Data.Hash.SL2

An algebraic hash function, inspired by the paper Hashing with SL2 by Tillich and Zemor.

The hash function is based on matrix multiplication in the special linear group of degree 2, over a Galois field of order 2^127, with all computations modulo the polynomial x^127 + x^63 + 1.

This construction gives some nice properties, which traditional bit-scambling hash functions don't possess, including it being composable. It holds:

hash (m1 <> m2) == hash m1 <> hash m2

Following that, the hash function is also parallelisable. If a message m can be divided into a list of chunks cs, the hash of the message can be calculated in parallel:

mconcat (parMap rpar hash cs) == hash m

All operations in this package are implemented in a very efficient manner using SSE instructions.

Documentation

data Hash

Hashing

hash :: ByteString -> Hash

O(n) Calculate the hash of the ByteString. Alias for (append unit).

append :: Hash -> ByteString -> Hash

O(n) Append the hash of the ByteString to the existing Hash. A significantly faster equivalent of ((. hash) . concat).

prepend :: ByteString -> Hash -> Hash

O(n) Prepend the hash of the ByteString to the existing Hash. A significantly faster equivalent of (concat . hash).

foldAppend :: Foldable t => Hash -> t ByteString -> Hash

O(n) Append the hash of every ByteString to the existing Hash, from left to right. A significantly faster equivalent of (foldl append).

foldPrepend :: Foldable t => t ByteString -> Hash -> Hash

O(n) Prepend the hash of every ByteString to the existing Hash, from right to left. A significantly faster equivalent of (flip (foldr prepend)).

Composition

unit :: Hash

O(1) The unit element for concatenation. Alias for mempty.

concat :: Hash -> Hash -> Hash

O(1) Concatenate two hashes. Alias for mappend.

concatAll :: [Hash] -> Hash

O(n) Concatenate a list of hashes. Alias for mconcat.

Parsing

parse :: String -> Maybe Hash

O(1) Parse the representation generated by show.

Validation

valid :: Hash -> Bool

O(1) Check a hash for bit-level validity.

validate :: Hash -> Maybe Hash

O(1) Validate a hash on the bit-level. From valid h == True follows validate h == Just h.

Packing

pack8 :: [Word8] -> Maybe Hash

O(1) Pack a list of 64 8-bit words.

pack16 :: [Word16] -> Maybe Hash

O(1) Pack a list of 32 16-bit words.

pack32 :: [Word32] -> Maybe Hash

O(1) Pack a list of 16 32-bit words.

pack64 :: [Word64] -> Maybe Hash

O(1) Pack a list of 8 64-bit words.

Unpacking

unpack8 :: Hash -> [Word8]

O(1) Unpack into list of 64 8-bit words.

unpack16 :: Hash -> [Word16]

O(1) Unpack into list of 32 16-bit words.

unpack32 :: Hash -> [Word32]

O(1) Unpack into list of 16 32-bit words.

unpack64 :: Hash -> [Word64]

O(1) Unpack into list of 8 64-bit words.