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Bug 1432431 - Land Cryptol/SAW specs for Poly1305 r=franziskus
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Summary:
I wrote Cryptol and SAW specs for Poly1305 that are able to verify our
implementations for a single input/key pair. The 128-bit multiplication isn't
verifiable as-is. It takes forever, almost literally. We would need to take
the HACL* approach and gently guide Z3 to link the mathematical spec to the
optimized spec.

Let's not do this now, let's just land the specs so we have them in the repo.

Reviewers: franziskus

Reviewed By: franziskus

Bug #: 1432431

Differential Revision: https://phabricator.services.mozilla.com/D430
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Tim Taubert committed Jan 26, 2018
1 parent cc239ff commit 78966f8
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38 changes: 38 additions & 0 deletions automation/saw/poly1305-hacl.saw
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// This Source Code Form is subject to the terms of the Mozilla Public
// License, v. 2.0. If a copy of the MPL was not distributed with this
// file, You can obtain one at http://mozilla.org/MPL/2.0/.

import "poly1305.cry" as poly1305;

print "Proving Poly1305 spec...";
prove_print abc {{ poly1305::allTestsPass }};

print "Loading LLVM bitcode...";
m <- llvm_load_module "../../../dist/Debug/lib/libfreeblpriv3.so.bc";

let SpecPoly1305 n = do {
llvm_ptr "output" (llvm_array 16 (llvm_int 8));
output <- llvm_var "*output" (llvm_array 16 (llvm_int 8));

llvm_ptr "input" (llvm_array n (llvm_int 8));
input <- llvm_var "*input" (llvm_array n (llvm_int 8));

llvm_var "len1" (llvm_int 64);
llvm_ptr "k1" (llvm_array 32 (llvm_int 8));
k1 <- llvm_var "*k1" (llvm_array 32 (llvm_int 8));

llvm_assert_eq "*input" {{ zero : [n][8] }};
llvm_assert_eq "len1" {{ `n : [64] }};

llvm_assert_eq "*k1" {{ zero : [32][8] }};

let res = {{ poly1305::Poly1305 input (take`{16} k1) (drop`{16} k1) }};
llvm_ensure_eq "*output" {{ res }};

llvm_verify_tactic abc;
};

print "Proving equality for a single block...";
// This is currently disabled as it takes way too long. We need to help Z3
// prove this before we can enable it on Taskcluster.
//time (llvm_verify m "Hacl_Poly1305_64_crypto_onetimeauth" [] (SpecPoly1305 16));
336 changes: 336 additions & 0 deletions automation/saw/poly1305.cry
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/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */

/* This file provides a spec of the Poly1305 one-time authenticator.
* See <https://tools.ietf.org/html/rfc7539> for details. */

module poly1305 where

P : [136]
P = 2^^130 - 5

Poly1305 : {n} (fin n) => [n][8] -> [16][8] -> [16][8] -> [16][8]
Poly1305 msg r s = reverse (groupBy (drop ((rounds ! 0) + s')))
where
rounds = [zero] # [ Poly1305_block acc r' b | b <- blocks | acc <- rounds ]
r' = zero # (Poly1305_clamp (join (reverse r)))
s' = zero # (join (reverse s))
blocks = Poly1305_split msg

private
// 0x0f - for r[3], r[7], r[11], r[15]
// 0xfc - for r[4], r[8], r[12]
Poly1305_clamp r = r && 0x0ffffffc0ffffffc0ffffffc0fffffff

// Poly1305_block : ((acc + msg) * r) % P
Poly1305_block : [136] -> [136] -> [136] -> [136]
Poly1305_block acc r msg = drop (prod % (zero # P))
where
acc' : [137]
// Add the current block to the accumulator.
acc' = (zero # acc) + (zero # msg)
prod : [273]
// Multiply the new accumulator value by r.
prod = ((zero : [137]) # r) * ((zero : [136]) # acc')

Poly1305_split : {n, nb, nf} (fin n, nf == n / 16, nb == (n + 15) / 16) => [n][8] -> [nb][136]
Poly1305_split msg = take ((h1 : [nf][136]) # h2)
where
// Split all full 16-byte blocks and append 0x01, then convert to LE.
h1 = [ join (reverse (b # [0x01])) | b <- groupBy`{16} (take msg)]
// Pad the remaining bytes (if any) and convert to LE.
h2 = [join (reverse ((drop`{nf * 16} msg) # [0x01] # zero))]

/* -------------------------------------------------------------------------- */
/* -- Tests ----------------------------------------------------------------- */

private
// https://tools.ietf.org/html/rfc7539#section-2.5.2
rval1 = [0x85, 0xd6, 0xbe, 0x78, 0x57, 0x55, 0x6d, 0x33,
0x7f, 0x44, 0x52, 0xfe, 0x42, 0xd5, 0x06, 0xa8]
sval1 = [0x01, 0x03, 0x80, 0x8a, 0xfb, 0x0d, 0xb2, 0xfd,
0x4a, 0xbf, 0xf6, 0xaf, 0x41, 0x49, 0xf5, 0x1b]
text1 = [0x43, 0x72, 0x79, 0x70, 0x74, 0x6f, 0x67, 0x72,
0x61, 0x70, 0x68, 0x69, 0x63, 0x20, 0x46, 0x6f,
0x72, 0x75, 0x6d, 0x20, 0x52, 0x65, 0x73, 0x65,
0x61, 0x72, 0x63, 0x68, 0x20, 0x47, 0x72, 0x6f,
0x75, 0x70]

rfctest01 = Poly1305 text1 rval1 sval1
== [0xa8, 0x06, 0x1d, 0xc1, 0x30, 0x51, 0x36, 0xc6,
0xc2, 0x2b, 0x8b, 0xaf, 0x0c, 0x01, 0x27, 0xa9]

// https://tools.ietf.org/html/rfc7539#appendix-A.3
// Test Vector #1
rval2 = [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
sval2 = [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
text2 = [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

rfctest02 = Poly1305 text2 rval2 sval2
== [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

// https://tools.ietf.org/html/rfc7539#appendix-A.3
// Test Vector #2
rval3 = [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
sval3 = [0x36, 0xe5, 0xf6, 0xb5, 0xc5, 0xe0, 0x60, 0x70,
0xf0, 0xef, 0xca, 0x96, 0x22, 0x7a, 0x86, 0x3e]
text3 = [0x41, 0x6e, 0x79, 0x20, 0x73, 0x75, 0x62, 0x6d,
0x69, 0x73, 0x73, 0x69, 0x6f, 0x6e, 0x20, 0x74,
0x6f, 0x20, 0x74, 0x68, 0x65, 0x20, 0x49, 0x45,
0x54, 0x46, 0x20, 0x69, 0x6e, 0x74, 0x65, 0x6e,
0x64, 0x65, 0x64, 0x20, 0x62, 0x79, 0x20, 0x74,
0x68, 0x65, 0x20, 0x43, 0x6f, 0x6e, 0x74, 0x72,
0x69, 0x62, 0x75, 0x74, 0x6f, 0x72, 0x20, 0x66,
0x6f, 0x72, 0x20, 0x70, 0x75, 0x62, 0x6c, 0x69,
0x63, 0x61, 0x74, 0x69, 0x6f, 0x6e, 0x20, 0x61,
0x73, 0x20, 0x61, 0x6c, 0x6c, 0x20, 0x6f, 0x72,
0x20, 0x70, 0x61, 0x72, 0x74, 0x20, 0x6f, 0x66,
0x20, 0x61, 0x6e, 0x20, 0x49, 0x45, 0x54, 0x46,
0x20, 0x49, 0x6e, 0x74, 0x65, 0x72, 0x6e, 0x65,
0x74, 0x2d, 0x44, 0x72, 0x61, 0x66, 0x74, 0x20,
0x6f, 0x72, 0x20, 0x52, 0x46, 0x43, 0x20, 0x61,
0x6e, 0x64, 0x20, 0x61, 0x6e, 0x79, 0x20, 0x73,
0x74, 0x61, 0x74, 0x65, 0x6d, 0x65, 0x6e, 0x74,
0x20, 0x6d, 0x61, 0x64, 0x65, 0x20, 0x77, 0x69,
0x74, 0x68, 0x69, 0x6e, 0x20, 0x74, 0x68, 0x65,
0x20, 0x63, 0x6f, 0x6e, 0x74, 0x65, 0x78, 0x74,
0x20, 0x6f, 0x66, 0x20, 0x61, 0x6e, 0x20, 0x49,
0x45, 0x54, 0x46, 0x20, 0x61, 0x63, 0x74, 0x69,
0x76, 0x69, 0x74, 0x79, 0x20, 0x69, 0x73, 0x20,
0x63, 0x6f, 0x6e, 0x73, 0x69, 0x64, 0x65, 0x72,
0x65, 0x64, 0x20, 0x61, 0x6e, 0x20, 0x22, 0x49,
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, 0x65, 0x6e,
0x74, 0x73, 0x20, 0x69, 0x6e, 0x63, 0x6c, 0x75,
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, 0x65, 0x6c, 0x65, 0x63,
0x74, 0x72, 0x6f, 0x6e, 0x69, 0x63, 0x20, 0x63,
0x6f, 0x6d, 0x6d, 0x75, 0x6e, 0x69, 0x63, 0x61,
0x74, 0x69, 0x6f, 0x6e, 0x73, 0x20, 0x6d, 0x61,
0x64, 0x65, 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 = Poly1305 text3 rval3 sval3
== [0x36, 0xe5, 0xf6, 0xb5, 0xc5, 0xe0, 0x60, 0x70,
0xf0, 0xef, 0xca, 0x96, 0x22, 0x7a, 0x86, 0x3e]

// https://tools.ietf.org/html/rfc7539#appendix-A.3
// Test Vector #3
rval4 = [0x36, 0xe5, 0xf6, 0xb5, 0xc5, 0xe0, 0x60, 0x70,
0xf0, 0xef, 0xca, 0x96, 0x22, 0x7a, 0x86, 0x3e]
sval4 = [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
text4 = [0x41, 0x6e, 0x79, 0x20, 0x73, 0x75, 0x62, 0x6d,
0x69, 0x73, 0x73, 0x69, 0x6f, 0x6e, 0x20, 0x74,
0x6f, 0x20, 0x74, 0x68, 0x65, 0x20, 0x49, 0x45,
0x54, 0x46, 0x20, 0x69, 0x6e, 0x74, 0x65, 0x6e,
0x64, 0x65, 0x64, 0x20, 0x62, 0x79, 0x20, 0x74,
0x68, 0x65, 0x20, 0x43, 0x6f, 0x6e, 0x74, 0x72,
0x69, 0x62, 0x75, 0x74, 0x6f, 0x72, 0x20, 0x66,
0x6f, 0x72, 0x20, 0x70, 0x75, 0x62, 0x6c, 0x69,
0x63, 0x61, 0x74, 0x69, 0x6f, 0x6e, 0x20, 0x61,
0x73, 0x20, 0x61, 0x6c, 0x6c, 0x20, 0x6f, 0x72,
0x20, 0x70, 0x61, 0x72, 0x74, 0x20, 0x6f, 0x66,
0x20, 0x61, 0x6e, 0x20, 0x49, 0x45, 0x54, 0x46,
0x20, 0x49, 0x6e, 0x74, 0x65, 0x72, 0x6e, 0x65,
0x74, 0x2d, 0x44, 0x72, 0x61, 0x66, 0x74, 0x20,
0x6f, 0x72, 0x20, 0x52, 0x46, 0x43, 0x20, 0x61,
0x6e, 0x64, 0x20, 0x61, 0x6e, 0x79, 0x20, 0x73,
0x74, 0x61, 0x74, 0x65, 0x6d, 0x65, 0x6e, 0x74,
0x20, 0x6d, 0x61, 0x64, 0x65, 0x20, 0x77, 0x69,
0x74, 0x68, 0x69, 0x6e, 0x20, 0x74, 0x68, 0x65,
0x20, 0x63, 0x6f, 0x6e, 0x74, 0x65, 0x78, 0x74,
0x20, 0x6f, 0x66, 0x20, 0x61, 0x6e, 0x20, 0x49,
0x45, 0x54, 0x46, 0x20, 0x61, 0x63, 0x74, 0x69,
0x76, 0x69, 0x74, 0x79, 0x20, 0x69, 0x73, 0x20,
0x63, 0x6f, 0x6e, 0x73, 0x69, 0x64, 0x65, 0x72,
0x65, 0x64, 0x20, 0x61, 0x6e, 0x20, 0x22, 0x49,
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, 0x65, 0x6e,
0x74, 0x73, 0x20, 0x69, 0x6e, 0x63, 0x6c, 0x75,
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, 0x65, 0x6c, 0x65, 0x63,
0x74, 0x72, 0x6f, 0x6e, 0x69, 0x63, 0x20, 0x63,
0x6f, 0x6d, 0x6d, 0x75, 0x6e, 0x69, 0x63, 0x61,
0x74, 0x69, 0x6f, 0x6e, 0x73, 0x20, 0x6d, 0x61,
0x64, 0x65, 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]

rfctest04 = Poly1305 text4 rval4 sval4
== [0xf3, 0x47, 0x7e, 0x7c, 0xd9, 0x54, 0x17, 0xaf,
0x89, 0xa6, 0xb8, 0x79, 0x4c, 0x31, 0x0c, 0xf0]

// https://tools.ietf.org/html/rfc7539#appendix-A.3
// Test Vector #4
rval5 = [0x1c, 0x92, 0x40, 0xa5, 0xeb, 0x55, 0xd3, 0x8a,
0xf3, 0x33, 0x88, 0x86, 0x04, 0xf6, 0xb5, 0xf0]
sval5 = [0x47, 0x39, 0x17, 0xc1, 0x40, 0x2b, 0x80, 0x09,
0x9d, 0xca, 0x5c, 0xbc, 0x20, 0x70, 0x75, 0xc0]
text5 = [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]

rfctest05 = Poly1305 text5 rval5 sval5
== [0x45, 0x41, 0x66, 0x9a, 0x7e, 0xaa, 0xee, 0x61,
0xe7, 0x08, 0xdc, 0x7c, 0xbc, 0xc5, 0xeb, 0x62]

// https://tools.ietf.org/html/rfc7539#appendix-A.3
// Test Vector #5
rval6 = [0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
sval6 = [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
text6 = [0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff]

rfctest06 = Poly1305 text6 rval6 sval6
== [0x03, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

// https://tools.ietf.org/html/rfc7539#appendix-A.3
// Test Vector #6
rval7 = [0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
sval7 = [0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff]
text7 = [0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

rfctest07 = Poly1305 text7 rval7 sval7
== [0x03, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

// https://tools.ietf.org/html/rfc7539#appendix-A.3
// Test Vector #7
rval8 = [0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
sval8 = [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
text8 = [0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0x11, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

rfctest08 = Poly1305 text8 rval8 sval8
== [0x05, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

// https://tools.ietf.org/html/rfc7539#appendix-A.3
// Test Vector #8
rval9 = [0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
sval9 = [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
text9 = [0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xfb, 0xfe, 0xfe, 0xfe, 0xfe, 0xfe, 0xfe, 0xfe,
0xfe, 0xfe, 0xfe, 0xfe, 0xfe, 0xfe, 0xfe, 0xfe,
0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01,
0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01]

rfctest09 = Poly1305 text9 rval9 sval9
== [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

// https://tools.ietf.org/html/rfc7539#appendix-A.3
// Test Vector #9
rval10 = [0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
sval10 = [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
text10 = [0xfd, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff]

rfctest10 = Poly1305 text10 rval10 sval10
== [0xfa, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff]

// https://tools.ietf.org/html/rfc7539#appendix-A.3
// Test Vector #10
rval11 = [0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
sval11 = [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
text11 = [0xe3, 0x35, 0x94, 0xd7, 0x50, 0x5e, 0x43, 0xb9,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x33, 0x94, 0xd7, 0x50, 0x5e, 0x43, 0x79, 0xcd,
0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

rfctest11 = Poly1305 text11 rval11 sval11
== [0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x55, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

// https://tools.ietf.org/html/rfc7539#appendix-A.3
// Test Vector #11
rval12 = [0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
sval12 = [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
text12 = [0xe3, 0x35, 0x94, 0xd7, 0x50, 0x5e, 0x43, 0xb9,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x33, 0x94, 0xd7, 0x50, 0x5e, 0x43, 0x79, 0xcd,
0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

rfctest12 = Poly1305 text12 rval12 sval12
== [0x13, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]

property allTestsPass =
([ // Full RFC test vectors
rfctest01, rfctest02, rfctest03, rfctest04,
rfctest05, rfctest06, rfctest07, rfctest08,
rfctest09, rfctest10, rfctest11, rfctest12
] : [_]Bit) == ~zero // All test bits should equal one

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