20 lines
623 B
Haskell
20 lines
623 B
Haskell
module ModularArithmeticUtils (modExp, modMul, legendre) where
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import Data.Bits (testBit, shiftR)
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-- Modular exponentiation: compute a^b mod m
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modExp :: Integer -> Integer -> Integer -> Integer
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modExp b 0 m = 1
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modExp b e m = t * modExp ((b * b) `mod` m) (shiftR e 1) m `mod` m
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where t = if testBit e 0 then b `mod` m else 1
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-- Compute (a * b) mod m
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modMul :: Integer -> Integer -> Integer -> Integer
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modMul a b m = (a * b) `mod` m
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-- Compute the Legendre symbol (a/p)
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-- (a/p) = a^((p-1)/2) mod p
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-- (a/p) in {-1, 0, 1}
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legendre :: Integer -> Integer -> Integer
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legendre a p = modExp a ((p - 1) `div` 2) p
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