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Time-constant modular inverse

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This commit is contained in:
Olivier Chéron 2017-10-08 09:21:45 +02:00
parent ce35a1e07d
commit 19b7ab375a
1 changed files with 6 additions and 0 deletions
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6
Crypto/Number/ModArithmetic.hs
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@ -16,6 +16,7 @@ module Crypto.Number.ModArithmetic
, inverse , inverse
, inverseCoprimes , inverseCoprimes
, jacobi , jacobi
, inverseFermat
) where ) where
import Control.Exception (throw, Exception) import Control.Exception (throw, Exception)
@ -120,3 +121,8 @@ jacobi a n
n1 = n `mod` a1 n1 = n `mod` a1
in if a1 == 1 then Just s in if a1 == 1 then Just s
else fmap (*s) (jacobi n1 a1) else fmap (*s) (jacobi n1 a1)
-- | Modular inverse using Fermat's little theorem. This works only when
-- the modulus is prime but avoids side channels like in 'expSafe'.
inverseFermat :: Integer -> Integer -> Integer
inverseFermat g p = expSafe g (p - 2) p