pike.git/ lib/ modules/ Crypto.pmod/ DH.pmod

Branch: Tag:

2014-04-16

2014-04-16 19:20:50 by Henrik Grubbström (Grubba) <grubba@grubba.org>

Crypto.DH: Added module.

This module currently just contains the DHParameters class and
the MODP groups from RFC 2409, RFC 3526 and RFC 5114. Actual
Diffie-Hellman key-exchange is not implemented here (yet).

1: + //! + //! Diffie-Hellman key-exchange related stuff. + //!    -  + private Crypto.DSA foo; +  + //! Diffie-Hellman parameters. + class DHParameters + { +  //! Prime. +  Gmp.mpz p; +  +  //! Generator. +  Gmp.mpz g; +  +  //! Subgroup size. +  Gmp.mpz q; +  +  //! Alias for @[q]. +  //! +  //! @deprecated q +  __deprecated__ Gmp.mpz `order() +  { +  return q; +  } +  +  //! Alias for @[q]. +  //! +  //! @deprecated q +  __deprecated__ void `order=(Gmp.mpz val) +  { +  q = val; +  } +  +  //! Initialize the set of Diffie-Hellman parameters. +  //! +  //! @param other +  //! Copy the parameters from this object. +  protected void create(this_program other) +  { +  p = other->p; +  g = other->g; +  q = other->q; +  } +  +  //! Initialize the set of Diffie-Hellman parameters. +  //! +  //! @param dsa +  //! Copy the parameters from this object. +  protected variant void create(Crypto.DSA dsa) +  { +  p = dsa->get_p(); +  g = dsa->get_g(); +  q = dsa->get_q(); +  } +  +  //! Initialize the set of Diffie-Hellman parameters. +  //! +  //! @param p +  //! The prime for the group. +  //! +  //! @param g +  //! The generator for the group. Defaults to @expr{2@}. +  //! +  //! @param q +  //! The order of the group. Defaults to @expr{(p-1)/2@}. +  protected variant void create(Gmp.mpz|int p, Gmp.mpz|int|void g, +  Gmp.mpz|int|void q) +  { +  this_program::p = p; +  this_program::g = g || Gmp.mpz(2); +  this_program::q = q || (p-1)/2; +  } + } +  + //! MODP Group 1 (768 bit) (aka First Oakley Group (aka ORM96 group 1)). + //! + //! RFC 2409 6.1 + //! + //! @note + //! Not allowed for use with FIPS 140. + DHParameters MODPGroup1 = +  /* p = 2^768 - 2 ^704 - 1 + 2^64 * floor( 2^638 Pi + 149686 ) */ +  DHParameters(Gmp.mpz("FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1" +  "29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD" +  "EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245" +  "E485B576 625E7EC6 F44C42E9 A63A3620 FFFFFFFF FFFFFFFF", +  16)); +  + //! MODP Group 2 (1024 bit) (aka Second Oakley Group (aka ORM96 group 2)). + //! + //! RFC 2409 6.2 + //! + //! @note + //! Not allowed for use with FIPS 140. + DHParameters MODPGroup2 = +  /* p = 2^1024 - 2^960 - 1 + 2^64 * floor( 2^894 Pi + 129093 ) */ +  DHParameters(Gmp.mpz("FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1" +  "29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD" +  "EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245" +  "E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED" +  "EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE65381" +  "FFFFFFFF FFFFFFFF", 16)); +  + //! MODP Group 5 (1536 bit). + //! + //! RFC 3526 2 + //! + //! @note + //! Not allowed for use with FIPS 140. + DHParameters MODPGroup5 = +  /* p = 2^1536 - 2^1472 - 1 + 2^64 * floor( 2^1406 Pi + 741804 ) */ +  DHParameters(Gmp.mpz("FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1" +  "29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD" +  "EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245" +  "E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED" +  "EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D" +  "C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F" +  "83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D" +  "670C354E 4ABC9804 F1746C08 CA237327 FFFFFFFF FFFFFFFF", +  16)); +  + //! MODP Group 14 (2048 bit). + //! + //! RFC 3526 3 + DHParameters MODPGroup14 = +  /* p = 2^2048 - 2^1984 - 1 + 2^64 * floor( 2^1918 Pi + 124476 ) */ +  DHParameters(Gmp.mpz("FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1" +  "29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD" +  "EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245" +  "E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED" +  "EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D" +  "C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F" +  "83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D" +  "670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B" +  "E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9" +  "DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510" +  "15728E5A 8AACAA68 FFFFFFFF FFFFFFFF", 16)); +  + //! MODP Group 15 (3072 bit). + //! + //! RFC 3526 3 + DHParameters MODPGroup15 = +  /* p = 2^3072 - 2^3008 - 1 + 2^64 * floor( 2^2942 Pi + 1690314 ) */ +  DHParameters(Gmp.mpz("FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1" +  "29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD" +  "EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245" +  "E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED" +  "EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D" +  "C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F" +  "83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D" +  "670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B" +  "E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9" +  "DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510" +  "15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64" +  "ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7" +  "ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B" +  "F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C" +  "BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31" +  "43DB5BFC E0FD108E 4B82D120 A93AD2CA FFFFFFFF FFFFFFFF", +  16)); +  + //! MODP Group 16 (4096 bit). + //! + //! RFC 3526 5 + DHParameters MODPGroup16 = +  /* p = 2^4096 - 2^4032 - 1 + 2^64 * floor( 2^3966 Pi + 240904 ) */ +  DHParameters(Gmp.mpz("FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1" +  "29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD" +  "EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245" +  "E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED" +  "EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D" +  "C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F" +  "83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D" +  "670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B" +  "E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9" +  "DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510" +  "15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64" +  "ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7" +  "ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B" +  "F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C" +  "BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31" +  "43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7" +  "88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA" +  "2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6" +  "287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED" +  "1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9" +  "93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34063199" +  "FFFFFFFF FFFFFFFF", 16)); +  + //! MODP Group 17 (6144 bit). + //! + //! RFC 3526 6 + DHParameters MODPGroup17 = +  /* p = 2^6144 - 2^6080 - 1 + 2^64 * floor( 2^6014 Pi + 929484 ) */ +  DHParameters( +  Gmp.mpz("FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08" +  "8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B" +  "302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9" +  "A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6" +  "49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8" +  "FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D" +  "670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C" +  "180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718" +  "3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D" +  "04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D" +  "B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226" +  "1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C" +  "BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC" +  "E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26" +  "99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB" +  "04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2" +  "233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127" +  "D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492" +  "36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD F8FF9406" +  "AD9E530E E5DB382F 413001AE B06A53ED 9027D831 179727B0 865A8918" +  "DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B DB7F1447 E6CC254B 33205151" +  "2BD7AF42 6FB8F401 378CD2BF 5983CA01 C64B92EC F032EA15 D1721D03" +  "F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F" +  "BEC7E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA" +  "CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B" +  "B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C DA56C9EC 2EF29632" +  "387FE8D7 6E3C0468 043E8F66 3F4860EE 12BF2D5B 0B7474D6 E694F91E" +  "6DCC4024 FFFFFFFF FFFFFFFF", 16)); +  + //! MODP Group 18 (8192 bit). + //! + //! RFC 3526 7 + DHParameters MODPGroup18 = +  /* p = 2^8192 - 2^8128 - 1 + 2^64 * floor( 2^8062 Pi + 4743158 ) */ +  DHParameters(Gmp.mpz("FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1" +  "29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD" +  "EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245" +  "E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED" +  "EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D" +  "C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F" +  "83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D" +  "670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B" +  "E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9" +  "DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510" +  "15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64" +  "ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7" +  "ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B" +  "F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C" +  "BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31" +  "43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7" +  "88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA" +  "2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6" +  "287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED" +  "1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9" +  "93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492" +  "36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD" +  "F8FF9406 AD9E530E E5DB382F 413001AE B06A53ED 9027D831" +  "179727B0 865A8918 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B" +  "DB7F1447 E6CC254B 33205151 2BD7AF42 6FB8F401 378CD2BF" +  "5983CA01 C64B92EC F032EA15 D1721D03 F482D7CE 6E74FEF6" +  "D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F BEC7E8F3" +  "23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA" +  "CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328" +  "06A1D58B B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C" +  "DA56C9EC 2EF29632 387FE8D7 6E3C0468 043E8F66 3F4860EE" +  "12BF2D5B 0B7474D6 E694F91E 6DBE1159 74A3926F 12FEE5E4" +  "38777CB6 A932DF8C D8BEC4D0 73B931BA 3BC832B6 8D9DD300" +  "741FA7BF 8AFC47ED 2576F693 6BA42466 3AAB639C 5AE4F568" +  "3423B474 2BF1C978 238F16CB E39D652D E3FDB8BE FC848AD9" +  "22222E04 A4037C07 13EB57A8 1A23F0C7 3473FC64 6CEA306B" +  "4BCBC886 2F8385DD FA9D4B7F A2C087E8 79683303 ED5BDD3A" +  "062B3CF5 B3A278A6 6D2A13F8 3F44F82D DF310EE0 74AB6A36" +  "4597E899 A0255DC1 64F31CC5 0846851D F9AB4819 5DED7EA1" +  "B1D510BD 7EE74D73 FAF36BC3 1ECFA268 359046F4 EB879F92" +  "4009438B 481C6CD7 889A002E D5EE382B C9190DA6 FC026E47" +  "9558E447 5677E9AA 9E3050E2 765694DF C81F56E8 80B96E71" +  "60C980DD 98EDD3DF FFFFFFFF FFFFFFFF", 16)); +  + //! MODP Group 22 (1024-bit with 160-bit Subgroup). + //! + //! RFC 5114 2.1 + DHParameters MODPGroup22 = +  DHParameters(Gmp.mpz("B10B8F96 A080E01D DE92DE5E AE5D54EC 52C99FBC FB06A3C6" +  "9A6A9DCA 52D23B61 6073E286 75A23D18 9838EF1E 2EE652C0" +  "13ECB4AE A9061123 24975C3C D49B83BF ACCBDD7D 90C4BD70" +  "98488E9C 219A7372 4EFFD6FA E5644738 FAA31A4F F55BCCC0" +  "A151AF5F 0DC8B4BD 45BF37DF 365C1A65 E68CFDA7 6D4DA708" +  "DF1FB2BC 2E4A4371", 16), +  Gmp.mpz("A4D1CBD5 C3FD3412 6765A442 EFB99905 F8104DD2 58AC507F" +  "D6406CFF 14266D31 266FEA1E 5C41564B 777E690F 5504F213" +  "160217B4 B01B886A 5E91547F 9E2749F4 D7FBD7D3 B9A92EE1" +  "909D0D22 63F80A76 A6A24C08 7A091F53 1DBF0A01 69B6A28A" +  "D662A4D1 8E73AFA3 2D779D59 18D08BC8 858F4DCE F97C2A24" +  "855E6EEB 22B3B2E5", 16), +  Gmp.mpz("F518AA87 81A8DF27 8ABA4E7D 64B7CB9D 49462353", 16)); +  + //! MODP Group 23 (2048-bit with 224-bit Subgroup). + //! + //! RFC 5114 2.2 + DHParameters MODPGroup = +  DHParameters(Gmp.mpz("AD107E1E 9123A9D0 D660FAA7 9559C51F A20D64E5 683B9FD1" +  "B54B1597 B61D0A75 E6FA141D F95A56DB AF9A3C40 7BA1DF15" +  "EB3D688A 309C180E 1DE6B85A 1274A0A6 6D3F8152 AD6AC212" +  "9037C9ED EFDA4DF8 D91E8FEF 55B7394B 7AD5B7D0 B6C12207" +  "C9F98D11 ED34DBF6 C6BA0B2C 8BBC27BE 6A00E0A0 B9C49708" +  "B3BF8A31 70918836 81286130 BC8985DB 1602E714 415D9330" +  "278273C7 DE31EFDC 7310F712 1FD5A074 15987D9A DC0A486D" +  "CDF93ACC 44328387 315D75E1 98C641A4 80CD86A1 B9E587E8" +  "BE60E69C C928B2B9 C52172E4 13042E9B 23F10B0E 16E79763" +  "C9B53DCF 4BA80A29 E3FB73C1 6B8E75B9 7EF363E2 FFA31F71" +  "CF9DE538 4E71B81C 0AC4DFFE 0C10E64F", 16), +  Gmp.mpz("AC4032EF 4F2D9AE3 9DF30B5C 8FFDAC50 6CDEBE7B 89998CAF" +  "74866A08 CFE4FFE3 A6824A4E 10B9A6F0 DD921F01 A70C4AFA" +  "AB739D77 00C29F52 C57DB17C 620A8652 BE5E9001 A8D66AD7" +  "C1766910 1999024A F4D02727 5AC1348B B8A762D0 521BC98A" +  "E2471504 22EA1ED4 09939D54 DA7460CD B5F6C6B2 50717CBE" +  "F180EB34 118E98D1 19529A45 D6F83456 6E3025E3 16A330EF" +  "BB77A86F 0C1AB15B 051AE3D4 28C8F8AC B70A8137 150B8EEB" +  "10E183ED D19963DD D9E263E4 770589EF 6AA21E7F 5F2FF381" +  "B539CCE3 409D13CD 566AFBB4 8D6C0191 81E1BCFE 94B30269" +  "EDFE72FE 9B6AA4BD 7B5A0F1C 71CFFF4C 19C418E1 F6EC0179" +  "81BC087F 2A7065B3 84B890D3 191F2BFA", 16), +  Gmp.mpz("801C0D34 C58D93FE 99717710 1F80535A 4738CEBC BF389A99" +  "B36371EB", 16)); +  + //! MODP Group 24 (2048-bit with 256-bit Subgroup). + //! + //! RFC 5114 2.3 + DHParameters MODPGroup24 = +  DHParameters(Gmp.mpz("87A8E61D B4B6663C FFBBD19C 65195999 8CEEF608 660DD0F2" +  "5D2CEED4 435E3B00 E00DF8F1 D61957D4 FAF7DF45 61B2AA30" +  "16C3D911 34096FAA 3BF4296D 830E9A7C 209E0C64 97517ABD" +  "5A8A9D30 6BCF67ED 91F9E672 5B4758C0 22E0B1EF 4275BF7B" +  "6C5BFC11 D45F9088 B941F54E B1E59BB8 BC39A0BF 12307F5C" +  "4FDB70C5 81B23F76 B63ACAE1 CAA6B790 2D525267 35488A0E" +  "F13C6D9A 51BFA4AB 3AD83477 96524D8E F6A167B5 A41825D9" +  "67E144E5 14056425 1CCACB83 E6B486F6 B3CA3F79 71506026" +  "C0B857F6 89962856 DED4010A BD0BE621 C3A3960A 54E710C3" +  "75F26375 D7014103 A4B54330 C198AF12 6116D227 6E11715F" +  "693877FA D7EF09CA DB094AE9 1E1A1597", 16), +  Gmp.mpz("3FB32C9B 73134D0B 2E775066 60EDBD48 4CA7B18F 21EF2054" +  "07F4793A 1A0BA125 10DBC150 77BE463F FF4FED4A AC0BB555" +  "BE3A6C1B 0C6B47B1 BC3773BF 7E8C6F62 901228F8 C28CBB18" +  "A55AE313 41000A65 0196F931 C77A57F2 DDF463E5 E9EC144B" +  "777DE62A AAB8A862 8AC376D2 82D6ED38 64E67982 428EBC83" +  "1D14348F 6F2F9193 B5045AF2 767164E1 DFC967C1 FB3F2E55" +  "A4BD1BFF E83B9C80 D052B985 D182EA0A DB2A3B73 13D3FE14" +  "C8484B1E 052588B9 B7D2BBD2 DF016199 ECD06E15 57CD0915" +  "B3353BBB 64E0EC37 7FD02837 0DF92B52 C7891428 CDC67EB6" +  "184B523D 1DB246C3 2F630784 90F00EF8 D647D148 D4795451" +  "5E2327CF EF98C582 664B4C0F 6CC41659", 16), +  Gmp.mpz("8CF83642 A709A097 B4479976 40129DA2 99B1A47D 1EB3750B" +  "A308B0FE 64F5FBD3", 16));   Newline at end of file added.