commit 69cea554c1eea158d41112b3db5f303bab7c7072
parent 332e5a88d027fa5f834c4f4ce0159d61ba4b27c0
Author: Jared Tobin <jared@jtobin.io>
Date: Sat, 5 Oct 2024 20:26:41 +0400
lib: skeleton
(copy-paste tweak of Crypto.Hash.SHA256)
Diffstat:
1 file changed, 482 insertions(+), 0 deletions(-)
diff --git a/lib/Crypto/Hash/SHA512.hs b/lib/Crypto/Hash/SHA512.hs
@@ -1,3 +1,485 @@
+{-# OPTIONS_GHC -funbox-small-strict-fields #-}
+{-# LANGUAGE BangPatterns #-}
+{-# LANGUAGE RecordWildCards #-}
+{-# LANGUAGE ViewPatterns #-}
+
+-- |
+-- Module: Crypto.Hash.SHA512
+-- Copyright: (c) 2024 Jared Tobin
+-- License: MIT
+-- Maintainer: Jared Tobin <jared@ppad.tech>
+--
+-- Pure SHA-512 and HMAC-SHA512 implementations for
+-- strict and lazy ByteStrings, as specified by RFC's
+-- [6234](https://datatracker.ietf.org/doc/html/rfc6234) and
+-- [2104](https://datatracker.ietf.org/doc/html/rfc2104).
module Crypto.Hash.SHA512 where
+import qualified Data.Bits as B
+import Data.Bits ((.|.), (.&.))
+import qualified Data.ByteString as BS
+import qualified Data.ByteString.Builder as BSB
+import qualified Data.ByteString.Builder.Extra as BE
+import qualified Data.ByteString.Internal as BI
+import qualified Data.ByteString.Lazy as BL
+import qualified Data.ByteString.Lazy.Internal as BLI
+import qualified Data.ByteString.Unsafe as BU
+import Data.Word (Word64)
+import Foreign.ForeignPtr (plusForeignPtr)
+
+-- preliminary utils ----------------------------------------------------------
+
+-- keystroke saver
+fi :: (Integral a, Num b) => a -> b
+fi = fromIntegral
+{-# INLINE fi #-}
+
+-- parse strict ByteString in BE order to Word64 (verbatim from
+-- Data.Binary)
+--
+-- invariant:
+-- the input bytestring is at least 64 bits in length
+unsafe_word64be :: BS.ByteString -> Word64
+unsafe_word64be s =
+ (fi (s `BU.unsafeIndex` 0) `B.unsafeShiftL` 56) .|.
+ (fi (s `BU.unsafeIndex` 1) `B.unsafeShiftL` 48) .|.
+ (fi (s `BU.unsafeIndex` 2) `B.unsafeShiftL` 40) .|.
+ (fi (s `BU.unsafeIndex` 3) `B.unsafeShiftL` 32) .|.
+ (fi (s `BU.unsafeIndex` 4) `B.unsafeShiftL` 24) .|.
+ (fi (s `BU.unsafeIndex` 5) `B.unsafeShiftL` 16) .|.
+ (fi (s `BU.unsafeIndex` 6) `B.unsafeShiftL` 8) .|.
+ (fi (s `BU.unsafeIndex` 7) )
+{-# INLINE unsafe_word64be #-}
+
+-- utility types for more efficient ByteString management
+
+data SSPair = SSPair
+ {-# UNPACK #-} !BS.ByteString
+ {-# UNPACK #-} !BS.ByteString
+
+data SLPair = SLPair {-# UNPACK #-} !BS.ByteString !BL.ByteString
+
+data WSPair = WSPair {-# UNPACK #-} !Word64 {-# UNPACK #-} !BS.ByteString
+
+-- unsafe version of splitAt that does no bounds checking
+--
+-- invariant:
+-- 0 <= n <= l
+unsafe_splitAt :: Int -> BS.ByteString -> SSPair
+unsafe_splitAt n (BI.BS x l) =
+ SSPair (BI.BS x n) (BI.BS (plusForeignPtr x n) (l - n))
+
+-- variant of Data.ByteString.Lazy.splitAt that returns the initial
+-- component as a strict, unboxed ByteString
+splitAt128 :: BL.ByteString -> SLPair
+splitAt128 = splitAt' (128 :: Int) where
+ splitAt' _ BLI.Empty = SLPair mempty BLI.Empty
+ splitAt' n (BLI.Chunk c cs) =
+ if n < BS.length c
+ then
+ -- n < BS.length c, so unsafe_splitAt is safe
+ let !(SSPair c0 c1) = unsafe_splitAt n c
+ in SLPair c0 (BLI.Chunk c1 cs)
+ else
+ let SLPair cs' cs'' = splitAt' (n - BS.length c) cs
+ in SLPair (c <> cs') cs''
+
+-- variant of Data.ByteString.splitAt that behaves like an incremental
+-- Word64 parser
+--
+-- invariant:
+-- the input bytestring is at least 64 bits in length
+unsafe_parseWsPair :: BS.ByteString -> WSPair
+unsafe_parseWsPair (BI.BS x l) =
+ WSPair (unsafe_word64be (BI.BS x 8)) (BI.BS (plusForeignPtr x 8) (l - 8))
+{-# INLINE unsafe_parseWsPair #-}
+
+-- message padding and parsing ------------------------------------------------
+-- https://datatracker.ietf.org/doc/html/rfc6234#section-4.1
+
+-- k such that (l + 1 + k) mod 128 = 112
+sol :: Word64 -> Word64
+sol l =
+ let r = 112 - fi l `mod` 128 - 1 :: Integer -- fi prevents underflow
+ in fi (if r < 0 then r + 128 else r)
+
+-- XX doesn't properly handle (> maxBound :: Word64) length
+
+-- RFC 6234 4.1 (strict)
+pad :: BS.ByteString -> BS.ByteString
+pad m = BL.toStrict . BSB.toLazyByteString $ padded where
+ l = fi (BS.length m)
+ padded = BSB.byteString m <> fill (sol l) (BSB.word8 0x80)
+
+ fill j !acc
+ | j == 0 = acc <> BSB.word64BE 0x00 <> BSB.word64BE (l * 8)
+ | otherwise = fill (pred j) (acc <> BSB.word8 0x00)
+
+-- RFC 6234 4.1 (lazy)
+pad_lazy :: BL.ByteString -> BL.ByteString
+pad_lazy (BL.toChunks -> m) = BL.fromChunks (walk 0 m) where
+ walk !l bs = case bs of
+ (c:cs) -> c : walk (l + fi (BS.length c)) cs
+ [] -> padding l (sol l) (BSB.word8 0x80)
+
+ padding l k bs
+ | k == 0 =
+ pure
+ . BL.toStrict
+ -- more efficient for small builder
+ . BE.toLazyByteStringWith
+ (BE.safeStrategy 128 BE.smallChunkSize) mempty
+ $ bs <> BSB.word64BE 0x00 <> BSB.word64BE (l * 8)
+ | otherwise =
+ let nacc = bs <> BSB.word8 0x00
+ in padding l (pred k) nacc
+
+-- functions and constants used -----------------------------------------------
+-- https://datatracker.ietf.org/doc/html/rfc6234#section-5.1
+
+ch :: Word64 -> Word64 -> Word64 -> Word64
+ch x y z = (x .&. y) `B.xor` (B.complement x .&. z)
+{-# INLINE ch #-}
+
+-- credit to SHA authors for the following optimisation. their text:
+--
+-- > note:
+-- > the original functions is (x & y) ^ (x & z) ^ (y & z)
+-- > if you fire off truth tables, this is equivalent to
+-- > (x & y) | (x & z) | (y & z)
+-- > which you can the use distribution on:
+-- > (x & (y | z)) | (y & z)
+-- > which saves us one operation.
+maj :: Word64 -> Word64 -> Word64 -> Word64
+maj x y z = (x .&. (y .|. z)) .|. (y .&. z)
+{-# INLINE maj #-}
+
+bsig0 :: Word64 -> Word64
+bsig0 x = B.rotateR x 2 `B.xor` B.rotateR x 13 `B.xor` B.rotateR x 22
+{-# INLINE bsig0 #-}
+
+bsig1 :: Word64 -> Word64
+bsig1 x = B.rotateR x 6 `B.xor` B.rotateR x 11 `B.xor` B.rotateR x 25
+{-# INLINE bsig1 #-}
+
+ssig0 :: Word64 -> Word64
+ssig0 x = B.rotateR x 7 `B.xor` B.rotateR x 18 `B.xor` B.unsafeShiftR x 3
+{-# INLINE ssig0 #-}
+
+ssig1 :: Word64 -> Word64
+ssig1 x = B.rotateR x 17 `B.xor` B.rotateR x 19 `B.xor` B.unsafeShiftR x 10
+{-# INLINE ssig1 #-}
+
+data Schedule = Schedule {
+ w00 :: !Word64, w01 :: !Word64, w02 :: !Word64, w03 :: !Word64
+ , w04 :: !Word64, w05 :: !Word64, w06 :: !Word64, w07 :: !Word64
+ , w08 :: !Word64, w09 :: !Word64, w10 :: !Word64, w11 :: !Word64
+ , w12 :: !Word64, w13 :: !Word64, w14 :: !Word64, w15 :: !Word64
+ , w16 :: !Word64, w17 :: !Word64, w18 :: !Word64, w19 :: !Word64
+ , w20 :: !Word64, w21 :: !Word64, w22 :: !Word64, w23 :: !Word64
+ , w24 :: !Word64, w25 :: !Word64, w26 :: !Word64, w27 :: !Word64
+ , w28 :: !Word64, w29 :: !Word64, w30 :: !Word64, w31 :: !Word64
+ , w32 :: !Word64, w33 :: !Word64, w34 :: !Word64, w35 :: !Word64
+ , w36 :: !Word64, w37 :: !Word64, w38 :: !Word64, w39 :: !Word64
+ , w40 :: !Word64, w41 :: !Word64, w42 :: !Word64, w43 :: !Word64
+ , w44 :: !Word64, w45 :: !Word64, w46 :: !Word64, w47 :: !Word64
+ , w48 :: !Word64, w49 :: !Word64, w50 :: !Word64, w51 :: !Word64
+ , w52 :: !Word64, w53 :: !Word64, w54 :: !Word64, w55 :: !Word64
+ , w56 :: !Word64, w57 :: !Word64, w58 :: !Word64, w59 :: !Word64
+ , w60 :: !Word64, w61 :: !Word64, w62 :: !Word64, w63 :: !Word64
+ , w64 :: !Word64, w65 :: !Word64, w66 :: !Word64, w67 :: !Word64
+ , w68 :: !Word64, w69 :: !Word64, w70 :: !Word64, w71 :: !Word64
+ , w72 :: !Word64, w73 :: !Word64, w74 :: !Word64, w75 :: !Word64
+ , w76 :: !Word64, w77 :: !Word64, w78 :: !Word64, w79 :: !Word64
+ }
+
+-- initialization -------------------------------------------------------------
+-- https://datatracker.ietf.org/doc/html/rfc6234#section-6.1
+
+data Registers = Registers {
+ h0 :: !Word64, h1 :: !Word64, h2 :: !Word64, h3 :: !Word64
+ , h4 :: !Word64, h5 :: !Word64, h6 :: !Word64, h7 :: !Word64
+ }
+
+-- first 64 bits of the fractional parts of the square roots of the
+-- first eight primes
+iv :: Registers
+iv = Registers
+ 0x6a09e667f3bcc908 0xbb67ae8584caa73b 0x3c6ef372fe94f82b 0xa54ff53a5f1d36f1
+ 0x510e527fade682d1 0x9b05688c2b3e6c1f 0x1f83d9abfb41bd6b 0x5be0cd19137e2179
+
+-- processing -----------------------------------------------------------------
+-- https://datatracker.ietf.org/doc/html/rfc6234#section-6.2
+
+data Block = Block {
+ m00 :: !Word64, m01 :: !Word64, m02 :: !Word64, m03 :: !Word64
+ , m04 :: !Word64, m05 :: !Word64, m06 :: !Word64, m07 :: !Word64
+ , m08 :: !Word64, m09 :: !Word64, m10 :: !Word64, m11 :: !Word64
+ , m12 :: !Word64, m13 :: !Word64, m14 :: !Word64, m15 :: !Word64
+ }
+
+-- parse strict bytestring to block
+--
+-- invariant:
+-- the input bytestring is exactly 1024 bits long
+unsafe_parse :: BS.ByteString -> Block
+unsafe_parse bs =
+ let !(WSPair m00 t00) = unsafe_parseWsPair bs
+ !(WSPair m01 t01) = unsafe_parseWsPair t00
+ !(WSPair m02 t02) = unsafe_parseWsPair t01
+ !(WSPair m03 t03) = unsafe_parseWsPair t02
+ !(WSPair m04 t04) = unsafe_parseWsPair t03
+ !(WSPair m05 t05) = unsafe_parseWsPair t04
+ !(WSPair m06 t06) = unsafe_parseWsPair t05
+ !(WSPair m07 t07) = unsafe_parseWsPair t06
+ !(WSPair m08 t08) = unsafe_parseWsPair t07
+ !(WSPair m09 t09) = unsafe_parseWsPair t08
+ !(WSPair m10 t10) = unsafe_parseWsPair t09
+ !(WSPair m11 t11) = unsafe_parseWsPair t10
+ !(WSPair m12 t12) = unsafe_parseWsPair t11
+ !(WSPair m13 t13) = unsafe_parseWsPair t12
+ !(WSPair m14 t14) = unsafe_parseWsPair t13
+ !(WSPair m15 t15) = unsafe_parseWsPair t14
+ in if BS.null t15
+ then Block {..}
+ else error "ppad-sha512: internal error (bytes remaining)"
+
+-- RFC 6234 6.2 step 1
+prepare_schedule :: Block -> Schedule
+prepare_schedule Block {..} = Schedule {..} where
+ w00 = m00; w01 = m01; w02 = m02; w03 = m03
+ w04 = m04; w05 = m05; w06 = m06; w07 = m07
+ w08 = m08; w09 = m09; w10 = m10; w11 = m11
+ w12 = m12; w13 = m13; w14 = m14; w15 = m15
+ w16 = ssig1 w14 + w09 + ssig0 w01 + w00
+ w17 = ssig1 w15 + w10 + ssig0 w02 + w01
+ w18 = ssig1 w16 + w11 + ssig0 w03 + w02
+ w19 = ssig1 w17 + w12 + ssig0 w04 + w03
+ w20 = ssig1 w18 + w13 + ssig0 w05 + w04
+ w21 = ssig1 w19 + w14 + ssig0 w06 + w05
+ w22 = ssig1 w20 + w15 + ssig0 w07 + w06
+ w23 = ssig1 w21 + w16 + ssig0 w08 + w07
+ w24 = ssig1 w22 + w17 + ssig0 w09 + w08
+ w25 = ssig1 w23 + w18 + ssig0 w10 + w09
+ w26 = ssig1 w24 + w19 + ssig0 w11 + w10
+ w27 = ssig1 w25 + w20 + ssig0 w12 + w11
+ w28 = ssig1 w26 + w21 + ssig0 w13 + w12
+ w29 = ssig1 w27 + w22 + ssig0 w14 + w13
+ w30 = ssig1 w28 + w23 + ssig0 w15 + w14
+ w31 = ssig1 w29 + w24 + ssig0 w16 + w15
+ w32 = ssig1 w30 + w25 + ssig0 w17 + w16
+ w33 = ssig1 w31 + w26 + ssig0 w18 + w17
+ w34 = ssig1 w32 + w27 + ssig0 w19 + w18
+ w35 = ssig1 w33 + w28 + ssig0 w20 + w19
+ w36 = ssig1 w34 + w29 + ssig0 w21 + w20
+ w37 = ssig1 w35 + w30 + ssig0 w22 + w21
+ w38 = ssig1 w36 + w31 + ssig0 w23 + w22
+ w39 = ssig1 w37 + w32 + ssig0 w24 + w23
+ w40 = ssig1 w38 + w33 + ssig0 w25 + w24
+ w41 = ssig1 w39 + w34 + ssig0 w26 + w25
+ w42 = ssig1 w40 + w35 + ssig0 w27 + w26
+ w43 = ssig1 w41 + w36 + ssig0 w28 + w27
+ w44 = ssig1 w42 + w37 + ssig0 w29 + w28
+ w45 = ssig1 w43 + w38 + ssig0 w30 + w29
+ w46 = ssig1 w44 + w39 + ssig0 w31 + w30
+ w47 = ssig1 w45 + w40 + ssig0 w32 + w31
+ w48 = ssig1 w46 + w41 + ssig0 w33 + w32
+ w49 = ssig1 w47 + w42 + ssig0 w34 + w33
+ w50 = ssig1 w48 + w43 + ssig0 w35 + w34
+ w51 = ssig1 w49 + w44 + ssig0 w36 + w35
+ w52 = ssig1 w50 + w45 + ssig0 w37 + w36
+ w53 = ssig1 w51 + w46 + ssig0 w38 + w37
+ w54 = ssig1 w52 + w47 + ssig0 w39 + w38
+ w55 = ssig1 w53 + w48 + ssig0 w40 + w39
+ w56 = ssig1 w54 + w49 + ssig0 w41 + w40
+ w57 = ssig1 w55 + w50 + ssig0 w42 + w41
+ w58 = ssig1 w56 + w51 + ssig0 w43 + w42
+ w59 = ssig1 w57 + w52 + ssig0 w44 + w43
+ w60 = ssig1 w58 + w53 + ssig0 w45 + w44
+ w61 = ssig1 w59 + w54 + ssig0 w46 + w45
+ w62 = ssig1 w60 + w55 + ssig0 w47 + w46
+ w63 = ssig1 w61 + w56 + ssig0 w48 + w47
+ w64 = ssig1 w62 + w57 + ssig0 w49 + w48
+ w65 = ssig1 w63 + w58 + ssig0 w50 + w49
+ w66 = ssig1 w64 + w59 + ssig0 w51 + w50
+ w67 = ssig1 w65 + w60 + ssig0 w52 + w51
+ w68 = ssig1 w66 + w61 + ssig0 w53 + w52
+ w69 = ssig1 w67 + w62 + ssig0 w54 + w53
+ w70 = ssig1 w68 + w63 + ssig0 w55 + w54
+ w71 = ssig1 w69 + w64 + ssig0 w56 + w55
+ w72 = ssig1 w70 + w65 + ssig0 w57 + w56
+ w73 = ssig1 w71 + w66 + ssig0 w58 + w57
+ w74 = ssig1 w72 + w67 + ssig0 w59 + w58
+ w75 = ssig1 w73 + w68 + ssig0 w60 + w59
+ w76 = ssig1 w74 + w69 + ssig0 w61 + w60
+ w77 = ssig1 w75 + w70 + ssig0 w62 + w61
+ w78 = ssig1 w76 + w71 + ssig0 w63 + w62
+ w79 = ssig1 w77 + w72 + ssig0 w64 + w63
+
+-- RFC 6234 6.2 steps 2, 3, 4
+block_hash :: Registers -> Schedule -> Registers
+block_hash r00@Registers {..} Schedule {..} =
+ -- constants are the first 64 bits of the fractional parts of the
+ -- cube roots of the first eighty prime numbers
+ let r01 = step r00 0x428a2f98d728ae22 w00
+ r02 = step r01 0x7137449123ef65cd w01
+ r03 = step r02 0xb5c0fbcfec4d3b2f w02
+ r04 = step r03 0xe9b5dba58189dbbc w03
+ r05 = step r04 0x3956c25bf348b538 w04
+ r06 = step r05 0x59f111f1b605d019 w05
+ r07 = step r06 0x923f82a4af194f9b w06
+ r08 = step r07 0xab1c5ed5da6d8118 w07
+ r09 = step r08 0xd807aa98a3030242 w08
+ r10 = step r09 0x12835b0145706fbe w09
+ r11 = step r10 0x243185be4ee4b28c w10
+ r12 = step r11 0x550c7dc3d5ffb4e2 w11
+ r13 = step r12 0x72be5d74f27b896f w12
+ r14 = step r13 0x80deb1fe3b1696b1 w13
+ r15 = step r14 0x9bdc06a725c71235 w14
+ r16 = step r15 0xc19bf174cf692694 w15
+ r17 = step r16 0xe49b69c19ef14ad2 w16
+ r18 = step r17 0xefbe4786384f25e3 w17
+ r19 = step r18 0x0fc19dc68b8cd5b5 w18
+ r20 = step r19 0x240ca1cc77ac9c65 w19
+ r21 = step r20 0x2de92c6f592b0275 w20
+ r22 = step r21 0x4a7484aa6ea6e483 w21
+ r23 = step r22 0x5cb0a9dcbd41fbd4 w22
+ r24 = step r23 0x76f988da831153b5 w23
+ r25 = step r24 0x983e5152ee66dfab w24
+ r26 = step r25 0xa831c66d2db43210 w25
+ r27 = step r26 0xb00327c898fb213f w26
+ r28 = step r27 0xbf597fc7beef0ee4 w27
+ r29 = step r28 0xc6e00bf33da88fc2 w28
+ r30 = step r29 0xd5a79147930aa725 w29
+ r31 = step r30 0x06ca6351e003826f w30
+ r32 = step r31 0x142929670a0e6e70 w31
+ r33 = step r32 0x27b70a8546d22ffc w32
+ r34 = step r33 0x2e1b21385c26c926 w33
+ r35 = step r34 0x4d2c6dfc5ac42aed w34
+ r36 = step r35 0x53380d139d95b3df w35
+ r37 = step r36 0x650a73548baf63de w36
+ r38 = step r37 0x766a0abb3c77b2a8 w37
+ r39 = step r38 0x81c2c92e47edaee6 w38
+ r40 = step r39 0x92722c851482353b w39
+ r41 = step r40 0xa2bfe8a14cf10364 w40
+ r42 = step r41 0xa81a664bbc423001 w41
+ r43 = step r42 0xc24b8b70d0f89791 w42
+ r44 = step r43 0xc76c51a30654be30 w43
+ r45 = step r44 0xd192e819d6ef5218 w44
+ r46 = step r45 0xd69906245565a910 w45
+ r47 = step r46 0xf40e35855771202a w46
+ r48 = step r47 0x106aa07032bbd1b8 w47
+ r49 = step r48 0x19a4c116b8d2d0c8 w48
+ r50 = step r49 0x1e376c085141ab53 w49
+ r51 = step r50 0x2748774cdf8eeb99 w50
+ r52 = step r51 0x34b0bcb5e19b48a8 w51
+ r53 = step r52 0x391c0cb3c5c95a63 w52
+ r54 = step r53 0x4ed8aa4ae3418acb w53
+ r55 = step r54 0x5b9cca4f7763e373 w54
+ r56 = step r55 0x682e6ff3d6b2b8a3 w55
+ r57 = step r56 0x748f82ee5defb2fc w56
+ r58 = step r57 0x78a5636f43172f60 w57
+ r59 = step r58 0x84c87814a1f0ab72 w58
+ r60 = step r59 0x8cc702081a6439ec w59
+ r61 = step r60 0x90befffa23631e28 w60
+ r62 = step r61 0xa4506cebde82bde9 w61
+ r63 = step r62 0xbef9a3f7b2c67915 w62
+ r64 = step r63 0xc67178f2e372532b w63
+ r65 = step r64 0xca273eceea26619c w64
+ r66 = step r65 0xd186b8c721c0c207 w65
+ r67 = step r66 0xeada7dd6cde0eb1e w66
+ r68 = step r67 0xf57d4f7fee6ed178 w67
+ r69 = step r68 0x06f067aa72176fba w68
+ r70 = step r69 0x0a637dc5a2c898a6 w69
+ r71 = step r70 0x113f9804bef90dae w70
+ r72 = step r71 0x1b710b35131c471b w71
+ r73 = step r72 0x28db77f523047d84 w72
+ r74 = step r73 0x32caab7b40c72493 w73
+ r75 = step r74 0x3c9ebe0a15c9bebc w74
+ r76 = step r75 0x431d67c49c100d4c w75
+ r77 = step r76 0x4cc5d4becb3e42b6 w76
+ r78 = step r77 0x597f299cfc657e2a w77
+ r79 = step r78 0x5fcb6fab3ad6faec w78
+ r80 = step r79 0x6c44198c4a475817 w79
+ !(Registers a b c d e f g h) = r80
+ in Registers
+ (a + h0) (b + h1) (c + h2) (d + h3)
+ (e + h4) (f + h5) (g + h6) (h + h7)
+
+step :: Registers -> Word64 -> Word64 -> Registers
+step (Registers a b c d e f g h) k w =
+ let t1 = h + bsig1 e + ch e f g + k + w
+ t2 = bsig0 a + maj a b c
+ in Registers (t1 + t2) a b c (d + t1) e f g
+
+-- RFC 6234 6.2 block pipeline
+--
+-- invariant:
+-- the input bytestring is exactly 1024 bits in length
+unsafe_hash_alg :: Registers -> BS.ByteString -> Registers
+unsafe_hash_alg rs bs = block_hash rs (prepare_schedule (unsafe_parse bs))
+
+-- register concatenation
+cat :: Registers -> BS.ByteString
+cat Registers {..} =
+ BL.toStrict
+ -- more efficient for small builder
+ . BE.toLazyByteStringWith (BE.safeStrategy 128 BE.smallChunkSize) mempty
+ $ mconcat [
+ BSB.word64BE h0, BSB.word64BE h1, BSB.word64BE h2, BSB.word64BE h3
+ , BSB.word64BE h4, BSB.word64BE h5, BSB.word64BE h6, BSB.word64BE h7
+ ]
+
+-- | Compute a condensed representation of a strict bytestring via
+-- SHA-512.
+--
+-- The 512-bit output digest is returned as a strict bytestring.
+--
+-- >>> hash "strict bytestring input"
+-- "<strict 512-bit message digest>"
+hash :: BS.ByteString -> BS.ByteString
+hash bs = cat (go iv (pad bs)) where
+ -- proof that 'go' always terminates safely:
+ --
+ -- let b = pad bs
+ -- then length(b) = n * 1024 bits for some n >= 0 (1)
+ go :: Registers -> BS.ByteString -> Registers
+ go !acc b
+ -- if n == 0, then 'go' terminates safely (2)
+ | BS.null b = acc
+ -- if n > 0, then
+ --
+ -- let (c, r) = unsafe_splitAt 128 b
+ -- then length(c) == 1024 bits by (1)
+ -- length(r) == m * 1024 bits for some m >= 0 by (1)
+ --
+ -- note 'unsafe_hash_alg' terminates safely for bytestring (3)
+ -- input of exactly 1024 bits in length
+ --
+ -- length(c) == 1024
+ -- => 'unsafe_hash_alg' terminates safely by (3)
+ -- => 'go' terminates safely (4)
+ -- length(r) == m * 1024 bits for m >= 0
+ -- => next invocation of 'go' terminates safely by (2), (4)
+ --
+ -- then by induction, 'go' always terminates safely (QED)
+ | otherwise = case unsafe_splitAt 128 b of
+ SSPair c r -> go (unsafe_hash_alg acc c) r
+
+-- | Compute a condensed representation of a lazy bytestring via
+-- SHA-512.
+--
+-- The 512-bit output digest is returned as a strict bytestring.
+--
+-- >>> hash_lazy "lazy bytestring input"
+-- "<strict 512-bit message digest>"
+hash_lazy :: BL.ByteString -> BS.ByteString
+hash_lazy bl = cat (go iv (pad_lazy bl)) where
+ -- proof of safety proceeds analogously
+ go :: Registers -> BL.ByteString -> Registers
+ go !acc bs
+ | BL.null bs = acc
+ | otherwise = case splitAt128 bs of
+ SLPair c r -> go (unsafe_hash_alg acc c) r
+
