xref: /aosp_15_r20/external/ms-tpm-20-ref/TPMCmd/tpm/src/crypt/PrimeData.c (revision 5c591343844d1f9da7da26467c4bf7efc8a7a413)

/* Microsoft Reference Implementation for TPM 2.0
 *
 *  The copyright in this software is being made available under the BSD License,
 *  included below. This software may be subject to other third party and
 *  contributor rights, including patent rights, and no such rights are granted
 *  under this license.
 *
 *  Copyright (c) Microsoft Corporation
 *
 *  All rights reserved.
 *
 *  BSD License
 *
 *  Redistribution and use in source and binary forms, with or without modification,
 *  are permitted provided that the following conditions are met:
 *
 *  Redistributions of source code must retain the above copyright notice, this list
 *  of conditions and the following disclaimer.
 *
 *  Redistributions in binary form must reproduce the above copyright notice, this
 *  list of conditions and the following disclaimer in the documentation and/or
 *  other materials provided with the distribution.
 *
 *  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ""AS IS""
 *  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 *  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 *  DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
 *  ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 *  (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 *  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
 *  ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 *  (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 *  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
#include "Tpm.h"

// This table is the product of all of the primes up to 1000.
// Checking to see if there is a GCD between a prime candidate
// and this number will eliminate many prime candidates from
// consideration before running Miller-Rabin on the result.

const BN_STRUCT(43 * RADIX_BITS) s_CompositeOfSmallPrimes_ =
{44, 44,
{ 0x2ED42696, 0x2BBFA177, 0x4820594F, 0xF73F4841,
0xBFAC313A, 0xCAC3EB81, 0xF6F26BF8, 0x7FAB5061,
0x59746FB7, 0xF71377F6, 0x3B19855B, 0xCBD03132,
0xBB92EF1B, 0x3AC3152C, 0xE87C8273, 0xC0AE0E69,
0x74A9E295, 0x448CCE86, 0x63CA1907, 0x8A0BF944,
0xF8CC3BE0, 0xC26F0AF5, 0xC501C02F, 0x6579441A,
0xD1099CDA, 0x6BC76A00, 0xC81A3228, 0xBFB1AB25,
0x70FA3841, 0x51B3D076, 0xCC2359ED, 0xD9EE0769,
0x75E47AF0, 0xD45FF31E, 0x52CCE4F6, 0x04DBC891,
0x96658ED2, 0x1753EFE5, 0x3AE4A5A6, 0x8FD4A97F,
0x8B15E7EB, 0x0243C3E1, 0xE0F0C31D, 0x0000000B }
};

bigConst        s_CompositeOfSmallPrimes = (const bigNum)&s_CompositeOfSmallPrimes_;

// This table contains a bit for each of the odd values between 1 and 2^16 + 1.
// This table allows fast checking of the primes in that range.
// Don't change the size of this table unless you are prepared to do redo
// IsPrimeInt().

const uint32_t      s_LastPrimeInTable = 65537;
const uint32_t      s_PrimeTableSize = 4097;
const uint32_t      s_PrimesInTable = 6542;
const unsigned char s_PrimeTable[] = {
    0x6e, 0xcb, 0xb4, 0x64, 0x9a, 0x12, 0x6d, 0x81, 0x32, 0x4c, 0x4a, 0x86,
    0x0d, 0x82, 0x96, 0x21, 0xc9, 0x34, 0x04, 0x5a, 0x20, 0x61, 0x89, 0xa4,
    0x44, 0x11, 0x86, 0x29, 0xd1, 0x82, 0x28, 0x4a, 0x30, 0x40, 0x42, 0x32,
    0x21, 0x99, 0x34, 0x08, 0x4b, 0x06, 0x25, 0x42, 0x84, 0x48, 0x8a, 0x14,
    0x05, 0x42, 0x30, 0x6c, 0x08, 0xb4, 0x40, 0x0b, 0xa0, 0x08, 0x51, 0x12,
    0x28, 0x89, 0x04, 0x65, 0x98, 0x30, 0x4c, 0x80, 0x96, 0x44, 0x12, 0x80,
    0x21, 0x42, 0x12, 0x41, 0xc9, 0x04, 0x21, 0xc0, 0x32, 0x2d, 0x98, 0x00,
    0x00, 0x49, 0x04, 0x08, 0x81, 0x96, 0x68, 0x82, 0xb0, 0x25, 0x08, 0x22,
    0x48, 0x89, 0xa2, 0x40, 0x59, 0x26, 0x04, 0x90, 0x06, 0x40, 0x43, 0x30,
    0x44, 0x92, 0x00, 0x69, 0x10, 0x82, 0x08, 0x08, 0xa4, 0x0d, 0x41, 0x12,
    0x60, 0xc0, 0x00, 0x24, 0xd2, 0x22, 0x61, 0x08, 0x84, 0x04, 0x1b, 0x82,
    0x01, 0xd3, 0x10, 0x01, 0x02, 0xa0, 0x44, 0xc0, 0x22, 0x60, 0x91, 0x14,
    0x0c, 0x40, 0xa6, 0x04, 0xd2, 0x94, 0x20, 0x09, 0x94, 0x20, 0x52, 0x00,
    0x08, 0x10, 0xa2, 0x4c, 0x00, 0x82, 0x01, 0x51, 0x10, 0x08, 0x8b, 0xa4,
    0x25, 0x9a, 0x30, 0x44, 0x81, 0x10, 0x4c, 0x03, 0x02, 0x25, 0x52, 0x80,
    0x08, 0x49, 0x84, 0x20, 0x50, 0x32, 0x00, 0x18, 0xa2, 0x40, 0x11, 0x24,
    0x28, 0x01, 0x84, 0x01, 0x01, 0xa0, 0x41, 0x0a, 0x12, 0x45, 0x00, 0x36,
    0x08, 0x00, 0x26, 0x29, 0x83, 0x82, 0x61, 0xc0, 0x80, 0x04, 0x10, 0x10,
    0x6d, 0x00, 0x22, 0x48, 0x58, 0x26, 0x0c, 0xc2, 0x10, 0x48, 0x89, 0x24,
    0x20, 0x58, 0x20, 0x45, 0x88, 0x24, 0x00, 0x19, 0x02, 0x25, 0xc0, 0x10,
    0x68, 0x08, 0x14, 0x01, 0xca, 0x32, 0x28, 0x80, 0x00, 0x04, 0x4b, 0x26,
    0x00, 0x13, 0x90, 0x60, 0x82, 0x80, 0x25, 0xd0, 0x00, 0x01, 0x10, 0x32,
    0x0c, 0x43, 0x86, 0x21, 0x11, 0x00, 0x08, 0x43, 0x24, 0x04, 0x48, 0x10,
    0x0c, 0x90, 0x92, 0x00, 0x43, 0x20, 0x2d, 0x00, 0x06, 0x09, 0x88, 0x24,
    0x40, 0xc0, 0x32, 0x09, 0x09, 0x82, 0x00, 0x53, 0x80, 0x08, 0x80, 0x96,
    0x41, 0x81, 0x00, 0x40, 0x48, 0x10, 0x48, 0x08, 0x96, 0x48, 0x58, 0x20,
    0x29, 0xc3, 0x80, 0x20, 0x02, 0x94, 0x60, 0x92, 0x00, 0x20, 0x81, 0x22,
    0x44, 0x10, 0xa0, 0x05, 0x40, 0x90, 0x01, 0x49, 0x20, 0x04, 0x0a, 0x00,
    0x24, 0x89, 0x34, 0x48, 0x13, 0x80, 0x2c, 0xc0, 0x82, 0x29, 0x00, 0x24,
    0x45, 0x08, 0x00, 0x08, 0x98, 0x36, 0x04, 0x52, 0x84, 0x04, 0xd0, 0x04,
    0x00, 0x8a, 0x90, 0x44, 0x82, 0x32, 0x65, 0x18, 0x90, 0x00, 0x0a, 0x02,
    0x01, 0x40, 0x02, 0x28, 0x40, 0xa4, 0x04, 0x92, 0x30, 0x04, 0x11, 0x86,
    0x08, 0x42, 0x00, 0x2c, 0x52, 0x04, 0x08, 0xc9, 0x84, 0x60, 0x48, 0x12,
    0x09, 0x99, 0x24, 0x44, 0x00, 0x24, 0x00, 0x03, 0x14, 0x21, 0x00, 0x10,
    0x01, 0x1a, 0x32, 0x05, 0x88, 0x20, 0x40, 0x40, 0x06, 0x09, 0xc3, 0x84,
    0x40, 0x01, 0x30, 0x60, 0x18, 0x02, 0x68, 0x11, 0x90, 0x0c, 0x02, 0xa2,
    0x04, 0x00, 0x86, 0x29, 0x89, 0x14, 0x24, 0x82, 0x02, 0x41, 0x08, 0x80,
    0x04, 0x19, 0x80, 0x08, 0x10, 0x12, 0x68, 0x42, 0xa4, 0x04, 0x00, 0x02,
    0x61, 0x10, 0x06, 0x0c, 0x10, 0x00, 0x01, 0x12, 0x10, 0x20, 0x03, 0x94,
    0x21, 0x42, 0x12, 0x65, 0x18, 0x94, 0x0c, 0x0a, 0x04, 0x28, 0x01, 0x14,
    0x29, 0x0a, 0xa4, 0x40, 0xd0, 0x00, 0x40, 0x01, 0x90, 0x04, 0x41, 0x20,
    0x2d, 0x40, 0x82, 0x48, 0xc1, 0x20, 0x00, 0x10, 0x30, 0x01, 0x08, 0x24,
    0x04, 0x59, 0x84, 0x24, 0x00, 0x02, 0x29, 0x82, 0x00, 0x61, 0x58, 0x02,
    0x48, 0x81, 0x16, 0x48, 0x10, 0x00, 0x21, 0x11, 0x06, 0x00, 0xca, 0xa0,
    0x40, 0x02, 0x00, 0x04, 0x91, 0xb0, 0x00, 0x42, 0x04, 0x0c, 0x81, 0x06,
    0x09, 0x48, 0x14, 0x25, 0x92, 0x20, 0x25, 0x11, 0xa0, 0x00, 0x0a, 0x86,
    0x0c, 0xc1, 0x02, 0x48, 0x00, 0x20, 0x45, 0x08, 0x32, 0x00, 0x98, 0x06,
    0x04, 0x13, 0x22, 0x00, 0x82, 0x04, 0x48, 0x81, 0x14, 0x44, 0x82, 0x12,
    0x24, 0x18, 0x10, 0x40, 0x43, 0x80, 0x28, 0xd0, 0x04, 0x20, 0x81, 0x24,
    0x64, 0xd8, 0x00, 0x2c, 0x09, 0x12, 0x08, 0x41, 0xa2, 0x00, 0x00, 0x02,
    0x41, 0xca, 0x20, 0x41, 0xc0, 0x10, 0x01, 0x18, 0xa4, 0x04, 0x18, 0xa4,
    0x20, 0x12, 0x94, 0x20, 0x83, 0xa0, 0x40, 0x02, 0x32, 0x44, 0x80, 0x04,
    0x00, 0x18, 0x00, 0x0c, 0x40, 0x86, 0x60, 0x8a, 0x00, 0x64, 0x88, 0x12,
    0x05, 0x01, 0x82, 0x00, 0x4a, 0xa2, 0x01, 0xc1, 0x10, 0x61, 0x09, 0x04,
    0x01, 0x88, 0x00, 0x60, 0x01, 0xb4, 0x40, 0x08, 0x06, 0x01, 0x03, 0x80,
    0x08, 0x40, 0x94, 0x04, 0x8a, 0x20, 0x29, 0x80, 0x02, 0x0c, 0x52, 0x02,
    0x01, 0x42, 0x84, 0x00, 0x80, 0x84, 0x64, 0x02, 0x32, 0x48, 0x00, 0x30,
    0x44, 0x40, 0x22, 0x21, 0x00, 0x02, 0x08, 0xc3, 0xa0, 0x04, 0xd0, 0x20,
    0x40, 0x18, 0x16, 0x40, 0x40, 0x00, 0x28, 0x52, 0x90, 0x08, 0x82, 0x14,
    0x01, 0x18, 0x10, 0x08, 0x09, 0x82, 0x40, 0x0a, 0xa0, 0x20, 0x93, 0x80,
    0x08, 0xc0, 0x00, 0x20, 0x52, 0x00, 0x05, 0x01, 0x10, 0x40, 0x11, 0x06,
    0x0c, 0x82, 0x00, 0x00, 0x4b, 0x90, 0x44, 0x9a, 0x00, 0x28, 0x80, 0x90,
    0x04, 0x4a, 0x06, 0x09, 0x43, 0x02, 0x28, 0x00, 0x34, 0x01, 0x18, 0x00,
    0x65, 0x09, 0x80, 0x44, 0x03, 0x00, 0x24, 0x02, 0x82, 0x61, 0x48, 0x14,
    0x41, 0x00, 0x12, 0x28, 0x00, 0x34, 0x08, 0x51, 0x04, 0x05, 0x12, 0x90,
    0x28, 0x89, 0x84, 0x60, 0x12, 0x10, 0x49, 0x10, 0x26, 0x40, 0x49, 0x82,
    0x00, 0x91, 0x10, 0x01, 0x0a, 0x24, 0x40, 0x88, 0x10, 0x4c, 0x10, 0x04,
    0x00, 0x50, 0xa2, 0x2c, 0x40, 0x90, 0x48, 0x0a, 0xb0, 0x01, 0x50, 0x12,
    0x08, 0x00, 0xa4, 0x04, 0x09, 0xa0, 0x28, 0x92, 0x02, 0x00, 0x43, 0x10,
    0x21, 0x02, 0x20, 0x41, 0x81, 0x32, 0x00, 0x08, 0x04, 0x0c, 0x52, 0x00,
    0x21, 0x49, 0x84, 0x20, 0x10, 0x02, 0x01, 0x81, 0x10, 0x48, 0x40, 0x22,
    0x01, 0x01, 0x84, 0x69, 0xc1, 0x30, 0x01, 0xc8, 0x02, 0x44, 0x88, 0x00,
    0x0c, 0x01, 0x02, 0x2d, 0xc0, 0x12, 0x61, 0x00, 0xa0, 0x00, 0xc0, 0x30,
    0x40, 0x01, 0x12, 0x08, 0x0b, 0x20, 0x00, 0x80, 0x94, 0x40, 0x01, 0x84,
    0x40, 0x00, 0x32, 0x00, 0x10, 0x84, 0x00, 0x0b, 0x24, 0x00, 0x01, 0x06,
    0x29, 0x8a, 0x84, 0x41, 0x80, 0x10, 0x08, 0x08, 0x94, 0x4c, 0x03, 0x80,
    0x01, 0x40, 0x96, 0x40, 0x41, 0x20, 0x20, 0x50, 0x22, 0x25, 0x89, 0xa2,
    0x40, 0x40, 0xa4, 0x20, 0x02, 0x86, 0x28, 0x01, 0x20, 0x21, 0x4a, 0x10,
    0x08, 0x00, 0x14, 0x08, 0x40, 0x04, 0x25, 0x42, 0x02, 0x21, 0x43, 0x10,
    0x04, 0x92, 0x00, 0x21, 0x11, 0xa0, 0x4c, 0x18, 0x22, 0x09, 0x03, 0x84,
    0x41, 0x89, 0x10, 0x04, 0x82, 0x22, 0x24, 0x01, 0x14, 0x08, 0x08, 0x84,
    0x08, 0xc1, 0x00, 0x09, 0x42, 0xb0, 0x41, 0x8a, 0x02, 0x00, 0x80, 0x36,
    0x04, 0x49, 0xa0, 0x24, 0x91, 0x00, 0x00, 0x02, 0x94, 0x41, 0x92, 0x02,
    0x01, 0x08, 0x06, 0x08, 0x09, 0x00, 0x01, 0xd0, 0x16, 0x28, 0x89, 0x80,
    0x60, 0x00, 0x00, 0x68, 0x01, 0x90, 0x0c, 0x50, 0x20, 0x01, 0x40, 0x80,
    0x40, 0x42, 0x30, 0x41, 0x00, 0x20, 0x25, 0x81, 0x06, 0x40, 0x49, 0x00,
    0x08, 0x01, 0x12, 0x49, 0x00, 0xa0, 0x20, 0x18, 0x30, 0x05, 0x01, 0xa6,
    0x00, 0x10, 0x24, 0x28, 0x00, 0x02, 0x20, 0xc8, 0x20, 0x00, 0x88, 0x12,
    0x0c, 0x90, 0x92, 0x00, 0x02, 0x26, 0x01, 0x42, 0x16, 0x49, 0x00, 0x04,
    0x24, 0x42, 0x02, 0x01, 0x88, 0x80, 0x0c, 0x1a, 0x80, 0x08, 0x10, 0x00,
    0x60, 0x02, 0x94, 0x44, 0x88, 0x00, 0x69, 0x11, 0x30, 0x08, 0x12, 0xa0,
    0x24, 0x13, 0x84, 0x00, 0x82, 0x00, 0x65, 0xc0, 0x10, 0x28, 0x00, 0x30,
    0x04, 0x03, 0x20, 0x01, 0x11, 0x06, 0x01, 0xc8, 0x80, 0x00, 0xc2, 0x20,
    0x08, 0x10, 0x82, 0x0c, 0x13, 0x02, 0x0c, 0x52, 0x06, 0x40, 0x00, 0xb0,
    0x61, 0x40, 0x10, 0x01, 0x98, 0x86, 0x04, 0x10, 0x84, 0x08, 0x92, 0x14,
    0x60, 0x41, 0x80, 0x41, 0x1a, 0x10, 0x04, 0x81, 0x22, 0x40, 0x41, 0x20,
    0x29, 0x52, 0x00, 0x41, 0x08, 0x34, 0x60, 0x10, 0x00, 0x28, 0x01, 0x10,
    0x40, 0x00, 0x84, 0x08, 0x42, 0x90, 0x20, 0x48, 0x04, 0x04, 0x52, 0x02,
    0x00, 0x08, 0x20, 0x04, 0x00, 0x82, 0x0d, 0x00, 0x82, 0x40, 0x02, 0x10,
    0x05, 0x48, 0x20, 0x40, 0x99, 0x00, 0x00, 0x01, 0x06, 0x24, 0xc0, 0x00,
    0x68, 0x82, 0x04, 0x21, 0x12, 0x10, 0x44, 0x08, 0x04, 0x00, 0x40, 0xa6,
    0x20, 0xd0, 0x16, 0x09, 0xc9, 0x24, 0x41, 0x02, 0x20, 0x0c, 0x09, 0x92,
    0x40, 0x12, 0x00, 0x00, 0x40, 0x00, 0x09, 0x43, 0x84, 0x20, 0x98, 0x02,
    0x01, 0x11, 0x24, 0x00, 0x43, 0x24, 0x00, 0x03, 0x90, 0x08, 0x41, 0x30,
    0x24, 0x58, 0x20, 0x4c, 0x80, 0x82, 0x08, 0x10, 0x24, 0x25, 0x81, 0x06,
    0x41, 0x09, 0x10, 0x20, 0x18, 0x10, 0x44, 0x80, 0x10, 0x00, 0x4a, 0x24,
    0x0d, 0x01, 0x94, 0x28, 0x80, 0x30, 0x00, 0xc0, 0x02, 0x60, 0x10, 0x84,
    0x0c, 0x02, 0x00, 0x09, 0x02, 0x82, 0x01, 0x08, 0x10, 0x04, 0xc2, 0x20,
    0x68, 0x09, 0x06, 0x04, 0x18, 0x00, 0x00, 0x11, 0x90, 0x08, 0x0b, 0x10,
    0x21, 0x82, 0x02, 0x0c, 0x10, 0xb6, 0x08, 0x00, 0x26, 0x00, 0x41, 0x02,
    0x01, 0x4a, 0x24, 0x21, 0x1a, 0x20, 0x24, 0x80, 0x00, 0x44, 0x02, 0x00,
    0x2d, 0x40, 0x02, 0x00, 0x8b, 0x94, 0x20, 0x10, 0x00, 0x20, 0x90, 0xa6,
    0x40, 0x13, 0x00, 0x2c, 0x11, 0x86, 0x61, 0x01, 0x80, 0x41, 0x10, 0x02,
    0x04, 0x81, 0x30, 0x48, 0x48, 0x20, 0x28, 0x50, 0x80, 0x21, 0x8a, 0x10,
    0x04, 0x08, 0x10, 0x09, 0x10, 0x10, 0x48, 0x42, 0xa0, 0x0c, 0x82, 0x92,
    0x60, 0xc0, 0x20, 0x05, 0xd2, 0x20, 0x40, 0x01, 0x00, 0x04, 0x08, 0x82,
    0x2d, 0x82, 0x02, 0x00, 0x48, 0x80, 0x41, 0x48, 0x10, 0x00, 0x91, 0x04,
    0x04, 0x03, 0x84, 0x00, 0xc2, 0x04, 0x68, 0x00, 0x00, 0x64, 0xc0, 0x22,
    0x40, 0x08, 0x32, 0x44, 0x09, 0x86, 0x00, 0x91, 0x02, 0x28, 0x01, 0x00,
    0x64, 0x48, 0x00, 0x24, 0x10, 0x90, 0x00, 0x43, 0x00, 0x21, 0x52, 0x86,
    0x41, 0x8b, 0x90, 0x20, 0x40, 0x20, 0x08, 0x88, 0x04, 0x44, 0x13, 0x20,
    0x00, 0x02, 0x84, 0x60, 0x81, 0x90, 0x24, 0x40, 0x30, 0x00, 0x08, 0x10,
    0x08, 0x08, 0x02, 0x01, 0x10, 0x04, 0x20, 0x43, 0xb4, 0x40, 0x90, 0x12,
    0x68, 0x01, 0x80, 0x4c, 0x18, 0x00, 0x08, 0xc0, 0x12, 0x49, 0x40, 0x10,
    0x24, 0x1a, 0x00, 0x41, 0x89, 0x24, 0x4c, 0x10, 0x00, 0x04, 0x52, 0x10,
    0x09, 0x4a, 0x20, 0x41, 0x48, 0x22, 0x69, 0x11, 0x14, 0x08, 0x10, 0x06,
    0x24, 0x80, 0x84, 0x28, 0x00, 0x10, 0x00, 0x40, 0x10, 0x01, 0x08, 0x26,
    0x08, 0x48, 0x06, 0x28, 0x00, 0x14, 0x01, 0x42, 0x84, 0x04, 0x0a, 0x20,
    0x00, 0x01, 0x82, 0x08, 0x00, 0x82, 0x24, 0x12, 0x04, 0x40, 0x40, 0xa0,
    0x40, 0x90, 0x10, 0x04, 0x90, 0x22, 0x40, 0x10, 0x20, 0x2c, 0x80, 0x10,
    0x28, 0x43, 0x00, 0x04, 0x58, 0x00, 0x01, 0x81, 0x10, 0x48, 0x09, 0x20,
    0x21, 0x83, 0x04, 0x00, 0x42, 0xa4, 0x44, 0x00, 0x00, 0x6c, 0x10, 0xa0,
    0x44, 0x48, 0x80, 0x00, 0x83, 0x80, 0x48, 0xc9, 0x00, 0x00, 0x00, 0x02,
    0x05, 0x10, 0xb0, 0x04, 0x13, 0x04, 0x29, 0x10, 0x92, 0x40, 0x08, 0x04,
    0x44, 0x82, 0x22, 0x00, 0x19, 0x20, 0x00, 0x19, 0x20, 0x01, 0x81, 0x90,
    0x60, 0x8a, 0x00, 0x41, 0xc0, 0x02, 0x45, 0x10, 0x04, 0x00, 0x02, 0xa2,
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    0x21, 0x81, 0x14, 0x04, 0x00, 0x02, 0x20, 0x89, 0xb4, 0x44, 0x12, 0x80,
    0x00, 0xd1, 0x00, 0x69, 0x40, 0x80, 0x00, 0x42, 0x12, 0x00, 0x18, 0x04,
    0x00, 0x49, 0x06, 0x21, 0x02, 0x04, 0x28, 0x02, 0x84, 0x01, 0xc0, 0x10,
    0x68, 0x00, 0x20, 0x08, 0x40, 0x00, 0x08, 0x91, 0x10, 0x01, 0x81, 0x24,
    0x04, 0xd2, 0x10, 0x4c, 0x88, 0x86, 0x00, 0x10, 0x80, 0x0c, 0x02, 0x14,
    0x00, 0x8a, 0x90, 0x40, 0x18, 0x20, 0x21, 0x80, 0xa4, 0x00, 0x58, 0x24,
    0x20, 0x10, 0x10, 0x60, 0xc1, 0x30, 0x41, 0x48, 0x02, 0x48, 0x09, 0x00,
    0x40, 0x09, 0x02, 0x05, 0x11, 0x82, 0x20, 0x4a, 0x20, 0x24, 0x18, 0x02,
    0x0c, 0x10, 0x22, 0x0c, 0x0a, 0x04, 0x00, 0x03, 0x06, 0x48, 0x48, 0x04,
    0x04, 0x02, 0x00, 0x21, 0x80, 0x84, 0x00, 0x18, 0x00, 0x0c, 0x02, 0x12,
    0x01, 0x00, 0x14, 0x05, 0x82, 0x10, 0x41, 0x89, 0x12, 0x08, 0x40, 0xa4,
    0x21, 0x01, 0x84, 0x48, 0x02, 0x10, 0x60, 0x40, 0x02, 0x28, 0x00, 0x14,
    0x08, 0x40, 0xa0, 0x20, 0x51, 0x12, 0x00, 0xc2, 0x00, 0x01, 0x1a, 0x30,
    0x40, 0x89, 0x12, 0x4c, 0x02, 0x80, 0x00, 0x00, 0x14, 0x01, 0x01, 0xa0,
    0x21, 0x18, 0x22, 0x21, 0x18, 0x06, 0x40, 0x01, 0x80, 0x00, 0x90, 0x04,
    0x48, 0x02, 0x30, 0x04, 0x08, 0x00, 0x05, 0x88, 0x24, 0x08, 0x48, 0x04,
    0x24, 0x02, 0x06, 0x00, 0x80, 0x00, 0x00, 0x00, 0x10, 0x65, 0x11, 0x90,
    0x00, 0x0a, 0x82, 0x04, 0xc3, 0x04, 0x60, 0x48, 0x24, 0x04, 0x92, 0x02,
    0x44, 0x88, 0x80, 0x40, 0x18, 0x06, 0x29, 0x80, 0x10, 0x01, 0x00, 0x00,
    0x44, 0xc8, 0x10, 0x21, 0x89, 0x30, 0x00, 0x4b, 0xa0, 0x01, 0x10, 0x14,
    0x00, 0x02, 0x94, 0x40, 0x00, 0x20, 0x65, 0x00, 0xa2, 0x0c, 0x40, 0x22,
    0x20, 0x81, 0x12, 0x20, 0x82, 0x04, 0x01, 0x10, 0x00, 0x08, 0x88, 0x00,
    0x00, 0x11, 0x80, 0x04, 0x42, 0x80, 0x40, 0x41, 0x14, 0x00, 0x40, 0x32,
    0x2c, 0x80, 0x24, 0x04, 0x19, 0x00, 0x00, 0x91, 0x00, 0x20, 0x83, 0x00,
    0x05, 0x40, 0x20, 0x09, 0x01, 0x84, 0x40, 0x40, 0x20, 0x20, 0x11, 0x00,
    0x40, 0x41, 0x90, 0x20, 0x00, 0x00, 0x40, 0x90, 0x92, 0x48, 0x18, 0x06,
    0x08, 0x81, 0x80, 0x48, 0x01, 0x34, 0x24, 0x10, 0x20, 0x04, 0x00, 0x20,
    0x04, 0x18, 0x06, 0x2d, 0x90, 0x10, 0x01, 0x00, 0x90, 0x00, 0x0a, 0x22,
    0x01, 0x00, 0x22, 0x00, 0x11, 0x84, 0x01, 0x01, 0x00, 0x20, 0x88, 0x00,
    0x44, 0x00, 0x22, 0x01, 0x00, 0xa6, 0x40, 0x02, 0x06, 0x20, 0x11, 0x00,
    0x01, 0xc8, 0xa0, 0x04, 0x8a, 0x00, 0x28, 0x19, 0x80, 0x00, 0x52, 0xa0,
    0x24, 0x12, 0x12, 0x09, 0x08, 0x24, 0x01, 0x48, 0x00, 0x04, 0x00, 0x24,
    0x40, 0x02, 0x84, 0x08, 0x00, 0x04, 0x48, 0x40, 0x90, 0x60, 0x0a, 0x22,
    0x01, 0x88, 0x14, 0x08, 0x01, 0x02, 0x08, 0xd3, 0x00, 0x20, 0xc0, 0x90,
    0x24, 0x10, 0x00, 0x00, 0x01, 0xb0, 0x08, 0x0a, 0xa0, 0x00, 0x80, 0x00,
    0x01, 0x09, 0x00, 0x20, 0x52, 0x02, 0x25, 0x00, 0x24, 0x04, 0x02, 0x84,
    0x24, 0x10, 0x92, 0x40, 0x02, 0xa0, 0x40, 0x00, 0x22, 0x08, 0x11, 0x04,
    0x08, 0x01, 0x22, 0x00, 0x42, 0x14, 0x00, 0x09, 0x90, 0x21, 0x00, 0x30,
    0x6c, 0x00, 0x00, 0x0c, 0x00, 0x22, 0x09, 0x90, 0x10, 0x28, 0x40, 0x00,
    0x20, 0xc0, 0x20, 0x00, 0x90, 0x00, 0x40, 0x01, 0x82, 0x05, 0x12, 0x12,
    0x09, 0xc1, 0x04, 0x61, 0x80, 0x02, 0x28, 0x81, 0x24, 0x00, 0x49, 0x04,
    0x08, 0x10, 0x86, 0x29, 0x41, 0x80, 0x21, 0x0a, 0x30, 0x49, 0x88, 0x90,
    0x00, 0x41, 0x04, 0x29, 0x81, 0x80, 0x41, 0x09, 0x00, 0x40, 0x12, 0x10,
    0x40, 0x00, 0x10, 0x40, 0x48, 0x02, 0x05, 0x80, 0x02, 0x21, 0x40, 0x20,
    0x00, 0x58, 0x20, 0x60, 0x00, 0x90, 0x48, 0x00, 0x80, 0x28, 0xc0, 0x80,
    0x48, 0x00, 0x00, 0x44, 0x80, 0x02, 0x00, 0x09, 0x06, 0x00, 0x12, 0x02,
    0x01, 0x00, 0x10, 0x08, 0x83, 0x10, 0x45, 0x12, 0x00, 0x2c, 0x08, 0x04,
    0x44, 0x00, 0x20, 0x20, 0xc0, 0x10, 0x20, 0x01, 0x00, 0x05, 0xc8, 0x20,
    0x04, 0x98, 0x10, 0x08, 0x10, 0x00, 0x24, 0x02, 0x16, 0x40, 0x88, 0x00,
    0x61, 0x88, 0x12, 0x24, 0x80, 0xa6, 0x00, 0x42, 0x00, 0x08, 0x10, 0x06,
    0x48, 0x40, 0xa0, 0x00, 0x50, 0x20, 0x04, 0x81, 0xa4, 0x40, 0x18, 0x00,
    0x08, 0x10, 0x80, 0x01, 0x01};

#if RSA_KEY_SIEVE && SIMULATION && RSA_INSTRUMENT
UINT32  PrimeIndex = 0;
UINT32  failedAtIteration[10] = {0};
UINT32  PrimeCounts[3] = {0};
UINT32  MillerRabinTrials[3] = {0};
UINT32  totalFieldsSieved[3] = {0};
UINT32  bitsInFieldAfterSieve[3] = {0};
UINT32  emptyFieldsSieved[3] = {0};
UINT32  noPrimeFields[3] = {0};
UINT32  primesChecked[3] = {0};
UINT16  lastSievePrime = 0;
#endif