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Volumn 72, Issue 242, 2003, Pages 953-967

Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the Gaussian integer method

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EID: 0037376560     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-02-01482-5     Document Type: Article
Times cited : (68)

References (42)
  • 2
    • 84955575947 scopus 로고
    • The magic words are sgueamish oasifrage
    • Advances in Cryptology - ASIACRYPT'94, Springer-Verlag, MR 97b;94019
    • D. Atkins, M. Graff, A. K. Lenstra, and P. C. Leyland, The magic words are sgueamish oasifrage, Advances in Cryptology - ASIACRYPT'94, Lecture Notes in Computer Science, vol. 917, Springer-Verlag, 1995, pp. 265-277. MR 97b;94019
    • (1995) Lecture Notes in Computer Science , vol.917 , pp. 265-277
    • Atkins, D.1    Graff, M.2    Lenstra, A.K.3    Leyland, P.C.4
  • 4
    • 85028745697 scopus 로고
    • An implementation of the general number field sieve
    • Advances in Cryptology - CRYPTO'93, MR 95e:11132
    • J. Buchmann, J. Loho, and J. Zayer, An implementation of the general number field sieve, Advances in Cryptology - CRYPTO'93, Lecture Notes in Computer Science, vol. 773, 1994, pp. 159-165. MR 95e:11132
    • (1994) Lecture Notes in Computer Science , vol.773 , pp. 159-165
    • Buchmann, J.1    Loho, J.2    Zayer, J.3
  • 6
    • 84946832616 scopus 로고    scopus 로고
    • Strategies in filtering in the number field sieve
    • Proceedings of the ANTS-IV conference (W. Bosma, ed.) Springer-Verlag, MR 2002h:11139
    • S. Cavallar, Strategies in filtering in the number field sieve, Proceedings of the ANTS-IV conference (W. Bosma, ed.), Lecture Notes in Computer Science, vol. 1838, Springer-Verlag, 2000, pp. 209-231. MR 2002h:11139
    • (2000) Lecture Notes in Computer Science , vol.1838 , pp. 209-231
    • Cavallar, S.1
  • 9
    • 0021468777 scopus 로고
    • Fast evaluation of logarithms in fields of characteristic two
    • MR 85h:65041
    • D. Coppersmith, Fast evaluation of logarithms in fields of characteristic two, IEEE transactions on information theory IT-30 (1984), no. 4, 587-594. MR 85h:65041
    • (1984) IEEE Transactions on Information Theory IT-30 , vol.4 , pp. 587-594
    • Coppersmith, D.1
  • 10
    • 0022953575 scopus 로고
    • Discrete logarithms in double-struck F signp
    • MR 87g:11167
    • D. Coppersmith, A. Odlyzko, and R. Schroppel. Discrete logarithms in double-struck F signp, Algorithmica 1 (1986), 1-15. MR 87g:11167
    • (1986) Algorithmica , vol.1 , pp. 1-15
    • Coppersmith, D.1    Odlyzko, A.2    Schroppel, R.3
  • 12
    • 84955611255 scopus 로고    scopus 로고
    • A world wide number field sieve factoring record: On to 512 bits
    • Advances in Cryptology - ASIACRYPT'96 (K. Kim and T. Matsumoto, eds.) Springer-Verlag, CMP 98:05
    • J. Cowie, B. Dodson, R. M. Elkenbracht-Huizing, A. K. Lenstra, P. L. Montgomery, and J. Zayer, A world wide number field sieve factoring record: On to 512 bits, Advances in Cryptology - ASIACRYPT'96 (K. Kim and T. Matsumoto, eds.), Lecture Notes in Computer Science, vol. 1163, Springer-Verlag, 1996, pp. 382-394. CMP 98:05
    • (1996) Lecture Notes in Computer Science , vol.1163 , pp. 382-394
    • Cowie, J.1    Dodson, B.2    Elkenbracht-Huizing, R.M.3    Lenstra, A.K.4    Montgomery, P.L.5    Zayer, J.6
  • 13
    • 21444455606 scopus 로고    scopus 로고
    • On the reduction of composed relations from the number field sieve
    • Proceedings of the ANTS-II conference (H. Cohen, ed.) Springer-Verlag, MR 98k:11184
    • Th. Denny and V. Müller, On the reduction of composed relations from the number field sieve, Proceedings of the ANTS-II conference (H. Cohen, ed.), Lecture Notes in Computer Science, vol. 1122, Springer-Verlag, 1996, pp. 75-90. MR 98k:11184
    • (1996) Lecture Notes in Computer Science , vol.1122 , pp. 75-90
    • Denny, Th.1    Müller, V.2
  • 14
    • 84957624792 scopus 로고
    • NFS with four large primes: An explosive experiment
    • Advances in Cryptology - CRYPTO'95, Springer-Verlag. MR 98d:11156
    • B. Dodson and A. K. Lenstra, NFS with four large primes: an explosive experiment, Advances in Cryptology - CRYPTO'95, Lecture Notes in Computer Science, vol. 963, Springer-Verlag, 1995, pp. 372-385. MR 98d:11156
    • (1995) Lecture Notes in Computer Science , vol.963 , pp. 372-385
    • Dodson, B.1    Lenstra, A.K.2
  • 15
    • 0012376699 scopus 로고    scopus 로고
    • The number field sieve on many computers
    • Fifth Conference of the Canadian Number Theory Association (Providence RI), Amer. Math. Soc., MR 2000e: 11157
    • R. M. Elkenbracht-Huizing, P. Montgomery, R. Silverman, R. K. Wackerbarth, and Jr. S. S. Wagstaff, The number field sieve on many computers, Fifth Conference of the Canadian Number Theory Association (Providence RI), CRM Proc. Lecture Notes, no. 19, Amer. Math. Soc., 1999. MR 2000e: 11157
    • (1999) CRM Proc. Lecture Notes , vol.19
    • Elkenbracht-Huizing, R.M.1    Montgomery, P.2    Silverman, R.3    Wackerbarth, R.K.4    Wagstaff S.S., Jr.5
  • 16
    • 0030300309 scopus 로고
    • An implementation of the number field sieve
    • Tech. Report NMR9511, CWI, MR 98a:11182
    • R.M. Elkenbracht-Huizing, An implementation of the number field sieve, Tech. Report NMR9511, CWI, 1995. Experiment. Math. 5 (1996), 231-253. MR 98a:11182
    • (1995) Experiment. Math. , vol.5 , pp. 231-253
    • Elkenbracht-Huizing, R.M.1
  • 17
    • 84958042915 scopus 로고    scopus 로고
    • A multiple polynomial general number field sieve
    • Proceedings of the ANTS-II conference (H. Cohen, ed.), Springer-Verlag, MR 98g:11142
    • _, A multiple polynomial general number field sieve, Proceedings of the ANTS-II conference (H. Cohen, ed.), Lecture Notes in Computer Science, vol. 1122, Springer-Verlag, 1996. MR 98g:11142
    • (1996) Lecture Notes in Computer Science , vol.1122
  • 18
    • 84957652084 scopus 로고
    • Lattice sieving and trial division
    • Proceedings of the ANTS-I conference, Springer-Verlag, MR 96a:11142
    • R. Golliver, A. K. Lenstra, and K. McCurley, Lattice sieving and trial division, Proceedings of the ANTS-I conference, Lecture Notes in Computer Science, vol. 877, Springer-Verlag, 1994, pp. 18-27. MR 96a:11142
    • (1994) Lecture Notes in Computer Science , vol.877 , pp. 18-27
    • Golliver, R.1    Lenstra, A.K.2    McCurley, K.3
  • 19
    • 0000303380 scopus 로고
    • Discrete logarithms in Fp using the number field sieve
    • MR 94d:11104
    • D. Gordon, Discrete logarithms in Fp using the number field sieve, SIAM J. Discrete Math 6 (1993), 124-138. MR 94d:11104
    • (1993) SIAM J. Discrete Math , vol.6 , pp. 124-138
    • Gordon, D.1
  • 20
    • 85013135541 scopus 로고
    • Massively parallel computation of discrete logarithms
    • Advances in Cryptology - CRYPTO'92, Springer-Verlag
    • D. Gordon and K. McCurley, Massively parallel computation of discrete logarithms, Advances in Cryptology - CRYPTO'92, Lecture Notes in Computer Science, vol. 740, Springer-Verlag, 1993, pp. 312-323.
    • (1993) Lecture Notes in Computer Science , vol.740 , pp. 312-323
    • Gordon, D.1    McCurley, K.2
  • 22
    • 0001134554 scopus 로고    scopus 로고
    • Lattice reduction: A toolbox for the cryptanalyst
    • MR 99c:94031
    • A. Joux and J. Stern, Lattice reduction: A toolbox for the cryptanalyst, J. Cryptology 11 (1998), 161-185. MR 99c:94031
    • (1998) J. Cryptology , vol.11 , pp. 161-185
    • Joux, A.1    Stern, J.2
  • 24
    • 0012438383 scopus 로고
    • Computation of discrete logarithms in prime fields, Designs
    • MR 92j:11148
    • B. A. LaMacchia and A. M. Odlyzko, Computation of discrete logarithms in prime fields, Designs, Codes and Cryptography 1 (1991), 47-62. MR 92j:11148
    • (1991) Codes and Cryptography , vol.1 , pp. 47-62
    • Lamacchia, B.A.1    Odlyzko, A.M.2
  • 25
    • 84988216913 scopus 로고
    • Solving large sparse linear systems over finite fields
    • Advances in Cryptology CRYPTO'90, Springer-Verlag
    • _, Solving large sparse linear systems over finite fields, Advances in Cryptology CRYPTO'90, Lecture Notes in Computer Science, vol. 537, Springer-Verlag, 1991, pp. 109-133.
    • (1991) Lecture Notes in Computer Science , vol.537 , pp. 109-133
  • 26
    • 0003291192 scopus 로고
    • The development of the number field sieve
    • Springer-Verlag, MR 96m:11116
    • A. K. Lenstra and H. W. Lenstra, Jr. (eds.), The development of the number field sieve, Lecture Notes in Mathematics, vol. 1554, Springer-Verlag, 1993. MR 96m:11116
    • (1993) Lecture Notes in Mathematics , vol.1554
    • Lenstra, A.K.1    Lenstra H.W., Jr.2
  • 27
    • 34250244723 scopus 로고
    • Factoring polynomials with rational coefficients
    • MR 84a:12002
    • A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovász, Factoring polynomials with rational coefficients, Mathematische Ann. 261 (1982), 513-534. MR 84a:12002
    • (1982) Mathematische Ann. , vol.261 , pp. 513-534
    • Lenstra, A.K.1    Lenstra H.W., Jr.2    Lovász, L.3
  • 29
    • 0003291192 scopus 로고
    • Springer-Verlag, (see [26]). CMP 95:09
    • _, The number field sieve, Springer-Verlag, 1993, pp. 11-42 (see [26]). CMP 95:09
    • (1993) The Number Field Sieve , pp. 11-42
  • 31
    • 84957682846 scopus 로고
    • A block Lanczos algorithm for finding dependencies over double-struck F sign2
    • Advances in Cryptology - EUROCRYP'95, Springer-Verlag, MR 97c:11115
    • P. L. Montgomery, A block Lanczos algorithm for finding dependencies over double-struck F sign2, Advances in Cryptology - EUROCRYP'95, Lecture Notes in Computer Science, vol. 921, Springer-Verlag, 1995, pp. 106-120. MR 97c:11115
    • (1995) Lecture Notes in Computer Science , vol.921 , pp. 106-120
    • Montgomery, P.L.1
  • 32
    • 84957014368 scopus 로고
    • Discrete logarithms in finite fields and their cryptographic significance
    • Advances in Cryptology - EUROCRYP'84 (T. Beth, N. Cot, and I. Ingemarsson, eds.) Springer-Verlag, MR 87g:11022
    • A. M. Odlyzko, Discrete logarithms in finite fields and their cryptographic significance, Advances in Cryptology - EUROCRYP'84 (T. Beth, N. Cot, and I. Ingemarsson, eds.), Lecture Notes in Computer Science, vol. 209, Springer-Verlag, 1985, pp. 224-314. MR 87g:11022
    • (1985) Lecture Notes in Computer Science , vol.209 , pp. 224-314
    • Odlyzko, A.M.1
  • 33
  • 34
    • 0039658797 scopus 로고
    • Springer-Verlag, CMP 95:09
    • _, The lattice sieve, Springer-Verlag, 1993, pp. 43-49. CMP 95:09
    • (1993) The Lattice Sieve , pp. 43-49
  • 35
    • 0001443138 scopus 로고
    • Discrete logarithms and local units
    • MR 95c:11156
    • O. Schirokauer, Discrete logarithms and local units, Phil. Trans. R. Soc. Lond. A 345 (1993), 409-423. MR 95c:11156
    • (1993) Phil. Trans. R. Soc. Lond. A , vol.345 , pp. 409-423
    • Schirokauer, O.1
  • 36
    • 84958036387 scopus 로고    scopus 로고
    • Discrete logarithms: The effectiveness of the index calculus method
    • Proceedings of the ANTS-II conference (H. Cohen, ed.) Springer-Verlag, MR 98i:11109
    • O. Schirokauer, D. Weber, and Th. Denny, Discrete logarithms: the effectiveness of the index calculus method, Proceedings of the ANTS-II conference (H. Cohen, ed.), Lecture Notes in Computer Science, vol. 1122, Springer-Verlag, 1996. MR 98i:11109
    • (1996) Lecture Notes in Computer Science , vol.1122
    • Schirokauer, O.1    Weber, D.2    Denny, Th.3
  • 37
  • 38
    • 84968510096 scopus 로고
    • The multiple polynomial quadratic sieve
    • MR 88c:11079
    • R. Silverman, The multiple polynomial quadratic sieve, Math. Comp. 48 (1987), 329-340. MR 88c:11079
    • (1987) Math. Comp. , vol.48 , pp. 329-340
    • Silverman, R.1
  • 39
    • 0012411518 scopus 로고    scopus 로고
    • Algèbre linéaire pour le logarithme discret
    • Master's thesis, Stage de fin d'étude et de DEA
    • F. Valette, Algèbre linéaire pour le logarithme discret, Master's thesis, ENSTA, 1999, Stage de fin d'étude et de DEA.
    • (1999) ENSTA
    • Valette, F.1
  • 40
    • 84958033848 scopus 로고    scopus 로고
    • Computing discrete logarithms with the number field sieve
    • Proceedings of the ANTS-II conference. Springer-Verlag, MR 98k:11186
    • D. Weber, Computing discrete logarithms with the number field sieve, Proceedings of the ANTS-II conference. Lecture Notes in Computer Science, vol. 1122, Springer-Verlag, 1996. MR 98k:11186
    • (1996) Lecture Notes in Computer Science , vol.1122
    • Weber, D.1
  • 41
    • 84956868710 scopus 로고    scopus 로고
    • Computing discrete logarithms with quadratic number rings
    • Advances in Cryptology - EUROCRYP'98 (K. Nyberg, ed.), Springer-Verlag. CMP 2000:07
    • _, Computing discrete logarithms with quadratic number rings, Advances in Cryptology - EUROCRYP'98 (K. Nyberg, ed.), Lecture Notes in Computer Science, vol. 1403, Springer-Verlag, 1998, pp. 171-183. CMP 2000:07
    • (1998) Lecture Notes in Computer Science , vol.1403 , pp. 171-183
  • 42
    • 84957715627 scopus 로고    scopus 로고
    • The solution of McCurley's discrete log challenge
    • Advances in Cryptology - CRYPTO'98 (H. Krawczyk, ed.), Springer-Verlag, MR 991:94057
    • D. Weber and Th. Denny, The solution of McCurley's discrete log challenge, Advances in Cryptology - CRYPTO'98 (H. Krawczyk, ed.), Lecture Notes in Computer Science, vol. 1462, Springer-Verlag, 1998, pp. 458-471. MR 991:94057
    • (1998) Lecture Notes in Computer Science , vol.1462 , pp. 458-471
    • Weber, D.1    Denny, Th.2


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