메뉴 건너뛰기




Volumn 3958 LNCS, Issue , 2006, Pages 174-190

An algorithm to solve the discrete logarithm problem with the number field sieve

Author keywords

Discrete Logarithms; Number Field Sieve

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CRYPTOGRAPHY; INTEGER PROGRAMMING; PROBLEM SOLVING;

EID: 33745863430     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11745853_12     Document Type: Conference Paper
Times cited : (26)

References (24)
  • 1
    • 0002768224 scopus 로고
    • On a problem of Oppenheim concerning "factorisatio numerorum"
    • Canfield, E., Erdös, P., Pomerance, C.: On a problem of Oppenheim concerning "factorisatio numerorum". J.Number Theory 17 (1983) 1-28
    • (1983) J.Number Theory , vol.17 , pp. 1-28
    • Canfield, E.1    Erdös, P.2    Pomerance, C.3
  • 2
    • 0021468777 scopus 로고
    • Fast evaluation of logarithms in fields of characteristic two
    • Coppersmith, D.: Fast Evaluation of Logarithms in Fields of Characteristic Two. IEEE Transactions on Information Theory IT-30 (1984) 587-594
    • (1984) IEEE Transactions on Information Theory , vol.IT-30 , pp. 587-594
    • Coppersmith, D.1
  • 3
    • 0027610980 scopus 로고
    • Modifications to the number field sieve
    • Coppersmith, D.: Modifications to the Number Field Sieve. J. Cryptology 6 (1993) 169-180
    • (1993) J. Cryptology , vol.6 , pp. 169-180
    • Coppersmith, D.1
  • 5
    • 0000303380 scopus 로고
    • Discrete logarithms in GF(p) using the number field sieve
    • Gordon, D.: Discrete logarithms in GF(p) using the number field sieve. SIAM Journal of Discrete Mathematics 6 (1993) 124-138
    • (1993) SIAM Journal of Discrete Mathematics , vol.6 , pp. 124-138
    • Gordon, D.1
  • 6
    • 0037376560 scopus 로고    scopus 로고
    • Improvements to the general Number Field Sieve for discrete logarithms in prime fields
    • Joux, A., Lercier, R.: Improvements to the general Number Field Sieve for discrete logarithms in prime fields. Mathematics of Computation 72 (2003) 953-967
    • (2003) Mathematics of Computation , vol.72 , pp. 953-967
    • Joux, A.1    Lercier, R.2
  • 7
    • 33745807298 scopus 로고    scopus 로고
    • Calcul de logarithmes discrets dans GF(p) - 130 chiffres
    • 6
    • Joux, A., Lercier, R.: Calcul de logarithmes discrets dans GF(p) - 130 chiffres. CRYPTO Mailing List (6/2005)
    • (2005) CRYPTO Mailing List
    • Joux, A.1    Lercier, R.2
  • 8
    • 0013460463 scopus 로고
    • The development of the number field sieve
    • Lenstra, A., Lenstra, H. (eds) Springer-Verlag
    • Lenstra, A., Lenstra, H. (eds): The Development of the Number Field Sieve. Lecture Notes in Mathematics 1554, Springer-Verlag, 1993
    • (1993) Lecture Notes in Mathematics , vol.1554
  • 9
    • 0001258323 scopus 로고
    • Factoring integers with elliptic curves
    • Lenstra, H.: Factoring integers with elliptic curves. Annals of Mathematics 126 (1987) 649-673
    • (1987) Annals of Mathematics , vol.126 , pp. 649-673
    • Lenstra, H.1
  • 10
    • 0037267485 scopus 로고    scopus 로고
    • On asymptotic complexity of computing discrete logarithms over GF(p)
    • Matyukhin, D.: On asymptotic complexity of computing discrete logarithms over GF(p). Discrete Mathematics and Applications 13 (2003) 27-50
    • (2003) Discrete Mathematics and Applications , vol.13 , pp. 27-50
    • Matyukhin, D.1
  • 11
    • 0002139049 scopus 로고
    • The discrete logarithm problem
    • Pomerance,C. (ed): Cryptography and Computational Number Theory. Amer. Math. Soc
    • McCurley, K.: The discrete logarithm problem, in: Pomerance,C. (ed): Cryptography and Computational Number Theory. Proc. Symp.Appl.Math. 42, Amer. Math. Soc.,1990, 49-74
    • (1990) Proc. Symp. Appl. Math. , vol.42 , pp. 49-74
    • McCurley, K.1
  • 12
    • 0001534053 scopus 로고    scopus 로고
    • Discrete logarithms: The past and the future
    • Odlyzko, A.: Discrete logarithms: The past and the future. Designs, Codes and Cryptography 19 (2000), 129-145.
    • (2000) Designs, Codes and Cryptography , vol.19 , pp. 129-145
    • Odlyzko, A.1
  • 13
    • 0010836364 scopus 로고
    • Discrete logarithms and smooth polynomials
    • Mullen, G., Shiue, P. (eds): Finite Fields: Theory, Applications and Algorithms. Amer. Math. Soc.
    • Odlyzko, A.: Discrete Logarithms and Smooth Polynomials, in: Mullen, G., Shiue, P. (eds): Finite Fields: Theory, Applications and Algorithms. Contemporary Math 168, Amer. Math. Soc.,1994, 269-278
    • (1994) Contemporary Math , vol.168 , pp. 269-278
    • Odlyzko, A.1
  • 14
    • 84957014368 scopus 로고
    • Discrete logarithms in finite fields and their cryptographic significance
    • Beth, T.,Cot, N., Ingemarsson, I. (eds): Advances in Cryptology: Proceedings of Eurocrypt '84. Springer-Verlag
    • Odlyzko, A.: Discrete logarithms in finite fields and their cryptographic significance, in: Beth, T.,Cot, N., Ingemarsson, I. (eds): Advances in Cryptology: Proceedings of Eurocrypt '84. Lecture Notes in Computer Science 208, Springer-Verlag,1985,224-314
    • (1985) Lecture Notes in Computer Science , vol.208 , pp. 224-314
    • Odlyzko, A.1
  • 15
    • 33745835139 scopus 로고
    • On the complexity of computing discrete logarithms and factoring integers
    • Cover,T. and Gopinath,B. (eds.). Springer
    • Odlyzko, A.: On the complexity of Computing Discrete Logarithms and Factoring Integers, in: Cover,T. and Gopinath,B. (eds.): Open Problems in Communication and Computation. Springer, 1987, 113-116
    • (1987) Open Problems in Communication and Computation , pp. 113-116
    • Odlyzko, A.1
  • 16
    • 84966238549 scopus 로고
    • Monte Carlo methods for index computations mod p
    • Pollard, J.: Monte Carlo methods for index computations mod p. Mathematics of Computation 32 (1978) 918-924
    • (1978) Mathematics of Computation , vol.32 , pp. 918-924
    • Pollard, J.1
  • 18
    • 0040235097 scopus 로고
    • Fast, rigorous factorization and discrete logarithm algorithms
    • Nozaki, N., Johnson, D., Nishizaki, T.,Wilf, H.(eds). Academic Press
    • Pomerance, C.: Fast, rigorous factorization and discrete logarithm algorithms, in: Nozaki, N., Johnson, D., Nishizaki, T.,Wilf, H.(eds): Discrete Algorithms and Complexity. Academic Press, 1987, 119-143
    • (1987) Discrete Algorithms and Complexity , pp. 119-143
    • Pomerance, C.1
  • 21
    • 0036003416 scopus 로고    scopus 로고
    • Special prime numbers and discrete logs in prime finite fields
    • Semaev, I.: Special prime numbers and discrete logs in prime finite fields. Mathematics of Computation 71 (2002) 363-377
    • (2002) Mathematics of Computation , vol.71 , pp. 363-377
    • Semaev, I.1
  • 22
    • 84968515930 scopus 로고
    • Searching for primitive roots in finite fields
    • Shoup, V.: Searching for primitive roots in finite fields. Mathematics of Computation 58 (1992) 918-924
    • (1992) Mathematics of Computation , vol.58 , pp. 918-924
    • Shoup, V.1
  • 23
    • 17444376558 scopus 로고    scopus 로고
    • Parallel collision search with cryptanalytic applications
    • van Oorschot, P., Wiener, M.: Parallel collision search with cryptanalytic applications. J. Cryptology 12 (1999) 1-28
    • (1999) J. Cryptology , vol.12 , pp. 1-28
    • Van Oorschot, P.1    Wiener, M.2
  • 24
    • 0022583143 scopus 로고
    • Solving sparse linear equations over finite fields
    • Wiedemann, D.: Solving sparse linear equations over finite fields. IEEE Trans.Inform. Theory 32 (1986) 54-62
    • (1986) IEEE Trans. Inform. Theory , vol.32 , pp. 54-62
    • Wiedemann, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.