358 lines
17 KiB
Plaintext
358 lines
17 KiB
Plaintext
/*
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** ChaCha20 specification
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** Author: Austin Seipp <aseipp@pobox.com>. Released in the Public Domain.
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**
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** Based on RFC 7539 - "ChaCha20 and Poly1305 for IETF Protocols"
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** https://tools.ietf.org/html/rfc7539
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*/
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module chacha20 where
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/* -------------------------------------------------------------------------- */
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/* -- Implementation -------------------------------------------------------- */
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type Round = [16][32] // An input to the ChaCha20 core function
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type Block = [64][8] // An output block from the ChaCha20 core function.
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type Key = [32][8] // A 32-byte input key
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type Nonce = [12][8] // A 12-byte nonce
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type Counter = [32] // Starting block counter. Usually 1 or 0.
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/* ---------------------------------- */
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/* -- Quarter Round ----------------- */
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// The quarter round. This takes 4 32-bit integers and diffuses them
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// appropriately, and is the core of the column and diagonal round.
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qround : [4][32] -> [4][32]
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qround [ a0, b0, c0, d0 ] = [ a2, b4, c2, d4 ]
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where
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a1 = a0 + b0 /* a += b; d ^= a; d <<<= 16 */
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d1 = d0 ^ a1
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d2 = d1 <<< 16
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c1 = c0 + d2 /* c += d; b ^= c; b <<<= 12 */
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b1 = b0 ^ c1
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b2 = b1 <<< 12
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a2 = a1 + b2 /* a += b; d ^= a; d <<<= 8 */
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d3 = d2 ^ a2
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d4 = d3 <<< 8
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c2 = c1 + d4 /* c += d; b ^= c; b <<<= 7 */
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b3 = b2 ^ c2
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b4 = b3 <<< 7
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/* ---------------------------------- */
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/* -- Column and diagonal rounds ---- */
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// Perform the column round, followed by the diagonal round on the
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// input state, which are both defined in terms of the quarter
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// round. ChaCha20 requires 20 total rounds of interleaving
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// column/diagonal passes on the state, and therefore `cdround` actually
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// does two passes at once (mostly for simplicity).
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cdround : Round -> Round
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cdround [ x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15 ]
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= [ z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, z13, z14, z15 ]
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where
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// Column round
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[ y0, y4, y8, y12 ] = qround [ x0, x4, x8, x12 ]
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[ y1, y5, y9, y13 ] = qround [ x1, x5, x9, x13 ]
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[ y2, y6, y10, y14 ] = qround [ x2, x6, x10, x14 ]
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[ y3, y7, y11, y15 ] = qround [ x3, x7, x11, x15 ]
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// Diagonal round
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[ z0, z5, z10, z15 ] = qround [ y0, y5, y10, y15 ]
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[ z1, z6, z11, z12 ] = qround [ y1, y6, y11, y12 ]
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[ z2, z7, z8, z13 ] = qround [ y2, y7, y8, y13 ]
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[ z3, z4, z9, z14 ] = qround [ y3, y4, y9, y14 ]
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/* ---------------------------------- */
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/* -- Block encryption -------------- */
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// Given an input round, calculate the core ChaCha20 algorithm over
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// the round and return an output block. These output blocks form the
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// stream which you XOR your plaintext with, and successive iterations of
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// the core algorithm result in an infinite stream you can use as a
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// cipher.
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core : Round -> Block
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core x = block
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where
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rounds = iterate cdround x // Do a bunch of column/diagonal passes...
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result = rounds @ 10 // And grab the 10th result (20 total passes)
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block = blocked (x + result) // Add to input, convert to output block
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/* ---------------------------------- */
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/* -- Key Expansion ----------------- */
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// Key expansion. Given a nonce and a key, compute a round (which is
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// fed to the core algorithm above) by taking the initial round state and
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// mixing in the key and nonce appropriately.
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kexp : Key -> Counter -> Nonce -> Round
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kexp k c n = [ c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15 ]
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where
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// The following describes the layout of the output round, which
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// is fed into the core algorithm successively.
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// Bytes 0-3: Constants
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[ c0, c1, c2, c3 ] = [ 0x61707865, 0x3320646e, 0x79622d32, 0x6b206574 ]
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// Bytes 4-11: Key
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[ c4, c5, c6, c7 ] = map rjoin (groupBy`{4} kslice1 : [4][4][8]) : [4][32]
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[ c8, c9, c10, c11 ] = map rjoin (groupBy`{4} kslice2 : [4][4][8]) : [4][32]
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kslice1 = k @@ ([ 0 .. 15 ] : [16][32]) // Top half
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kslice2 = k @@ ([ 16 .. 31 ] : [16][32]) // Bottom half
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// Bytes 12: Counter, starts off with whatever the user specified
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// (usually 0 or 1)
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[ c12 ] = [ c ]
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// Bytes 14-15: Nonce
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[ c13, c14, c15 ] = map rjoin (groupBy`{4} n)
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/* ---------------------------------- */
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/* -- Round increments -------------- */
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// Take a given number of iterations and the input round (after key
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// expansion!), and calculate the input round for the core algorithm
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// function. This allows you to index into a particular Round which
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// can be passed to the 'core' function.
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iround : [64] -> Round -> Round
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iround n r = (iterate once r) @ n where
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// Given a round, increment the counter inside (index no 12)
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once [ x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15 ]
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= [ x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12+1, x13, x14, x15 ]
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/* ---------------------------------- */
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/* -- ChaCha20 encryption ----------- */
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// Produce a psuedo-random stream given a nonce and a key, which can
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// be XOR'd with your data to encrypt it.
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stream : {n} (fin n) => Key -> Counter -> Nonce -> [n][8]
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stream k c n = take`{n} (join rounds) // Take n bytes from the final result
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where
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// Expand key
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key = kexp k c n
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// Produce the stream by successively incrementing the input round
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// by `i`, and running the core algorithm to get the resulting
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// stream for the `i`th input. Once these are concatenated, you have
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// an infinite list representing the ChaCha20 stream.
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rounds = [ core (iround i key) | i <- [ 0, 1 ... ] ]
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// Given an message, a nonce, and a key, produce an encrypted
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// message. This is simply defined as the XOR of the message and the
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// corresponding encryption stream.
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encrypt : {n} (fin n) => Key -> Counter -> Nonce -> [n][8] -> [n][8]
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encrypt k c n m = m ^ (stream k c n)
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/* -------------------------------------------------------------------------- */
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/* -- Theorems, tests ------------------------------------------------------- */
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// Tests are private
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private
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qround01 = qround in == out
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where
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in = [ 0x11111111, 0x01020304, 0x9b8d6f43, 0x01234567 ]
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out = [ 0xea2a92f4, 0xcb1cf8ce, 0x4581472e, 0x5881c4bb ]
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core01 = kexp k 1 n == out
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where
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n = [ 0x00, 0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x4a,
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0x00, 0x00, 0x00, 0x00 ]
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k = [ 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
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0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
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0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,
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0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f ]
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out = [ 0x61707865, 0x3320646e, 0x79622d32, 0x6b206574,
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0x03020100, 0x07060504, 0x0b0a0908, 0x0f0e0d0c,
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0x13121110, 0x17161514, 0x1b1a1918, 0x1f1e1d1c,
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0x00000001, 0x09000000, 0x4a000000, 0x00000000 ]
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core02 = core (kexp k 1 n) == out
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where
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n = [ 0x00, 0x00, 0x00, 0x09, 0x00, 0x00, 0x00, 0x4a,
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0x00, 0x00, 0x00, 0x00 ]
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k = [ 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
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0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
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0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,
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0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f ]
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out = [ 0x10, 0xf1, 0xe7, 0xe4, 0xd1, 0x3b, 0x59, 0x15,
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0x50, 0x0f, 0xdd, 0x1f, 0xa3, 0x20, 0x71, 0xc4,
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0xc7, 0xd1, 0xf4, 0xc7, 0x33, 0xc0, 0x68, 0x03,
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0x04, 0x22, 0xaa, 0x9a, 0xc3, 0xd4, 0x6c, 0x4e,
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0xd2, 0x82, 0x64, 0x46, 0x07, 0x9f, 0xaa, 0x09,
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0x14, 0xc2, 0xd7, 0x05, 0xd9, 0x8b, 0x02, 0xa2,
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0xb5, 0x12, 0x9c, 0xd1, 0xde, 0x16, 0x4e, 0xb9,
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0xcb, 0xd0, 0x83, 0xe8, 0xa2, 0x50, 0x3c, 0x4e ]
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rfctest01 = encrypt zero zero zero zero
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== [ 0x76, 0xb8, 0xe0, 0xad, 0xa0, 0xf1, 0x3d, 0x90, 0x40, 0x5d,
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0x6a, 0xe5, 0x53, 0x86, 0xbd, 0x28, 0xbd, 0xd2, 0x19, 0xb8,
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0xa0, 0x8d, 0xed, 0x1a, 0xa8, 0x36, 0xef, 0xcc, 0x8b, 0x77,
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0x0d, 0xc7, 0xda, 0x41, 0x59, 0x7c, 0x51, 0x57, 0x48, 0x8d,
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0x77, 0x24, 0xe0, 0x3f, 0xb8, 0xd8, 0x4a, 0x37, 0x6a, 0x43,
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0xb8, 0xf4, 0x15, 0x18, 0xa1, 0x1c, 0xc3, 0x87, 0xb6, 0x69,
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0xb2, 0xee, 0x65, 0x86 ]
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rfctest02 = encrypt (zero # [1]) 1 (zero # [2]) msg == out
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where
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out = [ 0xa3, 0xfb, 0xf0, 0x7d, 0xf3, 0xfa, 0x2f, 0xde, 0x4f, 0x37,
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0x6c, 0xa2, 0x3e, 0x82, 0x73, 0x70, 0x41, 0x60, 0x5d, 0x9f,
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0x4f, 0x4f, 0x57, 0xbd, 0x8c, 0xff, 0x2c, 0x1d, 0x4b, 0x79,
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0x55, 0xec, 0x2a, 0x97, 0x94, 0x8b, 0xd3, 0x72, 0x29, 0x15,
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0xc8, 0xf3, 0xd3, 0x37, 0xf7, 0xd3, 0x70, 0x05, 0x0e, 0x9e,
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0x96, 0xd6, 0x47, 0xb7, 0xc3, 0x9f, 0x56, 0xe0, 0x31, 0xca,
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0x5e, 0xb6, 0x25, 0x0d, 0x40, 0x42, 0xe0, 0x27, 0x85, 0xec,
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0xec, 0xfa, 0x4b, 0x4b, 0xb5, 0xe8, 0xea, 0xd0, 0x44, 0x0e,
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0x20, 0xb6, 0xe8, 0xdb, 0x09, 0xd8, 0x81, 0xa7, 0xc6, 0x13,
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0x2f, 0x42, 0x0e, 0x52, 0x79, 0x50, 0x42, 0xbd, 0xfa, 0x77,
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0x73, 0xd8, 0xa9, 0x05, 0x14, 0x47, 0xb3, 0x29, 0x1c, 0xe1,
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0x41, 0x1c, 0x68, 0x04, 0x65, 0x55, 0x2a, 0xa6, 0xc4, 0x05,
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0xb7, 0x76, 0x4d, 0x5e, 0x87, 0xbe, 0xa8, 0x5a, 0xd0, 0x0f,
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0x84, 0x49, 0xed, 0x8f, 0x72, 0xd0, 0xd6, 0x62, 0xab, 0x05,
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0x26, 0x91, 0xca, 0x66, 0x42, 0x4b, 0xc8, 0x6d, 0x2d, 0xf8,
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0x0e, 0xa4, 0x1f, 0x43, 0xab, 0xf9, 0x37, 0xd3, 0x25, 0x9d,
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0xc4, 0xb2, 0xd0, 0xdf, 0xb4, 0x8a, 0x6c, 0x91, 0x39, 0xdd,
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0xd7, 0xf7, 0x69, 0x66, 0xe9, 0x28, 0xe6, 0x35, 0x55, 0x3b,
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0xa7, 0x6c, 0x5c, 0x87, 0x9d, 0x7b, 0x35, 0xd4, 0x9e, 0xb2,
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0xe6, 0x2b, 0x08, 0x71, 0xcd, 0xac, 0x63, 0x89, 0x39, 0xe2,
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0x5e, 0x8a, 0x1e, 0x0e, 0xf9, 0xd5, 0x28, 0x0f, 0xa8, 0xca,
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0x32, 0x8b, 0x35, 0x1c, 0x3c, 0x76, 0x59, 0x89, 0xcb, 0xcf,
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0x3d, 0xaa, 0x8b, 0x6c, 0xcc, 0x3a, 0xaf, 0x9f, 0x39, 0x79,
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0xc9, 0x2b, 0x37, 0x20, 0xfc, 0x88, 0xdc, 0x95, 0xed, 0x84,
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0xa1, 0xbe, 0x05, 0x9c, 0x64, 0x99, 0xb9, 0xfd, 0xa2, 0x36,
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0xe7, 0xe8, 0x18, 0xb0, 0x4b, 0x0b, 0xc3, 0x9c, 0x1e, 0x87,
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0x6b, 0x19, 0x3b, 0xfe, 0x55, 0x69, 0x75, 0x3f, 0x88, 0x12,
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0x8c, 0xc0, 0x8a, 0xaa, 0x9b, 0x63, 0xd1, 0xa1, 0x6f, 0x80,
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0xef, 0x25, 0x54, 0xd7, 0x18, 0x9c, 0x41, 0x1f, 0x58, 0x69,
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0xca, 0x52, 0xc5, 0xb8, 0x3f, 0xa3, 0x6f, 0xf2, 0x16, 0xb9,
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0xc1, 0xd3, 0x00, 0x62, 0xbe, 0xbc, 0xfd, 0x2d, 0xc5, 0xbc,
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0xe0, 0x91, 0x19, 0x34, 0xfd, 0xa7, 0x9a, 0x86, 0xf6, 0xe6,
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0x98, 0xce, 0xd7, 0x59, 0xc3, 0xff, 0x9b, 0x64, 0x77, 0x33,
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0x8f, 0x3d, 0xa4, 0xf9, 0xcd, 0x85, 0x14, 0xea, 0x99, 0x82,
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0xcc, 0xaf, 0xb3, 0x41, 0xb2, 0x38, 0x4d, 0xd9, 0x02, 0xf3,
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0xd1, 0xab, 0x7a, 0xc6, 0x1d, 0xd2, 0x9c, 0x6f, 0x21, 0xba,
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0x5b, 0x86, 0x2f, 0x37, 0x30, 0xe3, 0x7c, 0xfd, 0xc4, 0xfd,
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0x80, 0x6c, 0x22, 0xf2, 0x21 ]
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msg = [ 0x41, 0x6e, 0x79, 0x20, 0x73, 0x75, 0x62, 0x6d, 0x69, 0x73,
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0x73, 0x69, 0x6f, 0x6e, 0x20, 0x74, 0x6f, 0x20, 0x74, 0x68,
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0x65, 0x20, 0x49, 0x45, 0x54, 0x46, 0x20, 0x69, 0x6e, 0x74,
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0x65, 0x6e, 0x64, 0x65, 0x64, 0x20, 0x62, 0x79, 0x20, 0x74,
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0x68, 0x65, 0x20, 0x43, 0x6f, 0x6e, 0x74, 0x72, 0x69, 0x62,
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0x75, 0x74, 0x6f, 0x72, 0x20, 0x66, 0x6f, 0x72, 0x20, 0x70,
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0x75, 0x62, 0x6c, 0x69, 0x63, 0x61, 0x74, 0x69, 0x6f, 0x6e,
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0x20, 0x61, 0x73, 0x20, 0x61, 0x6c, 0x6c, 0x20, 0x6f, 0x72,
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0x20, 0x70, 0x61, 0x72, 0x74, 0x20, 0x6f, 0x66, 0x20, 0x61,
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0x6e, 0x20, 0x49, 0x45, 0x54, 0x46, 0x20, 0x49, 0x6e, 0x74,
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0x65, 0x72, 0x6e, 0x65, 0x74, 0x2d, 0x44, 0x72, 0x61, 0x66,
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0x74, 0x20, 0x6f, 0x72, 0x20, 0x52, 0x46, 0x43, 0x20, 0x61,
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0x6e, 0x64, 0x20, 0x61, 0x6e, 0x79, 0x20, 0x73, 0x74, 0x61,
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0x74, 0x65, 0x6d, 0x65, 0x6e, 0x74, 0x20, 0x6d, 0x61, 0x64,
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0x65, 0x20, 0x77, 0x69, 0x74, 0x68, 0x69, 0x6e, 0x20, 0x74,
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0x68, 0x65, 0x20, 0x63, 0x6f, 0x6e, 0x74, 0x65, 0x78, 0x74,
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0x20, 0x6f, 0x66, 0x20, 0x61, 0x6e, 0x20, 0x49, 0x45, 0x54,
|
|
0x46, 0x20, 0x61, 0x63, 0x74, 0x69, 0x76, 0x69, 0x74, 0x79,
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0x20, 0x69, 0x73, 0x20, 0x63, 0x6f, 0x6e, 0x73, 0x69, 0x64,
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|
0x65, 0x72, 0x65, 0x64, 0x20, 0x61, 0x6e, 0x20, 0x22, 0x49,
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0x45, 0x54, 0x46, 0x20, 0x43, 0x6f, 0x6e, 0x74, 0x72, 0x69,
|
|
0x62, 0x75, 0x74, 0x69, 0x6f, 0x6e, 0x22, 0x2e, 0x20, 0x53,
|
|
0x75, 0x63, 0x68, 0x20, 0x73, 0x74, 0x61, 0x74, 0x65, 0x6d,
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0x65, 0x6e, 0x74, 0x73, 0x20, 0x69, 0x6e, 0x63, 0x6c, 0x75,
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|
0x64, 0x65, 0x20, 0x6f, 0x72, 0x61, 0x6c, 0x20, 0x73, 0x74,
|
|
0x61, 0x74, 0x65, 0x6d, 0x65, 0x6e, 0x74, 0x73, 0x20, 0x69,
|
|
0x6e, 0x20, 0x49, 0x45, 0x54, 0x46, 0x20, 0x73, 0x65, 0x73,
|
|
0x73, 0x69, 0x6f, 0x6e, 0x73, 0x2c, 0x20, 0x61, 0x73, 0x20,
|
|
0x77, 0x65, 0x6c, 0x6c, 0x20, 0x61, 0x73, 0x20, 0x77, 0x72,
|
|
0x69, 0x74, 0x74, 0x65, 0x6e, 0x20, 0x61, 0x6e, 0x64, 0x20,
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0x65, 0x6c, 0x65, 0x63, 0x74, 0x72, 0x6f, 0x6e, 0x69, 0x63,
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0x20, 0x63, 0x6f, 0x6d, 0x6d, 0x75, 0x6e, 0x69, 0x63, 0x61,
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0x74, 0x69, 0x6f, 0x6e, 0x73, 0x20, 0x6d, 0x61, 0x64, 0x65,
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0x20, 0x61, 0x74, 0x20, 0x61, 0x6e, 0x79, 0x20, 0x74, 0x69,
|
|
0x6d, 0x65, 0x20, 0x6f, 0x72, 0x20, 0x70, 0x6c, 0x61, 0x63,
|
|
0x65, 0x2c, 0x20, 0x77, 0x68, 0x69, 0x63, 0x68, 0x20, 0x61,
|
|
0x72, 0x65, 0x20, 0x61, 0x64, 0x64, 0x72, 0x65, 0x73, 0x73,
|
|
0x65, 0x64, 0x20, 0x74, 0x6f ]
|
|
|
|
rfctest03 = encrypt key 42 (zero # [2]) msg == out
|
|
where
|
|
key = [ 0x1c, 0x92, 0x40, 0xa5, 0xeb, 0x55, 0xd3, 0x8a, 0xf3, 0x33,
|
|
0x88, 0x86, 0x04, 0xf6, 0xb5, 0xf0, 0x47, 0x39, 0x17, 0xc1,
|
|
0x40, 0x2b, 0x80, 0x09, 0x9d, 0xca, 0x5c, 0xbc, 0x20, 0x70,
|
|
0x75, 0xc0 ]
|
|
out = [ 0x27, 0x54, 0x77, 0x61, 0x73, 0x20, 0x62, 0x72, 0x69, 0x6c,
|
|
0x6c, 0x69, 0x67, 0x2c, 0x20, 0x61, 0x6e, 0x64, 0x20, 0x74,
|
|
0x68, 0x65, 0x20, 0x73, 0x6c, 0x69, 0x74, 0x68, 0x79, 0x20,
|
|
0x74, 0x6f, 0x76, 0x65, 0x73, 0x0a, 0x44, 0x69, 0x64, 0x20,
|
|
0x67, 0x79, 0x72, 0x65, 0x20, 0x61, 0x6e, 0x64, 0x20, 0x67,
|
|
0x69, 0x6d, 0x62, 0x6c, 0x65, 0x20, 0x69, 0x6e, 0x20, 0x74,
|
|
0x68, 0x65, 0x20, 0x77, 0x61, 0x62, 0x65, 0x3a, 0x0a, 0x41,
|
|
0x6c, 0x6c, 0x20, 0x6d, 0x69, 0x6d, 0x73, 0x79, 0x20, 0x77,
|
|
0x65, 0x72, 0x65, 0x20, 0x74, 0x68, 0x65, 0x20, 0x62, 0x6f,
|
|
0x72, 0x6f, 0x67, 0x6f, 0x76, 0x65, 0x73, 0x2c, 0x0a, 0x41,
|
|
0x6e, 0x64, 0x20, 0x74, 0x68, 0x65, 0x20, 0x6d, 0x6f, 0x6d,
|
|
0x65, 0x20, 0x72, 0x61, 0x74, 0x68, 0x73, 0x20, 0x6f, 0x75,
|
|
0x74, 0x67, 0x72, 0x61, 0x62, 0x65, 0x2e ]
|
|
|
|
msg = [ 0x62, 0xe6, 0x34, 0x7f, 0x95, 0xed, 0x87, 0xa4, 0x5f, 0xfa,
|
|
0xe7, 0x42, 0x6f, 0x27, 0xa1, 0xdf, 0x5f, 0xb6, 0x91, 0x10,
|
|
0x04, 0x4c, 0x0d, 0x73, 0x11, 0x8e, 0xff, 0xa9, 0x5b, 0x01,
|
|
0xe5, 0xcf, 0x16, 0x6d, 0x3d, 0xf2, 0xd7, 0x21, 0xca, 0xf9,
|
|
0xb2, 0x1e, 0x5f, 0xb1, 0x4c, 0x61, 0x68, 0x71, 0xfd, 0x84,
|
|
0xc5, 0x4f, 0x9d, 0x65, 0xb2, 0x83, 0x19, 0x6c, 0x7f, 0xe4,
|
|
0xf6, 0x05, 0x53, 0xeb, 0xf3, 0x9c, 0x64, 0x02, 0xc4, 0x22,
|
|
0x34, 0xe3, 0x2a, 0x35, 0x6b, 0x3e, 0x76, 0x43, 0x12, 0xa6,
|
|
0x1a, 0x55, 0x32, 0x05, 0x57, 0x16, 0xea, 0xd6, 0x96, 0x25,
|
|
0x68, 0xf8, 0x7d, 0x3f, 0x3f, 0x77, 0x04, 0xc6, 0xa8, 0xd1,
|
|
0xbc, 0xd1, 0xbf, 0x4d, 0x50, 0xd6, 0x15, 0x4b, 0x6d, 0xa7,
|
|
0x31, 0xb1, 0x87, 0xb5, 0x8d, 0xfd, 0x72, 0x8a, 0xfa, 0x36,
|
|
0x75, 0x7a, 0x79, 0x7a, 0xc1, 0x88, 0xd1 ]
|
|
|
|
property allTestsPass =
|
|
([ // Basic tests
|
|
qround01, core01, core02
|
|
// Full RFC test vectors
|
|
, rfctest01, rfctest02, rfctest03
|
|
] : [_]Bit) == ~zero // All test bits should equal one
|
|
|
|
/* -------------------------------------------------------------------------- */
|
|
/* -- Private utilities ----------------------------------------------------- */
|
|
|
|
private
|
|
// Convert a round into a block, by splitting every 32-bit round entry
|
|
// into 4 bytes, and then serialize those values into a full block.
|
|
blocked : Round -> Block
|
|
blocked x = join (map toBytes x)
|
|
where
|
|
// This essentially splits a 32-bit number into 4-byte
|
|
// little-endian form, where 'rjoin' is the inverse and would merge
|
|
// 4 bytes as a 32-bit little endian number.
|
|
toBytes : [32] -> [4][8]
|
|
toBytes v = reverse (groupBy`{8} v)
|
|
|
|
// Map a function over a finite list.
|
|
map : { a, b, c }
|
|
(a -> b) -> [c]a -> [c]b
|
|
map f xs = [ f x | x <- xs ]
|
|
|
|
// Map a function iteratively over a seed value, producing an infinite
|
|
// list of successive function applications:
|
|
//
|
|
// iterate f 0 == [ 0, f 0, f (f 0), f (f (f 0)), ... ]
|
|
iterate : { a } (a -> a) -> a -> [inf]a
|
|
iterate f x = [x] # [ f v | v <- iterate f x ]
|
|
where
|
|
// NB: Needs a binded name in order to tie the recursive knot.
|
|
xs = [x] # [ f v | v <- xs ]
|
|
|
|
// rjoin = join . reverse
|
|
// This encodes a sequence of values as a little endian number
|
|
// e.g. [ 0xaa, 0xbb, 0xcc, 0xdd ] is serialized as \xdd\xcc\xbb\xaa
|
|
rjoin : {a, b, c}
|
|
( fin a, fin c
|
|
) => [c][a]b -> [a * c]b
|
|
rjoin x = join (reverse x)
|