    -----------------------------------------------------------------------------
    -- |
    -- Module    : Documentation.SBV.Examples.Crypto.SHA
    -- Copyright : (c) Levent Erkok
    -- License   : BSD3
    -- Maintainer: erkokl@gmail.com
    -- Stability : experimental
    --
    -- Implementation of SHA2 class of algorithms, closely following the spec
    -- <http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf>.
    --
    -- We support all variants of SHA in the spec, except for SHA1. Note that
    -- this implementation is really useful for code-generation purposes from
    -- SBV, as it is hard to state (or prove!) any particular properties of
    -- these algorithms that is suitable for SMT solving.
    -----------------------------------------------------------------------------

    {-# LANGUAGE DataKinds           #-}
    {-# LANGUAGE NamedFieldPuns      #-}
    {-# LANGUAGE Rank2Types          #-}
    {-# LANGUAGE ScopedTypeVariables #-}
    {-# LANGUAGE TypeApplications    #-}

    {-# OPTIONS_GHC -Wall -Werror -Wno-incomplete-uni-patterns #-}

    module Documentation.SBV.Examples.Crypto.SHA where

    import Data.SBV
    import Data.SBV.Tools.CodeGen

    import Prelude hiding (Foldable(..))
    import Data.Char (ord, toLower)
    import Data.List (genericLength, length, foldl')
    import Numeric   (showHex)

    import Data.Proxy (Proxy(..))

    -----------------------------------------------------------------------------
    -- * Parameterizing SHA
    -----------------------------------------------------------------------------

    -- | Parameterized SHA representation, that captures all the differences
    -- between variants of the algorithm. @w@ is the word-size type.
    data SHA w = SHA { forall w. SHA w -> Int
    wordSize           :: Int              -- ^ Section 1           : Word size we operate with
                     , forall w. SHA w -> Int
    blockSize          :: Int              -- ^ Section 1           : Block size for messages
                     , forall w. SHA w -> (Int, Int, Int)
    sum0Coefficients   :: (Int, Int, Int)  -- ^ Section 4.1.2-3     : Coefficients of the Sum0 function
                     , forall w. SHA w -> (Int, Int, Int)
    sum1Coefficients   :: (Int, Int, Int)  -- ^ Section 4.1.2-3     : Coefficients of the Sum1 function
                     , forall w. SHA w -> (Int, Int, Int)
    sigma0Coefficients :: (Int, Int, Int)  -- ^ Section 4.1.2-3     : Coefficients of the sigma0 function
                     , forall w. SHA w -> (Int, Int, Int)
    sigma1Coefficients :: (Int, Int, Int)  -- ^ Section 4.1.2-3     : Coefficients of the sigma1 function
                     , forall w. SHA w -> [w]
    shaConstants       :: [w]              -- ^ Section 4.2.2-3     : Magic SHA constants
                     , forall w. SHA w -> [w]
    h0                 :: [w]              -- ^ Section 5.3.2-6     : Initial hash value
                     , forall w. SHA w -> Int
    shaLoopCount       :: Int              -- ^ Section 6.2.2, 6.4.2: How many iterations are there in the inner loop
                     }

    -----------------------------------------------------------------------------
    -- * Section 4.1.2, SHA functions
    -----------------------------------------------------------------------------

    -- | The choose function.
    ch :: Bits a => a -> a -> a -> a
    ch :: forall a. Bits a => a -> a -> a -> a
    ch a
    x a
    y a
    z = (a
    x a -> a -> a
    forall a. Bits a => a -> a -> a
    .&. a
    y) a -> a -> a
    forall a. Bits a => a -> a -> a
    `xor` (a -> a
    forall a. Bits a => a -> a
    complement a
    x a -> a -> a
    forall a. Bits a => a -> a -> a
    .&. a
    z)

    -- | The majority function.
    maj :: Bits a => a -> a -> a -> a
    maj :: forall a. Bits a => a -> a -> a -> a
    maj a
    x a
    y a
    z = (a
    x a -> a -> a
    forall a. Bits a => a -> a -> a
    .&. a
    y) a -> a -> a
    forall a. Bits a => a -> a -> a
    `xor` (a
    x a -> a -> a
    forall a. Bits a => a -> a -> a
    .&. a
    z) a -> a -> a
    forall a. Bits a => a -> a -> a
    `xor` (a
    y a -> a -> a
    forall a. Bits a => a -> a -> a
    .&. a
    z)

    -- | The sum-0 function. We parameterize over the rotation amounts as different
    -- variants of SHA use different rotation amounts.
    sum0 :: Bits a => SHA w -> a -> a
    sum0 :: forall a w. Bits a => SHA w -> a -> a
    sum0 SHA{sum0Coefficients :: forall w. SHA w -> (Int, Int, Int)
    sum0Coefficients = (Int
    a, Int
    b, Int
    c)} a
    x = (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `rotateR` Int
    a) a -> a -> a
    forall a. Bits a => a -> a -> a
    `xor` (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `rotateR` Int
    b) a -> a -> a
    forall a. Bits a => a -> a -> a
    `xor` (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `rotateR` Int
    c)

    -- | The sum-1 function. Again, parameterized.
    sum1 :: Bits a => SHA w -> a -> a
    sum1 :: forall a w. Bits a => SHA w -> a -> a
    sum1 SHA{sum1Coefficients :: forall w. SHA w -> (Int, Int, Int)
    sum1Coefficients = (Int
    a, Int
    b, Int
    c)} a
    x = (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `rotateR` Int
    a) a -> a -> a
    forall a. Bits a => a -> a -> a
    `xor` (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `rotateR` Int
    b) a -> a -> a
    forall a. Bits a => a -> a -> a
    `xor` (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `rotateR` Int
    c)

    -- | The sigma0 function. Parameterized.
    sigma0 :: Bits a => SHA w -> a -> a
    sigma0 :: forall a w. Bits a => SHA w -> a -> a
    sigma0 SHA{sigma0Coefficients :: forall w. SHA w -> (Int, Int, Int)
    sigma0Coefficients = (Int
    a, Int
    b, Int
    c)} a
    x = (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `rotateR` Int
    a) a -> a -> a
    forall a. Bits a => a -> a -> a
    `xor` (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `rotateR` Int
    b) a -> a -> a
    forall a. Bits a => a -> a -> a
    `xor` (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `shiftR` Int
    c)

    -- | The sigma1 function. Parameterized.
    sigma1 :: Bits a => SHA w -> a -> a
    sigma1 :: forall a w. Bits a => SHA w -> a -> a
    sigma1 SHA{sigma1Coefficients :: forall w. SHA w -> (Int, Int, Int)
    sigma1Coefficients = (Int
    a, Int
    b, Int
    c)} a
    x = (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `rotateR` Int
    a) a -> a -> a
    forall a. Bits a => a -> a -> a
    `xor` (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `rotateR` Int
    b) a -> a -> a
    forall a. Bits a => a -> a -> a
    `xor` (a
    x a -> Int -> a
    forall a. Bits a => a -> Int -> a
    `shiftR` Int
    c)

    -----------------------------------------------------------------------------
    -- * SHA variants
    -----------------------------------------------------------------------------

    -- | Parameterization for SHA224.
    sha224P :: SHA (SWord 32)
    sha224P :: SHA (SWord 32)
    sha224P = SHA { wordSize :: Int
    wordSize           = Int
    32
                  , blockSize :: Int
    blockSize          = Int
    512
                  , sum0Coefficients :: (Int, Int, Int)
    sum0Coefficients   = ( Int
    2, Int
    13, Int
    22)
                  , sum1Coefficients :: (Int, Int, Int)
    sum1Coefficients   = ( Int
    6, Int
    11, Int
    25)
                  , sigma0Coefficients :: (Int, Int, Int)
    sigma0Coefficients = ( Int
    7, Int
    18,  Int
    3)
                  , sigma1Coefficients :: (Int, Int, Int)
    sigma1Coefficients = (Int
    17, Int
    19, Int
    10)
                  , shaConstants :: [SWord 32]
    shaConstants       = [ SWord 32
    0x428a2f98, SWord 32
    0x71374491, SWord 32
    0xb5c0fbcf, SWord 32
    0xe9b5dba5, SWord 32
    0x3956c25b, SWord 32
    0x59f111f1, SWord 32
    0x923f82a4, SWord 32
    0xab1c5ed5
                                         , SWord 32
    0xd807aa98, SWord 32
    0x12835b01, SWord 32
    0x243185be, SWord 32
    0x550c7dc3, SWord 32
    0x72be5d74, SWord 32
    0x80deb1fe, SWord 32
    0x9bdc06a7, SWord 32
    0xc19bf174
                                         , SWord 32
    0xe49b69c1, SWord 32
    0xefbe4786, SWord 32
    0x0fc19dc6, SWord 32
    0x240ca1cc, SWord 32
    0x2de92c6f, SWord 32
    0x4a7484aa, SWord 32
    0x5cb0a9dc, SWord 32
    0x76f988da
                                         , SWord 32
    0x983e5152, SWord 32
    0xa831c66d, SWord 32
    0xb00327c8, SWord 32
    0xbf597fc7, SWord 32
    0xc6e00bf3, SWord 32
    0xd5a79147, SWord 32
    0x06ca6351, SWord 32
    0x14292967
                                         , SWord 32
    0x27b70a85, SWord 32
    0x2e1b2138, SWord 32
    0x4d2c6dfc, SWord 32
    0x53380d13, SWord 32
    0x650a7354, SWord 32
    0x766a0abb, SWord 32
    0x81c2c92e, SWord 32
    0x92722c85
                                         , SWord 32
    0xa2bfe8a1, SWord 32
    0xa81a664b, SWord 32
    0xc24b8b70, SWord 32
    0xc76c51a3, SWord 32
    0xd192e819, SWord 32
    0xd6990624, SWord 32
    0xf40e3585, SWord 32
    0x106aa070
                                         , SWord 32
    0x19a4c116, SWord 32
    0x1e376c08, SWord 32
    0x2748774c, SWord 32
    0x34b0bcb5, SWord 32
    0x391c0cb3, SWord 32
    0x4ed8aa4a, SWord 32
    0x5b9cca4f, SWord 32
    0x682e6ff3
                                         , SWord 32
    0x748f82ee, SWord 32
    0x78a5636f, SWord 32
    0x84c87814, SWord 32
    0x8cc70208, SWord 32
    0x90befffa, SWord 32
    0xa4506ceb, SWord 32
    0xbef9a3f7, SWord 32
    0xc67178f2
                                         ]
                  , h0 :: [SWord 32]
    h0                 = [ SWord 32
    0xc1059ed8, SWord 32
    0x367cd507, SWord 32
    0x3070dd17, SWord 32
    0xf70e5939
                                         , SWord 32
    0xffc00b31, SWord 32
    0x68581511, SWord 32
    0x64f98fa7, SWord 32
    0xbefa4fa4
                                         ]
                  , shaLoopCount :: Int
    shaLoopCount       = Int
    64
                  }

    -- | Parameterization for SHA256. Inherits mostly from SHA224.
    sha256P :: SHA (SWord 32)
    sha256P :: SHA (SWord 32)
    sha256P = SHA (SWord 32)
    sha224P { h0 :: [SWord 32]
    h0 = [ SWord 32
    0x6a09e667, SWord 32
    0xbb67ae85, SWord 32
    0x3c6ef372, SWord 32
    0xa54ff53a
                             , SWord 32
    0x510e527f, SWord 32
    0x9b05688c, SWord 32
    0x1f83d9ab, SWord 32
    0x5be0cd19
                             ]
                      }

    -- | Parameterization for SHA384.
    sha384P :: SHA (SWord 64)
    sha384P :: SHA (SWord 64)
    sha384P = SHA { wordSize :: Int
    wordSize           = Int
    64
                  , blockSize :: Int
    blockSize          = Int
    1024
                  , sum0Coefficients :: (Int, Int, Int)
    sum0Coefficients   = (Int
    28, Int
    34, Int
    39)
                  , sum1Coefficients :: (Int, Int, Int)
    sum1Coefficients   = (Int
    14, Int
    18, Int
    41)
                  , sigma0Coefficients :: (Int, Int, Int)
    sigma0Coefficients = ( Int
    1,  Int
    8,  Int
    7)
                  , sigma1Coefficients :: (Int, Int, Int)
    sigma1Coefficients = (Int
    19, Int
    61,  Int
    6)
                  , shaConstants :: [SWord 64]
    shaConstants       = [ SWord 64
    0x428a2f98d728ae22, SWord 64
    0x7137449123ef65cd, SWord 64
    0xb5c0fbcfec4d3b2f, SWord 64
    0xe9b5dba58189dbbc
                                         , SWord 64
    0x3956c25bf348b538, SWord 64
    0x59f111f1b605d019, SWord 64
    0x923f82a4af194f9b, SWord 64
    0xab1c5ed5da6d8118
                                         , SWord 64
    0xd807aa98a3030242, SWord 64
    0x12835b0145706fbe, SWord 64
    0x243185be4ee4b28c, SWord 64
    0x550c7dc3d5ffb4e2
                                         , SWord 64
    0x72be5d74f27b896f, SWord 64
    0x80deb1fe3b1696b1, SWord 64
    0x9bdc06a725c71235, SWord 64
    0xc19bf174cf692694
                                         , SWord 64
    0xe49b69c19ef14ad2, SWord 64
    0xefbe4786384f25e3, SWord 64
    0x0fc19dc68b8cd5b5, SWord 64
    0x240ca1cc77ac9c65
                                         , SWord 64
    0x2de92c6f592b0275, SWord 64
    0x4a7484aa6ea6e483, SWord 64
    0x5cb0a9dcbd41fbd4, SWord 64
    0x76f988da831153b5
                                         , SWord 64
    0x983e5152ee66dfab, SWord 64
    0xa831c66d2db43210, SWord 64
    0xb00327c898fb213f, SWord 64
    0xbf597fc7beef0ee4
                                         , SWord 64
    0xc6e00bf33da88fc2, SWord 64
    0xd5a79147930aa725, SWord 64
    0x06ca6351e003826f, SWord 64
    0x142929670a0e6e70
                                         , SWord 64
    0x27b70a8546d22ffc, SWord 64
    0x2e1b21385c26c926, SWord 64
    0x4d2c6dfc5ac42aed, SWord 64
    0x53380d139d95b3df
                                         , SWord 64
    0x650a73548baf63de, SWord 64
    0x766a0abb3c77b2a8, SWord 64
    0x81c2c92e47edaee6, SWord 64
    0x92722c851482353b
                                         , SWord 64
    0xa2bfe8a14cf10364, SWord 64
    0xa81a664bbc423001, SWord 64
    0xc24b8b70d0f89791, SWord 64
    0xc76c51a30654be30
                                         , SWord 64
    0xd192e819d6ef5218, SWord 64
    0xd69906245565a910, SWord 64
    0xf40e35855771202a, SWord 64
    0x106aa07032bbd1b8
                                         , SWord 64
    0x19a4c116b8d2d0c8, SWord 64
    0x1e376c085141ab53, SWord 64
    0x2748774cdf8eeb99, SWord 64
    0x34b0bcb5e19b48a8
                                         , SWord 64
    0x391c0cb3c5c95a63, SWord 64
    0x4ed8aa4ae3418acb, SWord 64
    0x5b9cca4f7763e373, SWord 64
    0x682e6ff3d6b2b8a3
                                         , SWord 64
    0x748f82ee5defb2fc, SWord 64
    0x78a5636f43172f60, SWord 64
    0x84c87814a1f0ab72, SWord 64
    0x8cc702081a6439ec
                                         , SWord 64
    0x90befffa23631e28, SWord 64
    0xa4506cebde82bde9, SWord 64
    0xbef9a3f7b2c67915, SWord 64
    0xc67178f2e372532b
                                         , SWord 64
    0xca273eceea26619c, SWord 64
    0xd186b8c721c0c207, SWord 64
    0xeada7dd6cde0eb1e, SWord 64
    0xf57d4f7fee6ed178
                                         , SWord 64
    0x06f067aa72176fba, SWord 64
    0x0a637dc5a2c898a6, SWord 64
    0x113f9804bef90dae, SWord 64
    0x1b710b35131c471b
                                         , SWord 64
    0x28db77f523047d84, SWord 64
    0x32caab7b40c72493, SWord 64
    0x3c9ebe0a15c9bebc, SWord 64
    0x431d67c49c100d4c
                                         , SWord 64
    0x4cc5d4becb3e42b6, SWord 64
    0x597f299cfc657e2a, SWord 64
    0x5fcb6fab3ad6faec, SWord 64
    0x6c44198c4a475817
                                         ]
                  , h0 :: [SWord 64]
    h0                 = [ SWord 64
    0xcbbb9d5dc1059ed8, SWord 64
    0x629a292a367cd507, SWord 64
    0x9159015a3070dd17, SWord 64
    0x152fecd8f70e5939
                                         , SWord 64
    0x67332667ffc00b31, SWord 64
    0x8eb44a8768581511, SWord 64
    0xdb0c2e0d64f98fa7, SWord 64
    0x47b5481dbefa4fa4
                                         ]
                  , shaLoopCount :: Int
    shaLoopCount       = Int
    80
                  }

    -- | Parameterization for SHA512. Inherits mostly from SHA384.
    sha512P :: SHA (SWord 64)
    sha512P :: SHA (SWord 64)
    sha512P = SHA (SWord 64)
    sha384P { h0 :: [SWord 64]
    h0 = [ SWord 64
    0x6a09e667f3bcc908, SWord 64
    0xbb67ae8584caa73b, SWord 64
    0x3c6ef372fe94f82b, SWord 64
    0xa54ff53a5f1d36f1
                             , SWord 64
    0x510e527fade682d1, SWord 64
    0x9b05688c2b3e6c1f, SWord 64
    0x1f83d9abfb41bd6b, SWord 64
    0x5be0cd19137e2179
                             ]
                      }

    -- | Parameterization for SHA512_224. Inherits mostly from SHA512
    sha512_224P :: SHA (SWord 64)
    sha512_224P :: SHA (SWord 64)
    sha512_224P = SHA (SWord 64)
    sha512P { h0 :: [SWord 64]
    h0 = [ SWord 64
    0x8C3D37C819544DA2, SWord 64
    0x73E1996689DCD4D6, SWord 64
    0x1DFAB7AE32FF9C82, SWord 64
    0x679DD514582F9FCF
                                 , SWord 64
    0x0F6D2B697BD44DA8, SWord 64
    0x77E36F7304C48942, SWord 64
    0x3F9D85A86A1D36C8, SWord 64
    0x1112E6AD91D692A1
                                 ]
                          }

    -- | Parameterization for SHA512_256. Inherits mostly from SHA512
    sha512_256P :: SHA (SWord 64)
    sha512_256P :: SHA (SWord 64)
    sha512_256P = SHA (SWord 64)
    sha512P { h0 :: [SWord 64]
    h0 = [ SWord 64
    0x22312194FC2BF72C, SWord 64
    0x9F555FA3C84C64C2, SWord 64
    0x2393B86B6F53B151, SWord 64
    0x963877195940EABD
                                 , SWord 64
    0x96283EE2A88EFFE3, SWord 64
    0xBE5E1E2553863992, SWord 64
    0x2B0199FC2C85B8AA, SWord 64
    0x0EB72DDC81C52CA2
                                 ]
                          }

    -----------------------------------------------------------------------------
    -- * Section 5, Preprocessing
    -----------------------------------------------------------------------------

    -- | 'Block' is a  synonym for lists, but makes the intent clear.
    newtype Block a = Block [a]

    -- | Prepare the message by turning it into blocks. We also check for the message
    -- size requirement here. Note that this won't actually happen in practice as the input
    -- length would be > 2^64 (or 2^128), and you'd run out of memory first!
    prepareMessage :: forall w. (Num w, ByteConverter w) => SHA w -> String -> [Block w]
    prepareMessage :: forall w. (Num w, ByteConverter w) => SHA w -> String -> [Block w]
    prepareMessage SHA{Int
    wordSize :: forall w. SHA w -> Int
    wordSize :: Int
    wordSize, Int
    blockSize :: forall w. SHA w -> Int
    blockSize :: Int
    blockSize} String
    s
      | Integer
    msgLen Integer -> Integer -> Bool
    forall a. Ord a => a -> a -> Bool
    >= Integer
    maxLen
      = String -> [Block w]
    forall a. HasCallStack => String -> a
    error (String -> [Block w]) -> String -> [Block w]
    forall a b. (a -> b) -> a -> b
    $ String
    "Message is too big! Size: " String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ Integer -> String
    forall a. Show a => a -> String
    show Integer
    msgLen String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ String
    " Max: " String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ Integer -> String
    forall a. Show a => a -> String
    show Integer
    maxLen
      | Bool
    True
      = [w] -> [Block w]
    forall {a}. [a] -> [Block a]
    parse ([w] -> [Block w]) -> [w] -> [Block w]
    forall a b. (a -> b) -> a -> b
    $ Int -> ([SWord 8] -> w) -> [SWord 8] -> [w]
    forall a b. Int -> ([a] -> b) -> [a] -> [b]
    chunkBy (Int
    wordSize Int -> Int -> Int
    forall a. Integral a => a -> a -> a
    `div` Int
    8) [SWord 8] -> w
    forall a. ByteConverter a => [SWord 8] -> a
    fromBytes [SWord 8]
    padded
      where -- Maximum message size supported by the algorithm
            maxLen :: Integer
            maxLen :: Integer
    maxLen = Integer
    2Integer -> Integer -> Integer
    forall a b. (Num a, Integral b) => a -> b -> a
    ^(Integer
    2 Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    * Int -> Integer
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral Int
    wordSize :: Integer)

            -- Size of the input in bits
            msgLen :: Integer
            msgLen :: Integer
    msgLen = Integer
    8 Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    * String -> Integer
    forall i a. Num i => [a] -> i
    genericLength String
    s

            -- In all variants, we have 16-element blocks:
            --    SHA 224, 256                  :  512-bit block size with 32-bit word size: Total 16 words to a block
            --    SHA 384, 512, 512_224, 512_256: 1024-bit block size with 64-bit word size: Total 16 words to a block
            parse :: [a] -> [Block a]
    parse = Int -> ([a] -> Block a) -> [a] -> [Block a]
    forall a b. Int -> ([a] -> b) -> [a] -> [b]
    chunkBy Int
    16 [a] -> Block a
    forall a. [a] -> Block a
    Block

            msgSizeAsBytes :: [SWord 8]
            msgSizeAsBytes :: [SWord 8]
    msgSizeAsBytes
              | Int
    wordSize Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    32 = SWord 64 -> [SWord 8]
    forall a. ByteConverter a => a -> [SWord 8]
    toBytes (Integer -> SWord 64
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral Integer
    msgLen :: SWord  64)
              | Int
    wordSize Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    64 = SWord 128 -> [SWord 8]
    forall a. ByteConverter a => a -> [SWord 8]
    toBytes (Integer -> SWord 128
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral Integer
    msgLen :: SWord 128)
              | Bool
    True           = String -> [SWord 8]
    forall a. HasCallStack => String -> a
    error (String -> [SWord 8]) -> String -> [SWord 8]
    forall a b. (a -> b) -> a -> b
    $ String
    "prepareMessage: Unexpected word size: " String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ Int -> String
    forall a. Show a => a -> String
    show Int
    wordSize

            -- kLen is how many bits extra we need in the padding
            kLen :: Int
            kLen :: Int
    kLen = Int
    blockSize Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Integer -> Int
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral ((Integer
    msgLen Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    + Int -> Integer
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral (Int
    2 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    * Int
    wordSize)) Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    `mod` Int -> Integer
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral Int
    blockSize)

            -- Since message is always a multiple of 8, we need to pad it with the byte 0x80 for the first byte
            -- after it (1000 0000), and then enough bytes to fill to make it a multiple of the block size.
            padded :: [SWord 8]
            padded :: [SWord 8]
    padded = (Char -> SWord 8) -> String -> [SWord 8]
    forall a b. (a -> b) -> [a] -> [b]
    map (Int -> SWord 8
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral (Int -> SWord 8) -> (Char -> Int) -> Char -> SWord 8
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Char -> Int
    ord) String
    s [SWord 8] -> [SWord 8] -> [SWord 8]
    forall a. [a] -> [a] -> [a]
    ++ [SWord 8
    0x80] [SWord 8] -> [SWord 8] -> [SWord 8]
    forall a. [a] -> [a] -> [a]
    ++ Int -> SWord 8 -> [SWord 8]
    forall a. Int -> a -> [a]
    replicate ((Int
    kLen Int -> Int -> Int
    forall a. Integral a => a -> a -> a
    `div` Int
    8) Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    1) SWord 8
    0 [SWord 8] -> [SWord 8] -> [SWord 8]
    forall a. [a] -> [a] -> [a]
    ++ [SWord 8]
    msgSizeAsBytes

    -----------------------------------------------------------------------------
    -- * Section 6.2.2 and 6.4.2, Hash computation
    -----------------------------------------------------------------------------

    -- | Hash one block of message, starting from a previous hash. This function
    -- corresponds to body of the for-loop in the spec. This function always
    -- produces a list of length 8, corresponding to the final 8 values of the @H@.
    hashBlock :: (Num w, Bits w) => SHA w -> [w] -> Block w -> [w]
    hashBlock :: forall w. (Num w, Bits w) => SHA w -> [w] -> Block w -> [w]
    hashBlock p :: SHA w
    p@SHA{Int
    shaLoopCount :: forall w. SHA w -> Int
    shaLoopCount :: Int
    shaLoopCount, [w]
    shaConstants :: forall w. SHA w -> [w]
    shaConstants :: [w]
    shaConstants} [w]
    hPrev (Block [w]
    m) = [w]
    step4
       where lim :: Int
    lim = Int
    shaLoopCount Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    1

             -- Step 1: Prepare the message schedule:
             w :: Int -> w
    w Int
    t
              | Int
    0  Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    <= Int
    t Bool -> Bool -> Bool
    && Int
    t Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    <= Int
    15  = [w]
    m [w] -> Int -> w
    forall a. HasCallStack => [a] -> Int -> a
    !! Int
    t
              | Int
    16 Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    <= Int
    t Bool -> Bool -> Bool
    && Int
    t Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    <= Int
    lim = SHA w -> w -> w
    forall a w. Bits a => SHA w -> a -> a
    sigma1 SHA w
    p (Int -> w
    w (Int
    tInt -> Int -> Int
    forall a. Num a => a -> a -> a
    -Int
    2)) w -> w -> w
    forall a. Num a => a -> a -> a
    + Int -> w
    w (Int
    tInt -> Int -> Int
    forall a. Num a => a -> a -> a
    -Int
    7) w -> w -> w
    forall a. Num a => a -> a -> a
    + SHA w -> w -> w
    forall a w. Bits a => SHA w -> a -> a
    sigma0 SHA w
    p (Int -> w
    w (Int
    tInt -> Int -> Int
    forall a. Num a => a -> a -> a
    -Int
    15)) w -> w -> w
    forall a. Num a => a -> a -> a
    + Int -> w
    w (Int
    tInt -> Int -> Int
    forall a. Num a => a -> a -> a
    -Int
    16)
              | Bool
    True                = String -> w
    forall a. HasCallStack => String -> a
    error (String -> w) -> String -> w
    forall a b. (a -> b) -> a -> b
    $ String
    "hashBlock, unexpected t: " String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ Int -> String
    forall a. Show a => a -> String
    show Int
    t

             -- Step 2: Initialize working variables
             -- No code needed!

             -- Step 3 Body:
             step3Body :: [w] -> Int -> [w]
    step3Body [w
    a, w
    b, w
    c, w
    d, w
    e, w
    f, w
    g, w
    h] Int
    t = [w
    t1 w -> w -> w
    forall a. Num a => a -> a -> a
    + w
    t2, w
    a, w
    b, w
    c, w
    d w -> w -> w
    forall a. Num a => a -> a -> a
    + w
    t1, w
    e, w
    f, w
    g]
               where t1 :: w
    t1   = w
    h w -> w -> w
    forall a. Num a => a -> a -> a
    + SHA w -> w -> w
    forall a w. Bits a => SHA w -> a -> a
    sum1 SHA w
    p w
    e w -> w -> w
    forall a. Num a => a -> a -> a
    + w -> w -> w -> w
    forall a. Bits a => a -> a -> a -> a
    ch w
    e w
    f w
    g w -> w -> w
    forall a. Num a => a -> a -> a
    + [w]
    shaConstants [w] -> Int -> w
    forall a. HasCallStack => [a] -> Int -> a
    !! Int
    t w -> w -> w
    forall a. Num a => a -> a -> a
    + Int -> w
    w Int
    t
                     t2 :: w
    t2   = SHA w -> w -> w
    forall a w. Bits a => SHA w -> a -> a
    sum0 SHA w
    p w
    a w -> w -> w
    forall a. Num a => a -> a -> a
    + w -> w -> w -> w
    forall a. Bits a => a -> a -> a -> a
    maj w
    a w
    b w
    c
             step3Body [w]
    xs Int
    t = String -> [w]
    forall a. HasCallStack => String -> a
    error (String -> [w]) -> String -> [w]
    forall a b. (a -> b) -> a -> b
    $ String
    "Impossible! step3Body received a list of length " String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ Int -> String
    forall a. Show a => a -> String
    show ([w] -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [w]
    xs) String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ String
    ", iteration: " String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ Int -> String
    forall a. Show a => a -> String
    show Int
    t

             -- Step 3 simply folds the body for the required loop-count
             step3 :: [w]
    step3 = ([w] -> Int -> [w]) -> [w] -> [Int] -> [w]
    forall b a. (b -> a -> b) -> b -> [a] -> b
    forall (t :: * -> *) b a.
    Foldable t =>
    (b -> a -> b) -> b -> t a -> b
    foldl' [w] -> Int -> [w]
    step3Body [w]
    hPrev [Int
    0 .. Int
    lim]

             -- Step 4
             step4 :: [w]
    step4 = (w -> w -> w) -> [w] -> [w] -> [w]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    zipWith w -> w -> w
    forall a. Num a => a -> a -> a
    (+) [w]
    step3 [w]
    hPrev

    -- | Compute the hash of a given string using the specified parameterized hash algorithm.
    shaP :: (Num w, Bits w, ByteConverter w) => SHA w -> String -> [w]
    shaP :: forall w.
    (Num w, Bits w, ByteConverter w) =>
    SHA w -> String -> [w]
    shaP p :: SHA w
    p@SHA{[w]
    h0 :: forall w. SHA w -> [w]
    h0 :: [w]
    h0} = ([w] -> Block w -> [w]) -> [w] -> [Block w] -> [w]
    forall b a. (b -> a -> b) -> b -> [a] -> b
    forall (t :: * -> *) b a.
    Foldable t =>
    (b -> a -> b) -> b -> t a -> b
    foldl' (SHA w -> [w] -> Block w -> [w]
    forall w. (Num w, Bits w) => SHA w -> [w] -> Block w -> [w]
    hashBlock SHA w
    p) [w]
    h0 ([Block w] -> [w]) -> (String -> [Block w]) -> String -> [w]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . SHA w -> String -> [Block w]
    forall w. (Num w, ByteConverter w) => SHA w -> String -> [Block w]
    prepareMessage SHA w
    p

    -----------------------------------------------------------------------------
    -- * Computing the digest
    -----------------------------------------------------------------------------

    -- | SHA224 digest.
    sha224 :: String -> SWord 224
    sha224 :: String -> SWord 224
    sha224 String
    s = SWord 32
    h0 SWord 32 -> SBV (WordN 192) -> SBV (WordN (32 + 192))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h1 SWord 32 -> SBV (WordN 160) -> SBV (WordN (32 + 160))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h2 SWord 32 -> SWord 128 -> SBV (WordN (32 + 128))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h3 SWord 32 -> SBV (WordN 96) -> SBV (WordN (32 + 96))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h4 SWord 32 -> SWord 64 -> SBV (WordN (32 + 64))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h5 SWord 32 -> SWord 32 -> SBV (WordN (32 + 32))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h6
      where [SWord 32
    h0, SWord 32
    h1, SWord 32
    h2, SWord 32
    h3, SWord 32
    h4, SWord 32
    h5, SWord 32
    h6, SWord 32
    _] = SHA (SWord 32) -> String -> [SWord 32]
    forall w.
    (Num w, Bits w, ByteConverter w) =>
    SHA w -> String -> [w]
    shaP SHA (SWord 32)
    sha224P String
    s

    -- | SHA256 digest.
    sha256 :: String -> SWord 256
    sha256 :: String -> SWord 256
    sha256 String
    s = SWord 32
    h0 SWord 32 -> SWord 224 -> SBV (WordN (32 + 224))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h1 SWord 32 -> SBV (WordN 192) -> SBV (WordN (32 + 192))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h2 SWord 32 -> SBV (WordN 160) -> SBV (WordN (32 + 160))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h3 SWord 32 -> SWord 128 -> SBV (WordN (32 + 128))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h4 SWord 32 -> SBV (WordN 96) -> SBV (WordN (32 + 96))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h5 SWord 32 -> SWord 64 -> SBV (WordN (32 + 64))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h6 SWord 32 -> SWord 32 -> SBV (WordN (32 + 32))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h7
      where [SWord 32
    h0, SWord 32
    h1, SWord 32
    h2, SWord 32
    h3, SWord 32
    h4, SWord 32
    h5, SWord 32
    h6, SWord 32
    h7] = SHA (SWord 32) -> String -> [SWord 32]
    forall w.
    (Num w, Bits w, ByteConverter w) =>
    SHA w -> String -> [w]
    shaP SHA (SWord 32)
    sha256P String
    s

    -- | SHA384 digest.
    sha384 :: String -> SWord 384
    sha384 :: String -> SWord 384
    sha384 String
    s = SWord 64
    h0 SWord 64 -> SBV (WordN 320) -> SBV (WordN (64 + 320))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h1 SWord 64 -> SWord 256 -> SBV (WordN (64 + 256))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h2 SWord 64 -> SBV (WordN 192) -> SBV (WordN (64 + 192))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h3 SWord 64 -> SWord 128 -> SBV (WordN (64 + 128))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h4 SWord 64 -> SWord 64 -> SBV (WordN (64 + 64))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h5
      where [SWord 64
    h0, SWord 64
    h1, SWord 64
    h2, SWord 64
    h3, SWord 64
    h4, SWord 64
    h5, SWord 64
    _, SWord 64
    _] = SHA (SWord 64) -> String -> [SWord 64]
    forall w.
    (Num w, Bits w, ByteConverter w) =>
    SHA w -> String -> [w]
    shaP SHA (SWord 64)
    sha384P String
    s

    -- | SHA512 digest.
    sha512 :: String -> SWord 512
    sha512 :: String -> SWord 512
    sha512 String
    s = SWord 64
    h0 SWord 64 -> SBV (WordN 448) -> SBV (WordN (64 + 448))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h1 SWord 64 -> SWord 384 -> SBV (WordN (64 + 384))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h2 SWord 64 -> SBV (WordN 320) -> SBV (WordN (64 + 320))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h3 SWord 64 -> SWord 256 -> SBV (WordN (64 + 256))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h4 SWord 64 -> SBV (WordN 192) -> SBV (WordN (64 + 192))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h5 SWord 64 -> SWord 128 -> SBV (WordN (64 + 128))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h6 SWord 64 -> SWord 64 -> SBV (WordN (64 + 64))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h7
      where [SWord 64
    h0, SWord 64
    h1, SWord 64
    h2, SWord 64
    h3, SWord 64
    h4, SWord 64
    h5, SWord 64
    h6, SWord 64
    h7] = SHA (SWord 64) -> String -> [SWord 64]
    forall w.
    (Num w, Bits w, ByteConverter w) =>
    SHA w -> String -> [w]
    shaP SHA (SWord 64)
    sha512P String
    s

    -- | SHA512_224 digest.
    sha512_224 :: String -> SWord 224
    sha512_224 :: String -> SWord 224
    sha512_224 String
    s = SWord 64
    h0 SWord 64 -> SBV (WordN 160) -> SBV (WordN (64 + 160))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h1 SWord 64 -> SBV (WordN 96) -> SBV (WordN (64 + 96))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h2 SWord 64 -> SWord 32 -> SBV (WordN (64 + 32))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 32
    h3Top
      where [SWord 64
    h0, SWord 64
    h1, SWord 64
    h2, SWord 64
    h3, SWord 64
    _, SWord 64
    _, SWord 64
    _, SWord 64
    _] = SHA (SWord 64) -> String -> [SWord 64]
    forall w.
    (Num w, Bits w, ByteConverter w) =>
    SHA w -> String -> [w]
    shaP SHA (SWord 64)
    sha512_224P String
    s
            h3Top :: SBV (WordN ((63 - 32) + 1))
    h3Top                        = Proxy 63 -> Proxy 32 -> SWord 64 -> SBV (WordN ((63 - 32) + 1))
    forall (i :: Nat) (j :: Nat) (n :: Nat) (bv :: Nat -> *)
           (proxy :: Nat -> *).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat i, KnownNat j,
     (i + 1) <= n, j <= i, BVIsNonZero ((i - j) + 1)) =>
    proxy i -> proxy j -> SBV (bv n) -> SBV (bv ((i - j) + 1))
    bvExtract (forall (t :: Nat). Proxy t
    forall {k} (t :: k). Proxy t
    Proxy @63) (forall (t :: Nat). Proxy t
    forall {k} (t :: k). Proxy t
    Proxy @32) SWord 64
    h3

    -- | SHA512_256 digest.
    sha512_256 :: String -> SWord 256
    sha512_256 :: String -> SWord 256
    sha512_256 String
    s = SWord 64
    h0 SWord 64 -> SBV (WordN 192) -> SBV (WordN (64 + 192))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h1 SWord 64 -> SWord 128 -> SBV (WordN (64 + 128))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h2 SWord 64 -> SWord 64 -> SBV (WordN (64 + 64))
    forall (n :: Nat) (bv :: Nat -> *) (m :: Nat).
    (KnownNat n, BVIsNonZero n, SymVal (bv n), KnownNat m,
     BVIsNonZero m, SymVal (bv m)) =>
    SBV (bv n) -> SBV (bv m) -> SBV (bv (n + m))
    # SWord 64
    h3
      where [SWord 64
    h0, SWord 64
    h1, SWord 64
    h2, SWord 64
    h3, SWord 64
    _, SWord 64
    _, SWord 64
    _, SWord 64
    _] = SHA (SWord 64) -> String -> [SWord 64]
    forall w.
    (Num w, Bits w, ByteConverter w) =>
    SHA w -> String -> [w]
    shaP SHA (SWord 64)
    sha512_256P String
    s

    -----------------------------------------------------------------------------
    -- * Testing
    -----------------------------------------------------------------------------

    -- | Collection of known answer tests for SHA. Since these tests take too long during regular
    -- regression runs, we pass as an argument how many to run. Increase the below number to 24 to run all tests.
    -- We have:
    --
    -- >>> knownAnswerTests 1
    -- True
    knownAnswerTests :: Int -> Bool
    knownAnswerTests :: Int -> Bool
    knownAnswerTests Int
    nTest = [Bool] -> Bool
    forall (t :: * -> *). Foldable t => t Bool -> Bool
    and ([Bool] -> Bool) -> [Bool] -> Bool
    forall a b. (a -> b) -> a -> b
    $  Int -> [Bool] -> [Bool]
    forall a. Int -> [a] -> [a]
    take Int
    nTest ([Bool] -> [Bool]) -> [Bool] -> [Bool]
    forall a b. (a -> b) -> a -> b
    $  [SWord 224 -> String
    forall a. (Show a, Integral a, SymVal a) => SBV a -> String
    showHash (String -> SWord 224
    sha224     String
    t) String -> String -> Bool
    forall a. Eq a => a -> a -> Bool
    == (Char -> Char) -> String -> String
    forall a b. (a -> b) -> [a] -> [b]
    map Char -> Char
    toLower String
    r | (String
    t, String
    r) <- [(String, String)]
    sha224Kats    ]
                                               [Bool] -> [Bool] -> [Bool]
    forall a. [a] -> [a] -> [a]
    ++ [SWord 256 -> String
    forall a. (Show a, Integral a, SymVal a) => SBV a -> String
    showHash (String -> SWord 256
    sha256     String
    t) String -> String -> Bool
    forall a. Eq a => a -> a -> Bool
    == (Char -> Char) -> String -> String
    forall a b. (a -> b) -> [a] -> [b]
    map Char -> Char
    toLower String
    r | (String
    t, String
    r) <- [(String, String)]
    sha256Kats    ]
                                               [Bool] -> [Bool] -> [Bool]
    forall a. [a] -> [a] -> [a]
    ++ [SWord 384 -> String
    forall a. (Show a, Integral a, SymVal a) => SBV a -> String
    showHash (String -> SWord 384
    sha384     String
    t) String -> String -> Bool
    forall a. Eq a => a -> a -> Bool
    == (Char -> Char) -> String -> String
    forall a b. (a -> b) -> [a] -> [b]
    map Char -> Char
    toLower String
    r | (String
    t, String
    r) <- [(String, String)]
    sha384Kats    ]
                                               [Bool] -> [Bool] -> [Bool]
    forall a. [a] -> [a] -> [a]
    ++ [SWord 512 -> String
    forall a. (Show a, Integral a, SymVal a) => SBV a -> String
    showHash (String -> SWord 512
    sha512     String
    t) String -> String -> Bool
    forall a. Eq a => a -> a -> Bool
    == (Char -> Char) -> String -> String
    forall a b. (a -> b) -> [a] -> [b]
    map Char -> Char
    toLower String
    r | (String
    t, String
    r) <- [(String, String)]
    sha512Kats    ]
                                               [Bool] -> [Bool] -> [Bool]
    forall a. [a] -> [a] -> [a]
    ++ [SWord 224 -> String
    forall a. (Show a, Integral a, SymVal a) => SBV a -> String
    showHash (String -> SWord 224
    sha512_224 String
    t) String -> String -> Bool
    forall a. Eq a => a -> a -> Bool
    == (Char -> Char) -> String -> String
    forall a b. (a -> b) -> [a] -> [b]
    map Char -> Char
    toLower String
    r | (String
    t, String
    r) <- [(String, String)]
    sha512_224Kats]
                                               [Bool] -> [Bool] -> [Bool]
    forall a. [a] -> [a] -> [a]
    ++ [SWord 256 -> String
    forall a. (Show a, Integral a, SymVal a) => SBV a -> String
    showHash (String -> SWord 256
    sha512_256 String
    t) String -> String -> Bool
    forall a. Eq a => a -> a -> Bool
    == (Char -> Char) -> String -> String
    forall a b. (a -> b) -> [a] -> [b]
    map Char -> Char
    toLower String
    r | (String
    t, String
    r) <- [(String, String)]
    sha512_256Kats]

      where -- | From <http://github.com/bcgit/bc-java/blob/master/core/src/test/java/org/bouncycastle/crypto/test/SHA224DigestTest.java>
            sha224Kats :: [(String, String)]
            sha224Kats :: [(String, String)]
    sha224Kats = [ (String
    ""                                                        , String
    "d14a028c2a3a2bc9476102bb288234c415a2b01f828ea62ac5b3e42f")
                         , (String
    "a"                                                       , String
    "abd37534c7d9a2efb9465de931cd7055ffdb8879563ae98078d6d6d5")
                         , (String
    "abc"                                                     , String
    "23097d223405d8228642a477bda255b32aadbce4bda0b3f7e36c9da7")
                         , (String
    "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq", String
    "75388b16512776cc5dba5da1fd890150b0c6455cb4f58b1952522525")
                         ]

            -- | From: <http://github.com/bcgit/bc-java/blob/master/core/src/test/java/org/bouncycastle/crypto/test/SHA256DigestTest.java>
            sha256Kats :: [(String, String)]
            sha256Kats :: [(String, String)]
    sha256Kats = [ (String
    ""                                                        , String
    "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855")
                         , (String
    "a"                                                       , String
    "ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb")
                         , (String
    "abc"                                                     , String
    "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad")
                         , (String
    "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq", String
    "248d6a61d20638b8e5c026930c3e6039a33ce45964ff2167f6ecedd419db06c1")
                         ]

            -- | From: <http://github.com/bcgit/bc-java/blob/master/core/src/test/java/org/bouncycastle/crypto/test/SHA384DigestTest.java>
            sha384Kats :: [(String, String)]
            sha384Kats :: [(String, String)]
    sha384Kats = [ (String
    ""                                                                                                                , String
    "38b060a751ac96384cd9327eb1b1e36a21fdb71114be07434c0cc7bf63f6e1da274edebfe76f65fbd51ad2f14898b95b")
                         , (String
    "a"                                                                                                               , String
    "54a59b9f22b0b80880d8427e548b7c23abd873486e1f035dce9cd697e85175033caa88e6d57bc35efae0b5afd3145f31")
                         , (String
    "abc"                                                                                                             , String
    "cb00753f45a35e8bb5a03d699ac65007272c32ab0eded1631a8b605a43ff5bed8086072ba1e7cc2358baeca134c825a7")
                         , (String
    "abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrstu", String
    "09330c33f71147e83d192fc782cd1b4753111b173b3b05d22fa08086e3b0f712fcc7c71a557e2db966c3e9fa91746039")
                         ]

            -- | From: <http://github.com/bcgit/bc-java/blob/master/core/src/test/java/org/bouncycastle/crypto/test/SHA512DigestTest.java>
            sha512Kats :: [(String, String)]
            sha512Kats :: [(String, String)]
    sha512Kats = [ (String
    ""                                                                                                                , String
    "cf83e1357eefb8bdf1542850d66d8007d620e4050b5715dc83f4a921d36ce9ce47d0d13c5d85f2b0ff8318d2877eec2f63b931bd47417a81a538327af927da3e")
                         , (String
    "a"                                                                                                               , String
    "1f40fc92da241694750979ee6cf582f2d5d7d28e18335de05abc54d0560e0f5302860c652bf08d560252aa5e74210546f369fbbbce8c12cfc7957b2652fe9a75")
                         , (String
    "abc"                                                                                                             , String
    "ddaf35a193617abacc417349ae20413112e6fa4e89a97ea20a9eeee64b55d39a2192992a274fc1a836ba3c23a3feebbd454d4423643ce80e2a9ac94fa54ca49f")
                         , (String
    "abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrstu", String
    "8e959b75dae313da8cf4f72814fc143f8f7779c6eb9f7fa17299aeadb6889018501d289e4900f7e4331b99dec4b5433ac7d329eeb6dd26545e96e55b874be909")
                         ]

            -- | From: <http://github.com/bcgit/bc-java/blob/master/core/src/test/java/org/bouncycastle/crypto/test/SHA512t224DigestTest.java>
            sha512_224Kats :: [(String, String)]
            sha512_224Kats :: [(String, String)]
    sha512_224Kats = [ (String
    ""                                                                                                                , String
    "6ed0dd02806fa89e25de060c19d3ac86cabb87d6a0ddd05c333b84f4")
                             , (String
    "a"                                                                                                               , String
    "d5cdb9ccc769a5121d4175f2bfdd13d6310e0d3d361ea75d82108327")
                             , (String
    "abc"                                                                                                             , String
    "4634270F707B6A54DAAE7530460842E20E37ED265CEEE9A43E8924AA")
                             , (String
    "abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrstu", String
    "23FEC5BB94D60B23308192640B0C453335D664734FE40E7268674AF9")
                             ]

            -- | From: <http://github.com/bcgit/bc-java/blob/master/core/src/test/java/org/bouncycastle/crypto/test/SHA512t256DigestTest.java>
            sha512_256Kats :: [(String, String)]
            sha512_256Kats :: [(String, String)]
    sha512_256Kats = [ (String
    ""                                                                                                                , String
    "c672b8d1ef56ed28ab87c3622c5114069bdd3ad7b8f9737498d0c01ecef0967a")
                             , (String
    "a"                                                                                                               , String
    "455e518824bc0601f9fb858ff5c37d417d67c2f8e0df2babe4808858aea830f8")
                             , (String
    "abc"                                                                                                             , String
    "53048E2681941EF99B2E29B76B4C7DABE4C2D0C634FC6D46E0E2F13107E7AF23")
                             , (String
    "abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrstu", String
    "3928E184FB8690F840DA3988121D31BE65CB9D3EF83EE6146FEAC861E19B563A")
                             ]

    -----------------------------------------------------------------------------
    -- * Code generation
    -- ${codeGenIntro}
    -----------------------------------------------------------------------------
    {- $codeGenIntro
       It is not practical to generate SBV code for hashing an entire string, as it would
       require handling of a fixed size string. Instead we show how to generate code
       for hashing one block, which can then be incorporated into a larger program
       by providing the appropriate loop.
    -}

    -- | Generate code for one block of SHA256 in action, starting from an arbitrary hash value.
    cgSHA256 :: IO ()
    cgSHA256 :: IO ()
    cgSHA256 = Maybe String -> String -> SBVCodeGen () -> IO ()
    forall a. Maybe String -> String -> SBVCodeGen a -> IO a
    compileToC Maybe String
    forall a. Maybe a
    Nothing String
    "sha256" (SBVCodeGen () -> IO ()) -> SBVCodeGen () -> IO ()
    forall a b. (a -> b) -> a -> b
    $ do

            let algorithm :: SHA (SWord 32)
    algorithm = SHA (SWord 32)
    sha256P

            [SWord 8]
    hInBytes   <- Int -> String -> SBVCodeGen [SWord 8]
    forall a. SymVal a => Int -> String -> SBVCodeGen [SBV a]
    cgInputArr Int
    32 String
    "hIn"
            [SWord 8]
    blockBytes <- Int -> String -> SBVCodeGen [SWord 8]
    forall a. SymVal a => Int -> String -> SBVCodeGen [SBV a]
    cgInputArr Int
    64 String
    "block"

            let hIn :: [SWord 32]
    hIn   = Int -> ([SWord 8] -> SWord 32) -> [SWord 8] -> [SWord 32]
    forall a b. Int -> ([a] -> b) -> [a] -> [b]
    chunkBy Int
    4 [SWord 8] -> SWord 32
    forall a. ByteConverter a => [SWord 8] -> a
    fromBytes [SWord 8]
    hInBytes
                block :: [SWord 32]
    block = Int -> ([SWord 8] -> SWord 32) -> [SWord 8] -> [SWord 32]
    forall a b. Int -> ([a] -> b) -> [a] -> [b]
    chunkBy Int
    4 [SWord 8] -> SWord 32
    forall a. ByteConverter a => [SWord 8] -> a
    fromBytes [SWord 8]
    blockBytes

                result :: [SWord 32]
    result = SHA (SWord 32) -> [SWord 32] -> Block (SWord 32) -> [SWord 32]
    forall w. (Num w, Bits w) => SHA w -> [w] -> Block w -> [w]
    hashBlock SHA (SWord 32)
    algorithm [SWord 32]
    hIn ([SWord 32] -> Block (SWord 32)
    forall a. [a] -> Block a
    Block [SWord 32]
    block)

            String -> [SWord 8] -> SBVCodeGen ()
    forall a. SymVal a => String -> [SBV a] -> SBVCodeGen ()
    cgOutputArr String
    "hash" ([SWord 8] -> SBVCodeGen ()) -> [SWord 8] -> SBVCodeGen ()
    forall a b. (a -> b) -> a -> b
    $ (SWord 32 -> [SWord 8]) -> [SWord 32] -> [SWord 8]
    forall (t :: * -> *) a b. Foldable t => (a -> [b]) -> t a -> [b]
    concatMap SWord 32 -> [SWord 8]
    forall a. ByteConverter a => a -> [SWord 8]
    toBytes [SWord 32]
    result

    -- | Generate code for one block of SHA512 in action, starting from an arbitrary hash value.
    cgSHA512 :: IO ()
    cgSHA512 :: IO ()
    cgSHA512 = Maybe String -> String -> SBVCodeGen () -> IO ()
    forall a. Maybe String -> String -> SBVCodeGen a -> IO a
    compileToC Maybe String
    forall a. Maybe a
    Nothing String
    "sha512" (SBVCodeGen () -> IO ()) -> SBVCodeGen () -> IO ()
    forall a b. (a -> b) -> a -> b
    $ do

            let algorithm :: SHA (SWord 64)
    algorithm = SHA (SWord 64)
    sha512P

            [SWord 8]
    hInBytes   <- Int -> String -> SBVCodeGen [SWord 8]
    forall a. SymVal a => Int -> String -> SBVCodeGen [SBV a]
    cgInputArr  Int
    64 String
    "hIn"
            [SWord 8]
    blockBytes <- Int -> String -> SBVCodeGen [SWord 8]
    forall a. SymVal a => Int -> String -> SBVCodeGen [SBV a]
    cgInputArr Int
    128 String
    "block"

            let hIn :: [SWord 64]
    hIn   = Int -> ([SWord 8] -> SWord 64) -> [SWord 8] -> [SWord 64]
    forall a b. Int -> ([a] -> b) -> [a] -> [b]
    chunkBy Int
    8 [SWord 8] -> SWord 64
    forall a. ByteConverter a => [SWord 8] -> a
    fromBytes [SWord 8]
    hInBytes
                block :: [SWord 64]
    block = Int -> ([SWord 8] -> SWord 64) -> [SWord 8] -> [SWord 64]
    forall a b. Int -> ([a] -> b) -> [a] -> [b]
    chunkBy Int
    8 [SWord 8] -> SWord 64
    forall a. ByteConverter a => [SWord 8] -> a
    fromBytes [SWord 8]
    blockBytes

                result :: [SWord 64]
    result = SHA (SWord 64) -> [SWord 64] -> Block (SWord 64) -> [SWord 64]
    forall w. (Num w, Bits w) => SHA w -> [w] -> Block w -> [w]
    hashBlock SHA (SWord 64)
    algorithm [SWord 64]
    hIn ([SWord 64] -> Block (SWord 64)
    forall a. [a] -> Block a
    Block [SWord 64]
    block)

            String -> [SWord 8] -> SBVCodeGen ()
    forall a. SymVal a => String -> [SBV a] -> SBVCodeGen ()
    cgOutputArr String
    "hash" ([SWord 8] -> SBVCodeGen ()) -> [SWord 8] -> SBVCodeGen ()
    forall a b. (a -> b) -> a -> b
    $ (SWord 64 -> [SWord 8]) -> [SWord 64] -> [SWord 8]
    forall (t :: * -> *) a b. Foldable t => (a -> [b]) -> t a -> [b]
    concatMap SWord 64 -> [SWord 8]
    forall a. ByteConverter a => a -> [SWord 8]
    toBytes [SWord 64]
    result

    -----------------------------------------------------------------------------
    -- * Helpers
    -----------------------------------------------------------------------------

    -- | Helper for chunking a list by given lengths and combining each chunk with a function
    chunkBy :: Int -> ([a] -> b) -> [a] -> [b]
    chunkBy :: forall a b. Int -> ([a] -> b) -> [a] -> [b]
    chunkBy Int
    i [a] -> b
    f = [a] -> [b]
    go
      where go :: [a] -> [b]
    go [] = []
            go [a]
    xs
             | [a] -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [a]
    first Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    /= Int
    i = String -> [b]
    forall a. HasCallStack => String -> a
    error (String -> [b]) -> String -> [b]
    forall a b. (a -> b) -> a -> b
    $ String
    "chunkBy: Not a multiple of " String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ Int -> String
    forall a. Show a => a -> String
    show Int
    i String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ String
    ", got: " String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ Int -> String
    forall a. Show a => a -> String
    show ([a] -> Int
    forall a. [a] -> Int
    forall (t :: * -> *) a. Foldable t => t a -> Int
    length [a]
    first)
             | Bool
    True              = [a] -> b
    f [a]
    first b -> [b] -> [b]
    forall a. a -> [a] -> [a]
    : [a] -> [b]
    go [a]
    rest
             where ([a]
    first, [a]
    rest) = Int -> [a] -> ([a], [a])
    forall a. Int -> [a] -> ([a], [a])
    splitAt Int
    i [a]
    xs

    -- | Nicely lay out a hash value as a string
    showHash :: (Show a, Integral a, SymVal a) => SBV a -> String
    showHash :: forall a. (Show a, Integral a, SymVal a) => SBV a -> String
    showHash SBV a
    x = case (SBV a -> Kind
    forall a. HasKind a => a -> Kind
    kindOf SBV a
    x, SBV a -> Maybe a
    forall a. SymVal a => SBV a -> Maybe a
    unliteral SBV a
    x) of
                   (KBounded Bool
    False Int
    n, Just a
    v)  -> Int -> String -> String
    pad (Int
    n Int -> Int -> Int
    forall a. Integral a => a -> a -> a
    `div` Int
    4) (String -> String) -> String -> String
    forall a b. (a -> b) -> a -> b
    $ a -> String -> String
    forall a. Integral a => a -> String -> String
    showHex a
    v String
    ""
                   (Kind, Maybe a)
    _                           -> String -> String
    forall a. HasCallStack => String -> a
    error (String -> String) -> String -> String
    forall a b. (a -> b) -> a -> b
    $ String
    "Impossible happened: Unexpected hash value: " String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ SBV a -> String
    forall a. Show a => a -> String
    show SBV a
    x
      where pad :: Int -> String -> String
    pad Int
    l String
    s = String -> String
    forall a. [a] -> [a]
    reverse (String -> String) -> String -> String
    forall a b. (a -> b) -> a -> b
    $ Int -> String -> String
    forall a. Int -> [a] -> [a]
    take Int
    l (String -> String) -> String -> String
    forall a b. (a -> b) -> a -> b
    $ String -> String
    forall a. [a] -> [a]
    reverse String
    s String -> String -> String
    forall a. [a] -> [a] -> [a]
    ++ Char -> String
    forall a. a -> [a]
    repeat Char
    '0'