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zig/lib/std/crypto/chacha20.zig
Frank Denis 6f9ea9eaef Breaking: sort std/crypto functions into categories 
Instead of having all primitives and constructions share the same namespace,
they are now organized by category and function family.

Types within the same category are expected to share the exact same API.
2020-08-20 23:02:05 +02:00

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Zig
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// SPDX-License-Identifier: MIT
// Copyright (c) 2015-2020 Zig Contributors
// This file is part of [zig](https://ziglang.org/), which is MIT licensed.
// The MIT license requires this copyright notice to be included in all copies
// and substantial portions of the software.
// Based on public domain Supercop by Daniel J. Bernstein
const std = @import("../std.zig");
const mem = std.mem;
const endian = std.endian;
const assert = std.debug.assert;
const testing = std.testing;
const builtin = @import("builtin");
const maxInt = std.math.maxInt;
const Poly1305 = std.crypto.onetimeauth.Poly1305;
const QuarterRound = struct {
a: usize,
b: usize,
c: usize,
d: usize,
};
fn Rp(a: usize, b: usize, c: usize, d: usize) QuarterRound {
return QuarterRound{
.a = a,
.b = b,
.c = c,
.d = d,
};
}
fn initContext(key: [8]u32, d: [4]u32) [16]u32 {
var ctx: [16]u32 = undefined;
const c = "expand 32-byte k";
const constant_le = comptime [_]u32{
mem.readIntLittle(u32, c[0..4]),
mem.readIntLittle(u32, c[4..8]),
mem.readIntLittle(u32, c[8..12]),
mem.readIntLittle(u32, c[12..16]),
};
mem.copy(u32, ctx[0..], constant_le[0..4]);
mem.copy(u32, ctx[4..12], key[0..8]);
mem.copy(u32, ctx[12..16], d[0..4]);
return ctx;
}
// The chacha family of ciphers are based on the salsa family.
fn chacha20Core(x: []u32, input: [16]u32) void {
for (x) |_, i|
x[i] = input[i];
const rounds = comptime [_]QuarterRound{
Rp(0, 4, 8, 12),
Rp(1, 5, 9, 13),
Rp(2, 6, 10, 14),
Rp(3, 7, 11, 15),
Rp(0, 5, 10, 15),
Rp(1, 6, 11, 12),
Rp(2, 7, 8, 13),
Rp(3, 4, 9, 14),
};
comptime var j: usize = 0;
inline while (j < 20) : (j += 2) {
// two-round cycles
inline for (rounds) |r| {
x[r.a] +%= x[r.b];
x[r.d] = std.math.rotl(u32, x[r.d] ^ x[r.a], @as(u32, 16));
x[r.c] +%= x[r.d];
x[r.b] = std.math.rotl(u32, x[r.b] ^ x[r.c], @as(u32, 12));
x[r.a] +%= x[r.b];
x[r.d] = std.math.rotl(u32, x[r.d] ^ x[r.a], @as(u32, 8));
x[r.c] +%= x[r.d];
x[r.b] = std.math.rotl(u32, x[r.b] ^ x[r.c], @as(u32, 7));
}
}
}
fn hashToBytes(out: []u8, x: [16]u32) void {
for (x) |_, i| {
mem.writeIntLittle(u32, out[4 * i ..][0..4], x[i]);
}
}
fn chaCha20_internal(out: []u8, in: []const u8, key: [8]u32, counter: [4]u32) void {
var ctx = initContext(key, counter);
var remaining: usize = if (in.len > out.len) in.len else out.len;
var cursor: usize = 0;
while (true) {
var x: [16]u32 = undefined;
var buf: [64]u8 = undefined;
chacha20Core(x[0..], ctx);
for (x) |_, i| {
x[i] +%= ctx[i];
}
hashToBytes(buf[0..], x);
if (remaining < 64) {
var i: usize = 0;
while (i < remaining) : (i += 1)
out[cursor + i] = in[cursor + i] ^ buf[i];
return;
}
var i: usize = 0;
while (i < 64) : (i += 1)
out[cursor + i] = in[cursor + i] ^ buf[i];
cursor += 64;
remaining -= 64;
ctx[12] += 1;
}
}
fn keyToWords(key: [32]u8) [8]u32 {
var k: [8]u32 = undefined;
k[0] = mem.readIntLittle(u32, key[0..4]);
k[1] = mem.readIntLittle(u32, key[4..8]);
k[2] = mem.readIntLittle(u32, key[8..12]);
k[3] = mem.readIntLittle(u32, key[12..16]);
k[4] = mem.readIntLittle(u32, key[16..20]);
k[5] = mem.readIntLittle(u32, key[20..24]);
k[6] = mem.readIntLittle(u32, key[24..28]);
k[7] = mem.readIntLittle(u32, key[28..32]);
return k;
}
/// ChaCha20 avoids the possibility of timing attacks, as there are no branches
/// on secret key data.
///
/// in and out should be the same length.
/// counter should generally be 0 or 1
///
/// ChaCha20 is self-reversing. To decrypt just run the cipher with the same
/// counter, nonce, and key.
pub const ChaCha20IETF = struct {
pub fn xor(out: []u8, in: []const u8, counter: u32, key: [32]u8, nonce: [12]u8) void {
assert(in.len >= out.len);
assert((in.len >> 6) + counter <= maxInt(u32));
var c: [4]u32 = undefined;
c[0] = counter;
c[1] = mem.readIntLittle(u32, nonce[0..4]);
c[2] = mem.readIntLittle(u32, nonce[4..8]);
c[3] = mem.readIntLittle(u32, nonce[8..12]);
chaCha20_internal(out, in, keyToWords(key), c);
}
};
/// This is the original ChaCha20 before RFC 7539, which recommends using the
/// orgininal version on applications such as disk or file encryption that might
/// exceed the 256 GiB limit of the 96-bit nonce version.
pub const ChaCha20With64BitNonce = struct {
pub fn xor(out: []u8, in: []const u8, counter: u64, key: [32]u8, nonce: [8]u8) void {
assert(in.len >= out.len);
assert(counter +% (in.len >> 6) >= counter);
var cursor: usize = 0;
const k = keyToWords(key);
var c: [4]u32 = undefined;
c[0] = @truncate(u32, counter);
c[1] = @truncate(u32, counter >> 32);
c[2] = mem.readIntLittle(u32, nonce[0..4]);
c[3] = mem.readIntLittle(u32, nonce[4..8]);
const block_size = (1 << 6);
// The full block size is greater than the address space on a 32bit machine
const big_block = if (@sizeOf(usize) > 4) (block_size << 32) else maxInt(usize);
// first partial big block
if (((@intCast(u64, maxInt(u32) - @truncate(u32, counter)) + 1) << 6) < in.len) {
chaCha20_internal(out[cursor..big_block], in[cursor..big_block], k, c);
cursor = big_block - cursor;
c[1] += 1;
if (comptime @sizeOf(usize) > 4) {
// A big block is giant: 256 GiB, but we can avoid this limitation
var remaining_blocks: u32 = @intCast(u32, (in.len / big_block));
var i: u32 = 0;
while (remaining_blocks > 0) : (remaining_blocks -= 1) {
chaCha20_internal(out[cursor .. cursor + big_block], in[cursor .. cursor + big_block], k, c);
c[1] += 1; // upper 32-bit of counter, generic chaCha20_internal() doesn't know about this.
cursor += big_block;
}
}
}
chaCha20_internal(out[cursor..], in[cursor..], k, c);
}
};
// https://tools.ietf.org/html/rfc7539#section-2.4.2
test "crypto.chacha20 test vector sunscreen" {
const expected_result = [_]u8{
0x6e, 0x2e, 0x35, 0x9a, 0x25, 0x68, 0xf9, 0x80,
0x41, 0xba, 0x07, 0x28, 0xdd, 0x0d, 0x69, 0x81,
0xe9, 0x7e, 0x7a, 0xec, 0x1d, 0x43, 0x60, 0xc2,
0x0a, 0x27, 0xaf, 0xcc, 0xfd, 0x9f, 0xae, 0x0b,
0xf9, 0x1b, 0x65, 0xc5, 0x52, 0x47, 0x33, 0xab,
0x8f, 0x59, 0x3d, 0xab, 0xcd, 0x62, 0xb3, 0x57,
0x16, 0x39, 0xd6, 0x24, 0xe6, 0x51, 0x52, 0xab,
0x8f, 0x53, 0x0c, 0x35, 0x9f, 0x08, 0x61, 0xd8,
0x07, 0xca, 0x0d, 0xbf, 0x50, 0x0d, 0x6a, 0x61,
0x56, 0xa3, 0x8e, 0x08, 0x8a, 0x22, 0xb6, 0x5e,
0x52, 0xbc, 0x51, 0x4d, 0x16, 0xcc, 0xf8, 0x06,
0x81, 0x8c, 0xe9, 0x1a, 0xb7, 0x79, 0x37, 0x36,
0x5a, 0xf9, 0x0b, 0xbf, 0x74, 0xa3, 0x5b, 0xe6,
0xb4, 0x0b, 0x8e, 0xed, 0xf2, 0x78, 0x5e, 0x42,
0x87, 0x4d,
};
const input = "Ladies and Gentlemen of the class of '99: If I could offer you only one tip for the future, sunscreen would be it.";
var result: [114]u8 = undefined;
const key = [_]u8{
0, 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12, 13, 14, 15,
16, 17, 18, 19, 20, 21, 22, 23,
24, 25, 26, 27, 28, 29, 30, 31,
};
const nonce = [_]u8{
0, 0, 0, 0,
0, 0, 0, 0x4a,
0, 0, 0, 0,
};
ChaCha20IETF.xor(result[0..], input[0..], 1, key, nonce);
testing.expectEqualSlices(u8, &expected_result, &result);
// Chacha20 is self-reversing.
var plaintext: [114]u8 = undefined;
ChaCha20IETF.xor(plaintext[0..], result[0..], 1, key, nonce);
testing.expect(mem.order(u8, input, &plaintext) == .eq);
}
// https://tools.ietf.org/html/draft-agl-tls-chacha20poly1305-04#section-7
test "crypto.chacha20 test vector 1" {
const expected_result = [_]u8{
0x76, 0xb8, 0xe0, 0xad, 0xa0, 0xf1, 0x3d, 0x90,
0x40, 0x5d, 0x6a, 0xe5, 0x53, 0x86, 0xbd, 0x28,
0xbd, 0xd2, 0x19, 0xb8, 0xa0, 0x8d, 0xed, 0x1a,
0xa8, 0x36, 0xef, 0xcc, 0x8b, 0x77, 0x0d, 0xc7,
0xda, 0x41, 0x59, 0x7c, 0x51, 0x57, 0x48, 0x8d,
0x77, 0x24, 0xe0, 0x3f, 0xb8, 0xd8, 0x4a, 0x37,
0x6a, 0x43, 0xb8, 0xf4, 0x15, 0x18, 0xa1, 0x1c,
0xc3, 0x87, 0xb6, 0x69, 0xb2, 0xee, 0x65, 0x86,
};
const input = [_]u8{
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,
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,
};
var result: [64]u8 = undefined;
const key = [_]u8{
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
};
const nonce = [_]u8{ 0, 0, 0, 0, 0, 0, 0, 0 };
ChaCha20With64BitNonce.xor(result[0..], input[0..], 0, key, nonce);
testing.expectEqualSlices(u8, &expected_result, &result);
}
test "crypto.chacha20 test vector 2" {
const expected_result = [_]u8{
0x45, 0x40, 0xf0, 0x5a, 0x9f, 0x1f, 0xb2, 0x96,
0xd7, 0x73, 0x6e, 0x7b, 0x20, 0x8e, 0x3c, 0x96,
0xeb, 0x4f, 0xe1, 0x83, 0x46, 0x88, 0xd2, 0x60,
0x4f, 0x45, 0x09, 0x52, 0xed, 0x43, 0x2d, 0x41,
0xbb, 0xe2, 0xa0, 0xb6, 0xea, 0x75, 0x66, 0xd2,
0xa5, 0xd1, 0xe7, 0xe2, 0x0d, 0x42, 0xaf, 0x2c,
0x53, 0xd7, 0x92, 0xb1, 0xc4, 0x3f, 0xea, 0x81,
0x7e, 0x9a, 0xd2, 0x75, 0xae, 0x54, 0x69, 0x63,
};
const input = [_]u8{
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,
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,
};
var result: [64]u8 = undefined;
const key = [_]u8{
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1,
};
const nonce = [_]u8{ 0, 0, 0, 0, 0, 0, 0, 0 };
ChaCha20With64BitNonce.xor(result[0..], input[0..], 0, key, nonce);
testing.expectEqualSlices(u8, &expected_result, &result);
}
test "crypto.chacha20 test vector 3" {
const expected_result = [_]u8{
0xde, 0x9c, 0xba, 0x7b, 0xf3, 0xd6, 0x9e, 0xf5,
0xe7, 0x86, 0xdc, 0x63, 0x97, 0x3f, 0x65, 0x3a,
0x0b, 0x49, 0xe0, 0x15, 0xad, 0xbf, 0xf7, 0x13,
0x4f, 0xcb, 0x7d, 0xf1, 0x37, 0x82, 0x10, 0x31,
0xe8, 0x5a, 0x05, 0x02, 0x78, 0xa7, 0x08, 0x45,
0x27, 0x21, 0x4f, 0x73, 0xef, 0xc7, 0xfa, 0x5b,
0x52, 0x77, 0x06, 0x2e, 0xb7, 0xa0, 0x43, 0x3e,
0x44, 0x5f, 0x41, 0xe3,
};
const input = [_]u8{
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,
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,
};
var result: [60]u8 = undefined;
const key = [_]u8{
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
};
const nonce = [_]u8{ 0, 0, 0, 0, 0, 0, 0, 1 };
ChaCha20With64BitNonce.xor(result[0..], input[0..], 0, key, nonce);
testing.expectEqualSlices(u8, &expected_result, &result);
}
test "crypto.chacha20 test vector 4" {
const expected_result = [_]u8{
0xef, 0x3f, 0xdf, 0xd6, 0xc6, 0x15, 0x78, 0xfb,
0xf5, 0xcf, 0x35, 0xbd, 0x3d, 0xd3, 0x3b, 0x80,
0x09, 0x63, 0x16, 0x34, 0xd2, 0x1e, 0x42, 0xac,
0x33, 0x96, 0x0b, 0xd1, 0x38, 0xe5, 0x0d, 0x32,
0x11, 0x1e, 0x4c, 0xaf, 0x23, 0x7e, 0xe5, 0x3c,
0xa8, 0xad, 0x64, 0x26, 0x19, 0x4a, 0x88, 0x54,
0x5d, 0xdc, 0x49, 0x7a, 0x0b, 0x46, 0x6e, 0x7d,
0x6b, 0xbd, 0xb0, 0x04, 0x1b, 0x2f, 0x58, 0x6b,
};
const input = [_]u8{
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,
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,
};
var result: [64]u8 = undefined;
const key = [_]u8{
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
};
const nonce = [_]u8{ 1, 0, 0, 0, 0, 0, 0, 0 };
ChaCha20With64BitNonce.xor(result[0..], input[0..], 0, key, nonce);
testing.expectEqualSlices(u8, &expected_result, &result);
}
test "crypto.chacha20 test vector 5" {
const expected_result = [_]u8{
0xf7, 0x98, 0xa1, 0x89, 0xf1, 0x95, 0xe6, 0x69,
0x82, 0x10, 0x5f, 0xfb, 0x64, 0x0b, 0xb7, 0x75,
0x7f, 0x57, 0x9d, 0xa3, 0x16, 0x02, 0xfc, 0x93,
0xec, 0x01, 0xac, 0x56, 0xf8, 0x5a, 0xc3, 0xc1,
0x34, 0xa4, 0x54, 0x7b, 0x73, 0x3b, 0x46, 0x41,
0x30, 0x42, 0xc9, 0x44, 0x00, 0x49, 0x17, 0x69,
0x05, 0xd3, 0xbe, 0x59, 0xea, 0x1c, 0x53, 0xf1,
0x59, 0x16, 0x15, 0x5c, 0x2b, 0xe8, 0x24, 0x1a,
0x38, 0x00, 0x8b, 0x9a, 0x26, 0xbc, 0x35, 0x94,
0x1e, 0x24, 0x44, 0x17, 0x7c, 0x8a, 0xde, 0x66,
0x89, 0xde, 0x95, 0x26, 0x49, 0x86, 0xd9, 0x58,
0x89, 0xfb, 0x60, 0xe8, 0x46, 0x29, 0xc9, 0xbd,
0x9a, 0x5a, 0xcb, 0x1c, 0xc1, 0x18, 0xbe, 0x56,
0x3e, 0xb9, 0xb3, 0xa4, 0xa4, 0x72, 0xf8, 0x2e,
0x09, 0xa7, 0xe7, 0x78, 0x49, 0x2b, 0x56, 0x2e,
0xf7, 0x13, 0x0e, 0x88, 0xdf, 0xe0, 0x31, 0xc7,
0x9d, 0xb9, 0xd4, 0xf7, 0xc7, 0xa8, 0x99, 0x15,
0x1b, 0x9a, 0x47, 0x50, 0x32, 0xb6, 0x3f, 0xc3,
0x85, 0x24, 0x5f, 0xe0, 0x54, 0xe3, 0xdd, 0x5a,
0x97, 0xa5, 0xf5, 0x76, 0xfe, 0x06, 0x40, 0x25,
0xd3, 0xce, 0x04, 0x2c, 0x56, 0x6a, 0xb2, 0xc5,
0x07, 0xb1, 0x38, 0xdb, 0x85, 0x3e, 0x3d, 0x69,
0x59, 0x66, 0x09, 0x96, 0x54, 0x6c, 0xc9, 0xc4,
0xa6, 0xea, 0xfd, 0xc7, 0x77, 0xc0, 0x40, 0xd7,
0x0e, 0xaf, 0x46, 0xf7, 0x6d, 0xad, 0x39, 0x79,
0xe5, 0xc5, 0x36, 0x0c, 0x33, 0x17, 0x16, 0x6a,
0x1c, 0x89, 0x4c, 0x94, 0xa3, 0x71, 0x87, 0x6a,
0x94, 0xdf, 0x76, 0x28, 0xfe, 0x4e, 0xaa, 0xf2,
0xcc, 0xb2, 0x7d, 0x5a, 0xaa, 0xe0, 0xad, 0x7a,
0xd0, 0xf9, 0xd4, 0xb6, 0xad, 0x3b, 0x54, 0x09,
0x87, 0x46, 0xd4, 0x52, 0x4d, 0x38, 0x40, 0x7a,
0x6d, 0xeb, 0x3a, 0xb7, 0x8f, 0xab, 0x78, 0xc9,
};
const input = [_]u8{
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
};
var result: [256]u8 = undefined;
const key = [_]u8{
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,
0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f,
};
const nonce = [_]u8{
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
};
ChaCha20With64BitNonce.xor(result[0..], input[0..], 0, key, nonce);
testing.expectEqualSlices(u8, &expected_result, &result);
}
pub const chacha20poly1305_tag_size = 16;
fn chacha20poly1305SealDetached(ciphertext: []u8, tag: *[chacha20poly1305_tag_size]u8, plaintext: []const u8, data: []const u8, key: [32]u8, nonce: [12]u8) void {
assert(ciphertext.len >= plaintext.len);
// derive poly1305 key
var polyKey = [_]u8{0} ** 32;
ChaCha20IETF.xor(polyKey[0..], polyKey[0..], 0, key, nonce);
// encrypt plaintext
ChaCha20IETF.xor(ciphertext[0..plaintext.len], plaintext, 1, key, nonce);
// construct mac
var mac = Poly1305.init(polyKey[0..]);
mac.update(data);
if (data.len % 16 != 0) {
const zeros = [_]u8{0} ** 16;
const padding = 16 - (data.len % 16);
mac.update(zeros[0..padding]);
}
mac.update(ciphertext[0..plaintext.len]);
if (plaintext.len % 16 != 0) {
const zeros = [_]u8{0} ** 16;
const padding = 16 - (plaintext.len % 16);
mac.update(zeros[0..padding]);
}
var lens: [16]u8 = undefined;
mem.writeIntLittle(u64, lens[0..8], data.len);
mem.writeIntLittle(u64, lens[8..16], plaintext.len);
mac.update(lens[0..]);
mac.final(tag);
}
fn chacha20poly1305Seal(ciphertextAndTag: []u8, plaintext: []const u8, data: []const u8, key: [32]u8, nonce: [12]u8) void {
return chacha20poly1305SealDetached(ciphertextAndTag[0..plaintext.len], ciphertextAndTag[plaintext.len..][0..chacha20poly1305_tag_size], plaintext, data, key, nonce);
}
/// Verifies and decrypts an authenticated message produced by chacha20poly1305SealDetached.
fn chacha20poly1305OpenDetached(dst: []u8, ciphertext: []const u8, tag: *const [chacha20poly1305_tag_size]u8, data: []const u8, key: [32]u8, nonce: [12]u8) !void {
// split ciphertext and tag
assert(dst.len >= ciphertext.len);
// derive poly1305 key
var polyKey = [_]u8{0} ** 32;
ChaCha20IETF.xor(polyKey[0..], polyKey[0..], 0, key, nonce);
// construct mac
var mac = Poly1305.init(polyKey[0..]);
mac.update(data);
if (data.len % 16 != 0) {
const zeros = [_]u8{0} ** 16;
const padding = 16 - (data.len % 16);
mac.update(zeros[0..padding]);
}
mac.update(ciphertext);
if (ciphertext.len % 16 != 0) {
const zeros = [_]u8{0} ** 16;
const padding = 16 - (ciphertext.len % 16);
mac.update(zeros[0..padding]);
}
var lens: [16]u8 = undefined;
mem.writeIntLittle(u64, lens[0..8], data.len);
mem.writeIntLittle(u64, lens[8..16], ciphertext.len);
mac.update(lens[0..]);
var computedTag: [16]u8 = undefined;
mac.final(computedTag[0..]);
// verify mac in constant time
// TODO: we can't currently guarantee that this will run in constant time.
// See https://github.com/ziglang/zig/issues/1776
var acc: u8 = 0;
for (computedTag) |_, i| {
acc |= (computedTag[i] ^ tag[i]);
}
if (acc != 0) {
return error.AuthenticationFailed;
}
// decrypt ciphertext
ChaCha20IETF.xor(dst[0..ciphertext.len], ciphertext, 1, key, nonce);
}
/// Verifies and decrypts an authenticated message produced by chacha20poly1305Seal.
fn chacha20poly1305Open(dst: []u8, ciphertextAndTag: []const u8, data: []const u8, key: [32]u8, nonce: [12]u8) !void {
if (ciphertextAndTag.len < chacha20poly1305_tag_size) {
return error.InvalidMessage;
}
const ciphertextLen = ciphertextAndTag.len - chacha20poly1305_tag_size;
return try chacha20poly1305OpenDetached(dst, ciphertextAndTag[0..ciphertextLen], ciphertextAndTag[ciphertextLen..][0..chacha20poly1305_tag_size], data, key, nonce);
}
fn hchacha20(input: [16]u8, key: [32]u8) [32]u8 {
var c: [4]u32 = undefined;
for (c) |_, i| {
c[i] = mem.readIntLittle(u32, input[4 * i ..][0..4]);
}
const ctx = initContext(keyToWords(key), c);
var x: [16]u32 = undefined;
chacha20Core(x[0..], ctx);
var out: [32]u8 = undefined;
mem.writeIntLittle(u32, out[0..4], x[0]);
mem.writeIntLittle(u32, out[4..8], x[1]);
mem.writeIntLittle(u32, out[8..12], x[2]);
mem.writeIntLittle(u32, out[12..16], x[3]);
mem.writeIntLittle(u32, out[16..20], x[12]);
mem.writeIntLittle(u32, out[20..24], x[13]);
mem.writeIntLittle(u32, out[24..28], x[14]);
mem.writeIntLittle(u32, out[28..32], x[15]);
return out;
}
fn extend(key: [32]u8, nonce: [24]u8) struct { key: [32]u8, nonce: [12]u8 } {
var subnonce: [12]u8 = undefined;
mem.set(u8, subnonce[0..4], 0);
mem.copy(u8, subnonce[4..], nonce[16..24]);
return .{
.key = hchacha20(nonce[0..16].*, key),
.nonce = subnonce,
};
}
pub const XChaCha20IETF = struct {
pub fn xor(out: []u8, in: []const u8, counter: u32, key: [32]u8, nonce: [24]u8) void {
const extended = extend(key, nonce);
ChaCha20IETF.xor(out, in, counter, extended.key, extended.nonce);
}
};
pub const xchacha20poly1305_tag_size = 16;
fn xchacha20poly1305SealDetached(ciphertext: []u8, tag: *[chacha20poly1305_tag_size]u8, plaintext: []const u8, data: []const u8, key: [32]u8, nonce: [24]u8) void {
const extended = extend(key, nonce);
return chacha20poly1305SealDetached(ciphertext, tag, plaintext, data, extended.key, extended.nonce);
}
fn xchacha20poly1305Seal(ciphertextAndTag: []u8, plaintext: []const u8, data: []const u8, key: [32]u8, nonce: [24]u8) void {
const extended = extend(key, nonce);
return chacha20poly1305Seal(ciphertextAndTag, plaintext, data, extended.key, extended.nonce);
}
/// Verifies and decrypts an authenticated message produced by xchacha20poly1305SealDetached.
fn xchacha20poly1305OpenDetached(plaintext: []u8, ciphertext: []const u8, tag: *const [chacha20poly1305_tag_size]u8, data: []const u8, key: [32]u8, nonce: [24]u8) !void {
const extended = extend(key, nonce);
return try chacha20poly1305OpenDetached(plaintext, ciphertext, tag, data, extended.key, extended.nonce);
}
/// Verifies and decrypts an authenticated message produced by xchacha20poly1305Seal.
fn xchacha20poly1305Open(ciphertextAndTag: []u8, msgAndTag: []const u8, data: []const u8, key: [32]u8, nonce: [24]u8) !void {
const extended = extend(key, nonce);
return try chacha20poly1305Open(ciphertextAndTag, msgAndTag, data, extended.key, extended.nonce);
}
test "seal" {
{
const plaintext = "";
const data = "";
const key = [_]u8{
0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f,
0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f,
};
const nonce = [_]u8{ 0x7, 0x0, 0x0, 0x0, 0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47 };
const exp_out = [_]u8{ 0xa0, 0x78, 0x4d, 0x7a, 0x47, 0x16, 0xf3, 0xfe, 0xb4, 0xf6, 0x4e, 0x7f, 0x4b, 0x39, 0xbf, 0x4 };
var out: [exp_out.len]u8 = undefined;
chacha20poly1305Seal(out[0..], plaintext, data, key, nonce);
testing.expectEqualSlices(u8, exp_out[0..], out[0..]);
}
{
const plaintext = [_]u8{
0x4c, 0x61, 0x64, 0x69, 0x65, 0x73, 0x20, 0x61, 0x6e, 0x64, 0x20, 0x47, 0x65, 0x6e, 0x74, 0x6c,
0x65, 0x6d, 0x65, 0x6e, 0x20, 0x6f, 0x66, 0x20, 0x74, 0x68, 0x65, 0x20, 0x63, 0x6c, 0x61, 0x73,
0x73, 0x20, 0x6f, 0x66, 0x20, 0x27, 0x39, 0x39, 0x3a, 0x20, 0x49, 0x66, 0x20, 0x49, 0x20, 0x63,
0x6f, 0x75, 0x6c, 0x64, 0x20, 0x6f, 0x66, 0x66, 0x65, 0x72, 0x20, 0x79, 0x6f, 0x75, 0x20, 0x6f,
0x6e, 0x6c, 0x79, 0x20, 0x6f, 0x6e, 0x65, 0x20, 0x74, 0x69, 0x70, 0x20, 0x66, 0x6f, 0x72, 0x20,
0x74, 0x68, 0x65, 0x20, 0x66, 0x75, 0x74, 0x75, 0x72, 0x65, 0x2c, 0x20, 0x73, 0x75, 0x6e, 0x73,
0x63, 0x72, 0x65, 0x65, 0x6e, 0x20, 0x77, 0x6f, 0x75, 0x6c, 0x64, 0x20, 0x62, 0x65, 0x20, 0x69,
0x74, 0x2e,
};
const data = [_]u8{ 0x50, 0x51, 0x52, 0x53, 0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7 };
const key = [_]u8{
0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f,
0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f,
};
const nonce = [_]u8{ 0x7, 0x0, 0x0, 0x0, 0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47 };
const exp_out = [_]u8{
0xd3, 0x1a, 0x8d, 0x34, 0x64, 0x8e, 0x60, 0xdb, 0x7b, 0x86, 0xaf, 0xbc, 0x53, 0xef, 0x7e, 0xc2,
0xa4, 0xad, 0xed, 0x51, 0x29, 0x6e, 0x8, 0xfe, 0xa9, 0xe2, 0xb5, 0xa7, 0x36, 0xee, 0x62, 0xd6,
0x3d, 0xbe, 0xa4, 0x5e, 0x8c, 0xa9, 0x67, 0x12, 0x82, 0xfa, 0xfb, 0x69, 0xda, 0x92, 0x72, 0x8b,
0x1a, 0x71, 0xde, 0xa, 0x9e, 0x6, 0xb, 0x29, 0x5, 0xd6, 0xa5, 0xb6, 0x7e, 0xcd, 0x3b, 0x36,
0x92, 0xdd, 0xbd, 0x7f, 0x2d, 0x77, 0x8b, 0x8c, 0x98, 0x3, 0xae, 0xe3, 0x28, 0x9, 0x1b, 0x58,
0xfa, 0xb3, 0x24, 0xe4, 0xfa, 0xd6, 0x75, 0x94, 0x55, 0x85, 0x80, 0x8b, 0x48, 0x31, 0xd7, 0xbc,
0x3f, 0xf4, 0xde, 0xf0, 0x8e, 0x4b, 0x7a, 0x9d, 0xe5, 0x76, 0xd2, 0x65, 0x86, 0xce, 0xc6, 0x4b,
0x61, 0x16, 0x1a, 0xe1, 0xb, 0x59, 0x4f, 0x9, 0xe2, 0x6a, 0x7e, 0x90, 0x2e, 0xcb, 0xd0, 0x60,
0x6, 0x91,
};
var out: [exp_out.len]u8 = undefined;
chacha20poly1305Seal(out[0..], plaintext[0..], data[0..], key, nonce);
testing.expectEqualSlices(u8, exp_out[0..], out[0..]);
}
}
test "open" {
{
const ciphertext = [_]u8{ 0xa0, 0x78, 0x4d, 0x7a, 0x47, 0x16, 0xf3, 0xfe, 0xb4, 0xf6, 0x4e, 0x7f, 0x4b, 0x39, 0xbf, 0x4 };
const data = "";
const key = [_]u8{
0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f,
0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f,
};
const nonce = [_]u8{ 0x7, 0x0, 0x0, 0x0, 0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47 };
const exp_out = "";
var out: [exp_out.len]u8 = undefined;
try chacha20poly1305Open(out[0..], ciphertext[0..], data, key, nonce);
testing.expectEqualSlices(u8, exp_out[0..], out[0..]);
}
{
const ciphertext = [_]u8{
0xd3, 0x1a, 0x8d, 0x34, 0x64, 0x8e, 0x60, 0xdb, 0x7b, 0x86, 0xaf, 0xbc, 0x53, 0xef, 0x7e, 0xc2,
0xa4, 0xad, 0xed, 0x51, 0x29, 0x6e, 0x8, 0xfe, 0xa9, 0xe2, 0xb5, 0xa7, 0x36, 0xee, 0x62, 0xd6,
0x3d, 0xbe, 0xa4, 0x5e, 0x8c, 0xa9, 0x67, 0x12, 0x82, 0xfa, 0xfb, 0x69, 0xda, 0x92, 0x72, 0x8b,
0x1a, 0x71, 0xde, 0xa, 0x9e, 0x6, 0xb, 0x29, 0x5, 0xd6, 0xa5, 0xb6, 0x7e, 0xcd, 0x3b, 0x36,
0x92, 0xdd, 0xbd, 0x7f, 0x2d, 0x77, 0x8b, 0x8c, 0x98, 0x3, 0xae, 0xe3, 0x28, 0x9, 0x1b, 0x58,
0xfa, 0xb3, 0x24, 0xe4, 0xfa, 0xd6, 0x75, 0x94, 0x55, 0x85, 0x80, 0x8b, 0x48, 0x31, 0xd7, 0xbc,
0x3f, 0xf4, 0xde, 0xf0, 0x8e, 0x4b, 0x7a, 0x9d, 0xe5, 0x76, 0xd2, 0x65, 0x86, 0xce, 0xc6, 0x4b,
0x61, 0x16, 0x1a, 0xe1, 0xb, 0x59, 0x4f, 0x9, 0xe2, 0x6a, 0x7e, 0x90, 0x2e, 0xcb, 0xd0, 0x60,
0x6, 0x91,
};
const data = [_]u8{ 0x50, 0x51, 0x52, 0x53, 0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7 };
const key = [_]u8{
0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f,
0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f,
};
const nonce = [_]u8{ 0x7, 0x0, 0x0, 0x0, 0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47 };
const exp_out = [_]u8{
0x4c, 0x61, 0x64, 0x69, 0x65, 0x73, 0x20, 0x61, 0x6e, 0x64, 0x20, 0x47, 0x65, 0x6e, 0x74, 0x6c,
0x65, 0x6d, 0x65, 0x6e, 0x20, 0x6f, 0x66, 0x20, 0x74, 0x68, 0x65, 0x20, 0x63, 0x6c, 0x61, 0x73,
0x73, 0x20, 0x6f, 0x66, 0x20, 0x27, 0x39, 0x39, 0x3a, 0x20, 0x49, 0x66, 0x20, 0x49, 0x20, 0x63,
0x6f, 0x75, 0x6c, 0x64, 0x20, 0x6f, 0x66, 0x66, 0x65, 0x72, 0x20, 0x79, 0x6f, 0x75, 0x20, 0x6f,
0x6e, 0x6c, 0x79, 0x20, 0x6f, 0x6e, 0x65, 0x20, 0x74, 0x69, 0x70, 0x20, 0x66, 0x6f, 0x72, 0x20,
0x74, 0x68, 0x65, 0x20, 0x66, 0x75, 0x74, 0x75, 0x72, 0x65, 0x2c, 0x20, 0x73, 0x75, 0x6e, 0x73,
0x63, 0x72, 0x65, 0x65, 0x6e, 0x20, 0x77, 0x6f, 0x75, 0x6c, 0x64, 0x20, 0x62, 0x65, 0x20, 0x69,
0x74, 0x2e,
};
var out: [exp_out.len]u8 = undefined;
try chacha20poly1305Open(out[0..], ciphertext[0..], data[0..], key, nonce);
testing.expectEqualSlices(u8, exp_out[0..], out[0..]);
// corrupting the ciphertext, data, key, or nonce should cause a failure
var bad_ciphertext = ciphertext;
bad_ciphertext[0] ^= 1;
testing.expectError(error.AuthenticationFailed, chacha20poly1305Open(out[0..], bad_ciphertext[0..], data[0..], key, nonce));
var bad_data = data;
bad_data[0] ^= 1;
testing.expectError(error.AuthenticationFailed, chacha20poly1305Open(out[0..], ciphertext[0..], bad_data[0..], key, nonce));
var bad_key = key;
bad_key[0] ^= 1;
testing.expectError(error.AuthenticationFailed, chacha20poly1305Open(out[0..], ciphertext[0..], data[0..], bad_key, nonce));
var bad_nonce = nonce;
bad_nonce[0] ^= 1;
testing.expectError(error.AuthenticationFailed, chacha20poly1305Open(out[0..], ciphertext[0..], data[0..], key, bad_nonce));
// a short ciphertext should result in a different error
testing.expectError(error.InvalidMessage, chacha20poly1305Open(out[0..], "", data[0..], key, bad_nonce));
}
}
test "crypto.xchacha20" {
const key = [_]u8{69} ** 32;
const nonce = [_]u8{42} ** 24;
const input = "Ladies and Gentlemen of the class of '99: If I could offer you only one tip for the future, sunscreen would be it.";
{
var ciphertext: [input.len]u8 = undefined;
XChaCha20IETF.xor(ciphertext[0..], input[0..], 0, key, nonce);
var buf: [2 * ciphertext.len]u8 = undefined;
testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{ciphertext}), "E0A1BCF939654AFDBDC1746EC49832647C19D891F0D1A81FC0C1703B4514BDEA584B512F6908C2C5E9DD18D5CBC1805DE5803FE3B9CA5F193FB8359E91FAB0C3BB40309A292EB1CF49685C65C4A3ADF4F11DB0CD2B6B67FBC174BC2E860E8F769FD3565BBFAD1C845E05A0FED9BE167C240D");
}
{
const data = "Additional data";
var ciphertext: [input.len + xchacha20poly1305_tag_size]u8 = undefined;
xchacha20poly1305Seal(ciphertext[0..], input, data, key, nonce);
var out: [input.len]u8 = undefined;
try xchacha20poly1305Open(out[0..], ciphertext[0..], data, key, nonce);
var buf: [2 * ciphertext.len]u8 = undefined;
testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{ciphertext}), "994D2DD32333F48E53650C02C7A2ABB8E018B0836D7175AEC779F52E961780768F815C58F1AA52D211498DB89B9216763F569C9433A6BBFCEFB4D4A49387A4C5207FBB3B5A92B5941294DF30588C6740D39DC16FA1F0E634F7246CF7CDCB978E44347D89381B7A74EB7084F754B90BDE9AAF5A94B8F2A85EFD0B50692AE2D425E234");
testing.expectEqualSlices(u8, out[0..], input);
ciphertext[0] += 1;
testing.expectError(error.AuthenticationFailed, xchacha20poly1305Open(out[0..], ciphertext[0..], data, key, nonce));
}
}
pub const Chacha20Poly1305 = struct {
pub const tag_length = 16;
pub const nonce_length = 12;
pub const key_length = 32;
/// c: ciphertext: output buffer should be of size m.len
/// at: authentication tag: output MAC
/// m: message
/// ad: Associated Data
/// npub: public nonce
/// k: private key
pub fn encrypt(c: []u8, at: *[tag_length]u8, m: []const u8, ad: []const u8, npub: [nonce_length]u8, k: [key_length]u8) void {
assert(c.len == m.len);
return chacha20poly1305SealDetached(c, at, m, ad, k, npub);
}
/// m: message: output buffer should be of size c.len
/// c: ciphertext
/// at: authentication tag
/// ad: Associated Data
/// npub: public nonce
/// k: private key
/// NOTE: the check of the authentication tag is currently not done in constant time
pub fn decrypt(m: []u8, c: []const u8, at: [tag_length]u8, ad: []const u8, npub: [nonce_length]u8, k: [key_length]u8) !void {
assert(c.len == m.len);
return try chacha20poly1305OpenDetached(m, c, at[0..], ad, k, npub);
}
};
pub const XChacha20Poly1305 = struct {
pub const tag_length = 16;
pub const nonce_length = 24;
pub const key_length = 32;
/// c: ciphertext: output buffer should be of size m.len
/// at: authentication tag: output MAC
/// m: message
/// ad: Associated Data
/// npub: public nonce
/// k: private key
pub fn encrypt(c: []u8, at: *[tag_length]u8, m: []const u8, ad: []const u8, npub: [nonce_length]u8, k: [key_length]u8) void {
assert(c.len == m.len);
return xchacha20poly1305SealDetached(c, at, m, ad, k, npub);
}
/// m: message: output buffer should be of size c.len
/// c: ciphertext
/// at: authentication tag
/// ad: Associated Data
/// npub: public nonce
/// k: private key
/// NOTE: the check of the authentication tag is currently not done in constant time
pub fn decrypt(m: []u8, c: []const u8, at: [tag_length]u8, ad: []const u8, npub: [nonce_length]u8, k: [key_length]u8) !void {
assert(c.len == m.len);
return try xchacha20poly1305OpenDetached(m, c, at[0..], ad, k, npub);
}
};
test "chacha20 AEAD API" {
const aeads = [_]type{ Chacha20Poly1305, XChacha20Poly1305 };
const input = "Ladies and Gentlemen of the class of '99: If I could offer you only one tip for the future, sunscreen would be it.";
const data = "Additional data";
inline for (aeads) |aead| {
const key = [_]u8{69} ** aead.key_length;
const nonce = [_]u8{42} ** aead.nonce_length;
var ciphertext: [input.len]u8 = undefined;
var tag: [aead.tag_length]u8 = undefined;
var out: [input.len]u8 = undefined;
aead.encrypt(ciphertext[0..], tag[0..], input, data, nonce, key);
try aead.decrypt(out[0..], ciphertext[0..], tag, data[0..], nonce, key);
testing.expectEqualSlices(u8, out[0..], input);
ciphertext[0] += 1;
testing.expectError(error.AuthenticationFailed, aead.decrypt(out[0..], ciphertext[0..], tag, data[0..], nonce, key));
}
}
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