sha256

Pure Haskell SHA-256, HMAC-SHA256 (docs.ppad.tech/sha256).
git clone git://git.ppad.tech/sha256.git
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SHA256.hs (20098B)


      1 {-# OPTIONS_GHC -funbox-small-strict-fields #-}
      2 {-# LANGUAGE BangPatterns #-}
      3 {-# LANGUAGE RecordWildCards #-}
      4 {-# LANGUAGE ViewPatterns #-}
      5 
      6 -- |
      7 -- Module: Crypto.Hash.SHA256
      8 -- Copyright: (c) 2024 Jared Tobin
      9 -- License: MIT
     10 -- Maintainer: Jared Tobin <jared@ppad.tech>
     11 --
     12 -- Pure SHA-256 and HMAC-SHA256 implementations for
     13 -- strict and lazy ByteStrings, as specified by RFC's
     14 -- [6234](https://datatracker.ietf.org/doc/html/rfc6234) and
     15 -- [2104](https://datatracker.ietf.org/doc/html/rfc2104).
     16 
     17 module Crypto.Hash.SHA256 (
     18   -- * SHA-256 message digest functions
     19     hash
     20   , hash_lazy
     21 
     22   -- * SHA256-based MAC functions
     23   , hmac
     24   , hmac_lazy
     25   ) where
     26 
     27 import qualified Data.Bits as B
     28 import Data.Bits ((.|.), (.&.))
     29 import qualified Data.ByteString as BS
     30 import qualified Data.ByteString.Builder as BSB
     31 import qualified Data.ByteString.Builder.Extra as BE
     32 import qualified Data.ByteString.Internal as BI
     33 import qualified Data.ByteString.Lazy as BL
     34 import qualified Data.ByteString.Lazy.Internal as BLI
     35 import qualified Data.ByteString.Unsafe as BU
     36 import Data.Word (Word32, Word64)
     37 import Foreign.ForeignPtr (plusForeignPtr)
     38 
     39 -- preliminary utils
     40 
     41 -- keystroke saver
     42 fi :: (Integral a, Num b) => a -> b
     43 fi = fromIntegral
     44 {-# INLINE fi #-}
     45 
     46 -- parse strict ByteString in BE order to Word32 (verbatim from
     47 -- Data.Binary)
     48 --
     49 -- invariant:
     50 --   the input bytestring is at least 32 bits in length
     51 unsafe_word32be :: BS.ByteString -> Word32
     52 unsafe_word32be s =
     53   (fi (s `BU.unsafeIndex` 0) `B.unsafeShiftL` 24) .|.
     54   (fi (s `BU.unsafeIndex` 1) `B.unsafeShiftL` 16) .|.
     55   (fi (s `BU.unsafeIndex` 2) `B.unsafeShiftL`  8) .|.
     56   (fi (s `BU.unsafeIndex` 3))
     57 {-# INLINE unsafe_word32be #-}
     58 
     59 -- utility types for more efficient ByteString management
     60 
     61 data SSPair = SSPair
     62   {-# UNPACK #-} !BS.ByteString
     63   {-# UNPACK #-} !BS.ByteString
     64 
     65 data SLPair = SLPair {-# UNPACK #-} !BS.ByteString !BL.ByteString
     66 
     67 data WSPair = WSPair {-# UNPACK #-} !Word32 {-# UNPACK #-} !BS.ByteString
     68 
     69 -- unsafe version of splitAt that does no bounds checking
     70 --
     71 -- invariant:
     72 --   0 <= n <= l
     73 unsafe_splitAt :: Int -> BS.ByteString -> SSPair
     74 unsafe_splitAt n (BI.BS x l) =
     75   SSPair (BI.BS x n) (BI.BS (plusForeignPtr x n) (l - n))
     76 
     77 -- variant of Data.ByteString.Lazy.splitAt that returns the initial
     78 -- component as a strict, unboxed ByteString
     79 splitAt64 :: BL.ByteString -> SLPair
     80 splitAt64 = splitAt' (64 :: Int) where
     81   splitAt' _ BLI.Empty        = SLPair mempty BLI.Empty
     82   splitAt' n (BLI.Chunk c@(BI.PS _ _ l) cs) =
     83     if    n < l
     84     then
     85       -- n < BS.length c, so unsafe_splitAt is safe
     86       let !(SSPair c0 c1) = unsafe_splitAt n c
     87       in  SLPair c0 (BLI.Chunk c1 cs)
     88     else
     89       let SLPair cs' cs'' = splitAt' (n - l) cs
     90       in  SLPair (c <> cs') cs''
     91 
     92 -- variant of Data.ByteString.splitAt that behaves like an incremental
     93 -- Word32 parser
     94 --
     95 -- invariant:
     96 --   the input bytestring is at least 32 bits in length
     97 unsafe_parseWsPair :: BS.ByteString -> WSPair
     98 unsafe_parseWsPair (BI.BS x l) =
     99   WSPair (unsafe_word32be (BI.BS x 4)) (BI.BS (plusForeignPtr x 4) (l - 4))
    100 {-# INLINE unsafe_parseWsPair #-}
    101 
    102 -- builder realization strategies
    103 
    104 to_strict :: BSB.Builder -> BS.ByteString
    105 to_strict = BL.toStrict . BSB.toLazyByteString
    106 
    107 to_strict_small :: BSB.Builder -> BS.ByteString
    108 to_strict_small = BL.toStrict . BE.toLazyByteStringWith
    109   (BE.safeStrategy 128 BE.smallChunkSize) mempty
    110 
    111 -- message padding and parsing
    112 -- https://datatracker.ietf.org/doc/html/rfc6234#section-4.1
    113 
    114 -- k such that (l + 1 + k) mod 64 = 56
    115 sol :: Word64 -> Word64
    116 sol l =
    117   let r = 56 - fi l `rem` 64 - 1 :: Integer -- fi prevents underflow
    118   in  fi (if r < 0 then r + 64 else r)
    119 
    120 -- RFC 6234 4.1 (strict)
    121 pad :: BS.ByteString -> BS.ByteString
    122 pad m@(BI.PS _ _ (fi -> l))
    123     | l < 128 = to_strict_small padded
    124     | otherwise = to_strict padded
    125   where
    126     padded = BSB.byteString m
    127           <> fill (sol l) (BSB.word8 0x80)
    128           <> BSB.word64BE (l * 8)
    129 
    130     fill j !acc
    131       | j `rem` 8 == 0 =
    132              loop64 j acc
    133       | (j - 7) `rem` 8 == 0 =
    134              loop64 (j - 7) acc
    135           <> BSB.word32BE 0x00
    136           <> BSB.word16BE 0x00
    137           <> BSB.word8 0x00
    138       | (j - 6) `rem` 8 == 0 =
    139              loop64 (j - 6) acc
    140           <> BSB.word32BE 0x00
    141           <> BSB.word16BE 0x00
    142       | (j - 5) `rem` 8 == 0 =
    143              loop64 (j - 5) acc
    144           <> BSB.word32BE 0x00
    145           <> BSB.word8 0x00
    146       | (j - 4) `rem` 8 == 0 =
    147              loop64 (j - 4) acc
    148           <> BSB.word32BE 0x00
    149       | (j - 3) `rem` 8 == 0 =
    150              loop64 (j - 3) acc
    151           <> BSB.word16BE 0x00
    152           <> BSB.word8 0x00
    153       | (j - 2) `rem` 8 == 0 =
    154              loop64 (j - 2) acc
    155           <> BSB.word16BE 0x00
    156       | (j - 1) `rem` 8 == 0 =
    157              loop64 (j - 1) acc
    158           <> BSB.word8 0x00
    159 
    160       | j `rem` 4 == 0 =
    161              loop32 j acc
    162       | (j - 3) `rem` 4 == 0 =
    163              loop32 (j - 3) acc
    164           <> BSB.word16BE 0x00
    165           <> BSB.word8 0x00
    166       | (j - 2) `rem` 4 == 0 =
    167              loop32 (j - 2) acc
    168           <> BSB.word16BE 0x00
    169       | (j - 1) `rem` 4 == 0 =
    170              loop32 (j - 1) acc
    171           <> BSB.word8 0x00
    172 
    173       | j `rem` 2 == 0 =
    174              loop16 j acc
    175       | (j - 1) `rem` 2 == 0 =
    176              loop16 (j - 1) acc
    177           <> BSB.word8 0x00
    178 
    179       | otherwise =
    180             loop8 j acc
    181 
    182     loop64 j !acc
    183       | j == 0 = acc
    184       | otherwise = loop64 (j - 8) (acc <> BSB.word64BE 0x00)
    185 
    186     loop32 j !acc
    187       | j == 0 = acc
    188       | otherwise = loop32 (j - 4) (acc <> BSB.word32BE 0x00)
    189 
    190     loop16 j !acc
    191       | j == 0 = acc
    192       | otherwise = loop16 (j - 2) (acc <> BSB.word16BE 0x00)
    193 
    194     loop8 j !acc
    195       | j == 0 = acc
    196       | otherwise = loop8 (pred j) (acc <> BSB.word8 0x00)
    197 
    198 -- RFC 6234 4.1 (lazy)
    199 pad_lazy :: BL.ByteString -> BL.ByteString
    200 pad_lazy (BL.toChunks -> m) = BL.fromChunks (walk 0 m) where
    201   walk !l bs = case bs of
    202     (c:cs) -> c : walk (l + fi (BS.length c)) cs
    203     [] -> padding l (sol l) (BSB.word8 0x80)
    204 
    205   padding l k bs
    206     | k == 0 =
    207           pure
    208         . to_strict
    209           -- more efficient for small builder
    210         $ bs <> BSB.word64BE (l * 8)
    211     | otherwise =
    212         let nacc = bs <> BSB.word8 0x00
    213         in  padding l (pred k) nacc
    214 
    215 -- functions and constants used
    216 -- https://datatracker.ietf.org/doc/html/rfc6234#section-5.1
    217 
    218 ch :: Word32 -> Word32 -> Word32 -> Word32
    219 ch x y z = (x .&. y) `B.xor` (B.complement x .&. z)
    220 {-# INLINE ch #-}
    221 
    222 -- credit to SHA authors for the following optimisation. their text:
    223 --
    224 -- > note:
    225 -- >   the original functions is (x & y) ^ (x & z) ^ (y & z)
    226 -- >   if you fire off truth tables, this is equivalent to
    227 -- >     (x & y) | (x & z) | (y & z)
    228 -- >   which you can the use distribution on:
    229 -- >     (x & (y | z)) | (y & z)
    230 -- >   which saves us one operation.
    231 maj :: Word32 -> Word32 -> Word32 -> Word32
    232 maj x y z = (x .&. (y .|. z)) .|. (y .&. z)
    233 {-# INLINE maj #-}
    234 
    235 bsig0 :: Word32 -> Word32
    236 bsig0 x = B.rotateR x 2 `B.xor` B.rotateR x 13 `B.xor` B.rotateR x 22
    237 {-# INLINE bsig0 #-}
    238 
    239 bsig1 :: Word32 -> Word32
    240 bsig1 x = B.rotateR x 6 `B.xor` B.rotateR x 11 `B.xor` B.rotateR x 25
    241 {-# INLINE bsig1 #-}
    242 
    243 ssig0 :: Word32 -> Word32
    244 ssig0 x = B.rotateR x 7 `B.xor` B.rotateR x 18 `B.xor` B.unsafeShiftR x 3
    245 {-# INLINE ssig0 #-}
    246 
    247 ssig1 :: Word32 -> Word32
    248 ssig1 x = B.rotateR x 17 `B.xor` B.rotateR x 19 `B.xor` B.unsafeShiftR x 10
    249 {-# INLINE ssig1 #-}
    250 
    251 data Schedule = Schedule {
    252     w00 :: !Word32, w01 :: !Word32, w02 :: !Word32, w03 :: !Word32
    253   , w04 :: !Word32, w05 :: !Word32, w06 :: !Word32, w07 :: !Word32
    254   , w08 :: !Word32, w09 :: !Word32, w10 :: !Word32, w11 :: !Word32
    255   , w12 :: !Word32, w13 :: !Word32, w14 :: !Word32, w15 :: !Word32
    256   , w16 :: !Word32, w17 :: !Word32, w18 :: !Word32, w19 :: !Word32
    257   , w20 :: !Word32, w21 :: !Word32, w22 :: !Word32, w23 :: !Word32
    258   , w24 :: !Word32, w25 :: !Word32, w26 :: !Word32, w27 :: !Word32
    259   , w28 :: !Word32, w29 :: !Word32, w30 :: !Word32, w31 :: !Word32
    260   , w32 :: !Word32, w33 :: !Word32, w34 :: !Word32, w35 :: !Word32
    261   , w36 :: !Word32, w37 :: !Word32, w38 :: !Word32, w39 :: !Word32
    262   , w40 :: !Word32, w41 :: !Word32, w42 :: !Word32, w43 :: !Word32
    263   , w44 :: !Word32, w45 :: !Word32, w46 :: !Word32, w47 :: !Word32
    264   , w48 :: !Word32, w49 :: !Word32, w50 :: !Word32, w51 :: !Word32
    265   , w52 :: !Word32, w53 :: !Word32, w54 :: !Word32, w55 :: !Word32
    266   , w56 :: !Word32, w57 :: !Word32, w58 :: !Word32, w59 :: !Word32
    267   , w60 :: !Word32, w61 :: !Word32, w62 :: !Word32, w63 :: !Word32
    268   }
    269 
    270 -- initialization
    271 -- https://datatracker.ietf.org/doc/html/rfc6234#section-6.1
    272 
    273 data Registers = Registers {
    274     h0 :: !Word32, h1 :: !Word32, h2 :: !Word32, h3 :: !Word32
    275   , h4 :: !Word32, h5 :: !Word32, h6 :: !Word32, h7 :: !Word32
    276   }
    277 
    278 -- first 32 bits of the fractional parts of the square roots of the
    279 -- first eight primes
    280 iv :: Registers
    281 iv = Registers
    282   0x6a09e667 0xbb67ae85 0x3c6ef372 0xa54ff53a
    283   0x510e527f 0x9b05688c 0x1f83d9ab 0x5be0cd19
    284 
    285 -- processing
    286 -- https://datatracker.ietf.org/doc/html/rfc6234#section-6.2
    287 
    288 data Block = Block {
    289     m00 :: !Word32, m01 :: !Word32, m02 :: !Word32, m03 :: !Word32
    290   , m04 :: !Word32, m05 :: !Word32, m06 :: !Word32, m07 :: !Word32
    291   , m08 :: !Word32, m09 :: !Word32, m10 :: !Word32, m11 :: !Word32
    292   , m12 :: !Word32, m13 :: !Word32, m14 :: !Word32, m15 :: !Word32
    293   }
    294 
    295 -- parse strict bytestring to block
    296 --
    297 -- invariant:
    298 --   the input bytestring is exactly 512 bits long
    299 unsafe_parse :: BS.ByteString -> Block
    300 unsafe_parse bs =
    301   let !(WSPair m00 t00) = unsafe_parseWsPair bs
    302       !(WSPair m01 t01) = unsafe_parseWsPair t00
    303       !(WSPair m02 t02) = unsafe_parseWsPair t01
    304       !(WSPair m03 t03) = unsafe_parseWsPair t02
    305       !(WSPair m04 t04) = unsafe_parseWsPair t03
    306       !(WSPair m05 t05) = unsafe_parseWsPair t04
    307       !(WSPair m06 t06) = unsafe_parseWsPair t05
    308       !(WSPair m07 t07) = unsafe_parseWsPair t06
    309       !(WSPair m08 t08) = unsafe_parseWsPair t07
    310       !(WSPair m09 t09) = unsafe_parseWsPair t08
    311       !(WSPair m10 t10) = unsafe_parseWsPair t09
    312       !(WSPair m11 t11) = unsafe_parseWsPair t10
    313       !(WSPair m12 t12) = unsafe_parseWsPair t11
    314       !(WSPair m13 t13) = unsafe_parseWsPair t12
    315       !(WSPair m14 t14) = unsafe_parseWsPair t13
    316       !(WSPair m15 t15) = unsafe_parseWsPair t14
    317   in  if   BS.null t15
    318       then Block {..}
    319       else error "ppad-sha256: internal error (bytes remaining)"
    320 
    321 -- RFC 6234 6.2 step 1
    322 prepare_schedule :: Block -> Schedule
    323 prepare_schedule Block {..} = Schedule {..} where
    324   w00 = m00; w01 = m01; w02 = m02; w03 = m03
    325   w04 = m04; w05 = m05; w06 = m06; w07 = m07
    326   w08 = m08; w09 = m09; w10 = m10; w11 = m11
    327   w12 = m12; w13 = m13; w14 = m14; w15 = m15
    328   w16 = ssig1 w14 + w09 + ssig0 w01 + w00
    329   w17 = ssig1 w15 + w10 + ssig0 w02 + w01
    330   w18 = ssig1 w16 + w11 + ssig0 w03 + w02
    331   w19 = ssig1 w17 + w12 + ssig0 w04 + w03
    332   w20 = ssig1 w18 + w13 + ssig0 w05 + w04
    333   w21 = ssig1 w19 + w14 + ssig0 w06 + w05
    334   w22 = ssig1 w20 + w15 + ssig0 w07 + w06
    335   w23 = ssig1 w21 + w16 + ssig0 w08 + w07
    336   w24 = ssig1 w22 + w17 + ssig0 w09 + w08
    337   w25 = ssig1 w23 + w18 + ssig0 w10 + w09
    338   w26 = ssig1 w24 + w19 + ssig0 w11 + w10
    339   w27 = ssig1 w25 + w20 + ssig0 w12 + w11
    340   w28 = ssig1 w26 + w21 + ssig0 w13 + w12
    341   w29 = ssig1 w27 + w22 + ssig0 w14 + w13
    342   w30 = ssig1 w28 + w23 + ssig0 w15 + w14
    343   w31 = ssig1 w29 + w24 + ssig0 w16 + w15
    344   w32 = ssig1 w30 + w25 + ssig0 w17 + w16
    345   w33 = ssig1 w31 + w26 + ssig0 w18 + w17
    346   w34 = ssig1 w32 + w27 + ssig0 w19 + w18
    347   w35 = ssig1 w33 + w28 + ssig0 w20 + w19
    348   w36 = ssig1 w34 + w29 + ssig0 w21 + w20
    349   w37 = ssig1 w35 + w30 + ssig0 w22 + w21
    350   w38 = ssig1 w36 + w31 + ssig0 w23 + w22
    351   w39 = ssig1 w37 + w32 + ssig0 w24 + w23
    352   w40 = ssig1 w38 + w33 + ssig0 w25 + w24
    353   w41 = ssig1 w39 + w34 + ssig0 w26 + w25
    354   w42 = ssig1 w40 + w35 + ssig0 w27 + w26
    355   w43 = ssig1 w41 + w36 + ssig0 w28 + w27
    356   w44 = ssig1 w42 + w37 + ssig0 w29 + w28
    357   w45 = ssig1 w43 + w38 + ssig0 w30 + w29
    358   w46 = ssig1 w44 + w39 + ssig0 w31 + w30
    359   w47 = ssig1 w45 + w40 + ssig0 w32 + w31
    360   w48 = ssig1 w46 + w41 + ssig0 w33 + w32
    361   w49 = ssig1 w47 + w42 + ssig0 w34 + w33
    362   w50 = ssig1 w48 + w43 + ssig0 w35 + w34
    363   w51 = ssig1 w49 + w44 + ssig0 w36 + w35
    364   w52 = ssig1 w50 + w45 + ssig0 w37 + w36
    365   w53 = ssig1 w51 + w46 + ssig0 w38 + w37
    366   w54 = ssig1 w52 + w47 + ssig0 w39 + w38
    367   w55 = ssig1 w53 + w48 + ssig0 w40 + w39
    368   w56 = ssig1 w54 + w49 + ssig0 w41 + w40
    369   w57 = ssig1 w55 + w50 + ssig0 w42 + w41
    370   w58 = ssig1 w56 + w51 + ssig0 w43 + w42
    371   w59 = ssig1 w57 + w52 + ssig0 w44 + w43
    372   w60 = ssig1 w58 + w53 + ssig0 w45 + w44
    373   w61 = ssig1 w59 + w54 + ssig0 w46 + w45
    374   w62 = ssig1 w60 + w55 + ssig0 w47 + w46
    375   w63 = ssig1 w61 + w56 + ssig0 w48 + w47
    376 
    377 -- RFC 6234 6.2 steps 2, 3, 4
    378 block_hash :: Registers -> Schedule -> Registers
    379 block_hash r00@Registers {..} Schedule {..} =
    380   -- constants are the first 32 bits of the fractional parts of the
    381   -- cube roots of the first sixty-four prime numbers
    382   let r01 = step r00 0x428a2f98 w00; r02 = step r01 0x71374491 w01
    383       r03 = step r02 0xb5c0fbcf w02; r04 = step r03 0xe9b5dba5 w03
    384       r05 = step r04 0x3956c25b w04; r06 = step r05 0x59f111f1 w05
    385       r07 = step r06 0x923f82a4 w06; r08 = step r07 0xab1c5ed5 w07
    386       r09 = step r08 0xd807aa98 w08; r10 = step r09 0x12835b01 w09
    387       r11 = step r10 0x243185be w10; r12 = step r11 0x550c7dc3 w11
    388       r13 = step r12 0x72be5d74 w12; r14 = step r13 0x80deb1fe w13
    389       r15 = step r14 0x9bdc06a7 w14; r16 = step r15 0xc19bf174 w15
    390       r17 = step r16 0xe49b69c1 w16; r18 = step r17 0xefbe4786 w17
    391       r19 = step r18 0x0fc19dc6 w18; r20 = step r19 0x240ca1cc w19
    392       r21 = step r20 0x2de92c6f w20; r22 = step r21 0x4a7484aa w21
    393       r23 = step r22 0x5cb0a9dc w22; r24 = step r23 0x76f988da w23
    394       r25 = step r24 0x983e5152 w24; r26 = step r25 0xa831c66d w25
    395       r27 = step r26 0xb00327c8 w26; r28 = step r27 0xbf597fc7 w27
    396       r29 = step r28 0xc6e00bf3 w28; r30 = step r29 0xd5a79147 w29
    397       r31 = step r30 0x06ca6351 w30; r32 = step r31 0x14292967 w31
    398       r33 = step r32 0x27b70a85 w32; r34 = step r33 0x2e1b2138 w33
    399       r35 = step r34 0x4d2c6dfc w34; r36 = step r35 0x53380d13 w35
    400       r37 = step r36 0x650a7354 w36; r38 = step r37 0x766a0abb w37
    401       r39 = step r38 0x81c2c92e w38; r40 = step r39 0x92722c85 w39
    402       r41 = step r40 0xa2bfe8a1 w40; r42 = step r41 0xa81a664b w41
    403       r43 = step r42 0xc24b8b70 w42; r44 = step r43 0xc76c51a3 w43
    404       r45 = step r44 0xd192e819 w44; r46 = step r45 0xd6990624 w45
    405       r47 = step r46 0xf40e3585 w46; r48 = step r47 0x106aa070 w47
    406       r49 = step r48 0x19a4c116 w48; r50 = step r49 0x1e376c08 w49
    407       r51 = step r50 0x2748774c w50; r52 = step r51 0x34b0bcb5 w51
    408       r53 = step r52 0x391c0cb3 w52; r54 = step r53 0x4ed8aa4a w53
    409       r55 = step r54 0x5b9cca4f w54; r56 = step r55 0x682e6ff3 w55
    410       r57 = step r56 0x748f82ee w56; r58 = step r57 0x78a5636f w57
    411       r59 = step r58 0x84c87814 w58; r60 = step r59 0x8cc70208 w59
    412       r61 = step r60 0x90befffa w60; r62 = step r61 0xa4506ceb w61
    413       r63 = step r62 0xbef9a3f7 w62; r64 = step r63 0xc67178f2 w63
    414       !(Registers a b c d e f g h) = r64
    415   in  Registers
    416         (a + h0) (b + h1) (c + h2) (d + h3)
    417         (e + h4) (f + h5) (g + h6) (h + h7)
    418 
    419 step :: Registers -> Word32 -> Word32 -> Registers
    420 step (Registers a b c d e f g h) k w =
    421   let t1 = h + bsig1 e + ch e f g + k + w
    422       t2 = bsig0 a + maj a b c
    423   in  Registers (t1 + t2) a b c (d + t1) e f g
    424 {-# INLINE step #-}
    425 
    426 -- RFC 6234 6.2 block pipeline
    427 --
    428 -- invariant:
    429 --   the input bytestring is exactly 512 bits in length
    430 unsafe_hash_alg :: Registers -> BS.ByteString -> Registers
    431 unsafe_hash_alg rs bs = block_hash rs (prepare_schedule (unsafe_parse bs))
    432 
    433 -- register concatenation
    434 cat :: Registers -> BS.ByteString
    435 cat Registers {..} = to_strict_small $
    436        BSB.word64BE w64_0 <> BSB.word64BE w64_1
    437     <> BSB.word64BE w64_2 <> BSB.word64BE w64_3
    438   where
    439     !w64_0 = fi h0 `B.unsafeShiftL` 32 .|. fi h1
    440     !w64_1 = fi h2 `B.unsafeShiftL` 32 .|. fi h3
    441     !w64_2 = fi h4 `B.unsafeShiftL` 32 .|. fi h5
    442     !w64_3 = fi h6 `B.unsafeShiftL` 32 .|. fi h7
    443 
    444 -- | Compute a condensed representation of a strict bytestring via
    445 --   SHA-256.
    446 --
    447 --   The 256-bit output digest is returned as a strict bytestring.
    448 --
    449 --   >>> hash "strict bytestring input"
    450 --   "<strict 256-bit message digest>"
    451 hash :: BS.ByteString -> BS.ByteString
    452 hash bs = cat (go iv (pad bs)) where
    453   -- proof that 'go' always terminates safely:
    454   --
    455   -- let b = pad bs
    456   -- then length(b) = n * 512 bits for some n >= 0                  (1)
    457   go :: Registers -> BS.ByteString -> Registers
    458   go !acc b
    459     -- if n == 0, then 'go' terminates safely                       (2)
    460     | BS.null b = acc
    461     -- if n > 0, then
    462     --
    463     -- let (c, r) = unsafe_splitAt 64 b
    464     -- then length(c) == 512 bits                                   by (1)
    465     --      length(r) == m * 512 bits for some m >= 0               by (1)
    466     --
    467     -- note 'unsafe_hash_alg' terminates safely for bytestring      (3)
    468     -- input of exactly 512 bits in length
    469     --
    470     -- length(c) == 512
    471     --   => 'unsafe_hash_alg' terminates safely                     by (3)
    472     --   => 'go' terminates safely                                  (4)
    473     -- length(r) == m * 512 bits for m >= 0
    474     --   => next invocation of 'go' terminates safely               by (2), (4)
    475     --
    476     -- then by induction, 'go' always terminates safely (QED)
    477     | otherwise = case unsafe_splitAt 64 b of
    478         SSPair c r -> go (unsafe_hash_alg acc c) r
    479 
    480 -- | Compute a condensed representation of a lazy bytestring via
    481 --   SHA-256.
    482 --
    483 --   The 256-bit output digest is returned as a strict bytestring.
    484 --
    485 --   >>> hash_lazy "lazy bytestring input"
    486 --   "<strict 256-bit message digest>"
    487 hash_lazy :: BL.ByteString -> BS.ByteString
    488 hash_lazy bl = cat (go iv (pad_lazy bl)) where
    489   -- proof of safety proceeds analogously
    490   go :: Registers -> BL.ByteString -> Registers
    491   go !acc bs
    492     | BL.null bs = acc
    493     | otherwise = case splitAt64 bs of
    494         SLPair c r -> go (unsafe_hash_alg acc c) r
    495 
    496 -- HMAC -----------------------------------------------------------------------
    497 -- https://datatracker.ietf.org/doc/html/rfc2104#section-2
    498 
    499 data KeyAndLen = KeyAndLen
    500   {-# UNPACK #-} !BS.ByteString
    501   {-# UNPACK #-} !Int
    502 
    503 -- | Produce a message authentication code for a strict bytestring,
    504 --   based on the provided (strict, bytestring) key, via SHA-256.
    505 --
    506 --   The 256-bit MAC is returned as a strict bytestring.
    507 --
    508 --   Per RFC 2104, the key /should/ be a minimum of 32 bytes long. Keys
    509 --   exceeding 64 bytes in length will first be hashed (via SHA-256).
    510 --
    511 --   >>> hmac "strict bytestring key" "strict bytestring input"
    512 --   "<strict 256-bit MAC>"
    513 hmac
    514   :: BS.ByteString -- ^ key
    515   -> BS.ByteString -- ^ text
    516   -> BS.ByteString
    517 hmac mk@(BI.PS _ _ l) text =
    518     let step1 = k <> BS.replicate (64 - lk) 0x00
    519         step2 = BS.map (B.xor 0x36) step1
    520         step3 = step2 <> text
    521         step4 = hash step3
    522         step5 = BS.map (B.xor 0x5C) step1
    523         step6 = step5 <> step4
    524     in  hash step6
    525   where
    526     !(KeyAndLen k lk)
    527       | l > 64    = KeyAndLen (hash mk) 32
    528       | otherwise = KeyAndLen mk l
    529 
    530 -- | Produce a message authentication code for a lazy bytestring, based
    531 --   on the provided (strict, bytestring) key, via SHA-256.
    532 --
    533 --   The 256-bit MAC is returned as a strict bytestring.
    534 --
    535 --   Per RFC 2104, the key /should/ be a minimum of 32 bytes long. Keys
    536 --   exceeding 64 bytes in length will first be hashed (via SHA-256).
    537 --
    538 --   >>> hmac_lazy "strict bytestring key" "lazy bytestring input"
    539 --   "<strict 256-bit MAC>"
    540 hmac_lazy
    541   :: BS.ByteString -- ^ key
    542   -> BL.ByteString -- ^ text
    543   -> BS.ByteString
    544 hmac_lazy mk@(BI.PS _ _ l) text =
    545     let step1 = k <> BS.replicate (64 - lk) 0x00
    546         step2 = BS.map (B.xor 0x36) step1
    547         step3 = BL.fromStrict step2 <> text
    548         step4 = hash_lazy step3
    549         step5 = BS.map (B.xor 0x5C) step1
    550         step6 = step5 <> step4
    551     in  hash step6
    552   where
    553     !(KeyAndLen k lk)
    554       | l > 64    = KeyAndLen (hash mk) 32
    555       | otherwise = KeyAndLen mk l
    556