation

type IsDivisibleBy8 (bitLen :: Nat) = IsDiv8 bitLen bitLen ~ 'True #

ensure the given `bitlen` is divisible by 8

type IsAtMost (bitlen :: Nat) (n :: Nat) = IsLE bitlen n (bitlen <=? n) ~ 'True #

ensure the given `bitlen` is lesser or equal to `n`

type IsAtLeast (bitlen :: Nat) (n :: Nat) = IsGE bitlen n (n <=? bitlen) ~ 'True #

ensure the given `bitlen` is greater or equal to `n`

isDivisibleBy8 :: forall (n :: Nat) proxy. KnownNat n => proxy n -> Maybe (IsDiv8 n n :~: 'True) #

get a runtime proof that the constraint ``IsDivisibleBy8` n` is satified

isAtMost :: forall (value :: Nat) (bound :: Nat) proxy proxy'. (KnownNat value, KnownNat bound) => proxy value -> proxy' bound -> Maybe ((value <=? bound) :~: 'True) #

get a runtime proof that the constraint ``IsAtMost` value bound` is satified

isAtLeast :: forall (value :: Nat) (bound :: Nat) proxy proxy'. (KnownNat value, KnownNat bound) => proxy value -> proxy' bound -> Maybe ((bound <=? value) :~: 'True) #

get a runtime proof that the constraint ``IsAtLeast` value bound` is satified