메뉴 건너뛰기




Volumn 2894, Issue , 2003, Pages 311-325

On class group computations using the number field sieve

Author keywords

Class groups; Hyperelliptic curve discrete logarithm; Imaginary quadratic function fields; Imaginary quadratic number fields; Number field sieve

Indexed keywords

ALGORITHMS; CODES (SYMBOLS); COMPUTATION THEORY; GEOMETRY; SECURITY OF DATA; SIEVES;

EID: 0344196670     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-40061-5_19     Document Type: Article
Times cited : (2)

References (15)
  • 1
    • 0012607754 scopus 로고    scopus 로고
    • A subexponential algorithm for discrete logarithms over hyperelliptic curves of large genus over GF(q)
    • ADLEMAN, L. M., DEMARRAIS, J., AND HUANG, M.-D. A subexponential algorithm for discrete logarithms over hyperelliptic curves of large genus over GF(q). Theoretical Computer Science 226, 1-2 (1999), 7-18.
    • (1999) Theoretical Computer Science , vol.226 , Issue.1-2 , pp. 7-18
    • Adleman, L.M.1    Demarrais, J.2    Huang, M.-D.3
  • 2
    • 0013415910 scopus 로고
    • Factoring integers with the number field sieve
    • A. K. Lenstra and H. W. Lenstra, Eds., LNM. Springer-Verlag
    • BUHLER, J. P., LENSTRA, JR., H. W., AND POMERANCE, C. Factoring integers with the number field sieve. In The development of the number field sieve, A. K. Lenstra and H. W. Lenstra, Eds., no. 1554 in LNM. Springer-Verlag, 1993, pp. 50-94.
    • (1993) The Development of the Number Field Sieve , vol.1554 , pp. 50-94
    • Buhler, J.P.1    Lenstra Jr., H.W.2    Pomerance, C.3
  • 3
    • 0011002453 scopus 로고
    • A Course in Computational Algebraic Number Theory
    • Springer-Verlag
    • COHEN, H. A Course in Computational Algebraic Number Theory, vol. 138 of GTM. Springer-Verlag, 1995.
    • (1995) GTM , vol.138
    • Cohen, H.1
  • 5
    • 84958774556 scopus 로고    scopus 로고
    • A statistically-hiding integer commitment scheme based on groups with hidden order
    • Advances in Cryptology - ASIACRYPT 2002 Y. Zheng, Ed., Springer-Verlag
    • DAMGÅRD, I., AND FUJISAKI, E. A statistically-hiding integer commitment scheme based on groups with hidden order. In Advances in Cryptology - ASIACRYPT 2002 (2002), Y. Zheng, Ed., vol. 2501 of LNCS, Springer-Verlag, pp. 125-142.
    • (2002) LNCS , vol.2501 , pp. 125-142
    • Damgård, I.1    Fujisaki, E.2
  • 6
    • 0042833029 scopus 로고    scopus 로고
    • A general framework for subexponential discrete logarithm algorithms
    • ENGE, A., AND GAUDRY, P. A. A general framework for subexponential discrete logarithm algorithms. Acta Arithmetica 102, 1 (2002), 83-103.
    • (2002) Acta Arithmetica , vol.102 , Issue.1 , pp. 83-103
    • Enge, A.1    Gaudry, P.A.2
  • 7
    • 0000303380 scopus 로고
    • Discrete logarithms in gf(p) using the number field sieve
    • GORDON, D. M. Discrete logarithms in gf(p) using the number field sieve. SIAM Journal of Discrete Mathematics 6, 1 (1993), 124-138.
    • (1993) SIAM Journal of Discrete Mathematics , vol.6 , Issue.1 , pp. 124-138
    • Gordon, D.M.1
  • 8
    • 35248838315 scopus 로고    scopus 로고
    • IQ cryptography: A secure and efficient alternative
    • Submitted
    • HAMDY, S. IQ cryptography: A secure and efficient alternative. Journal of Cryptology (2003). Submitted.
    • (2003) Journal of Cryptology
    • Hamdy, S.1
  • 9
    • 0033472659 scopus 로고    scopus 로고
    • Applying sieving to the computation of quadratic class groups
    • JACOBSON, JR., M. J. Applying sieving to the computation of quadratic class groups. Mathematics of Computation 68, 226 (1999), 859-867.
    • (1999) Mathematics of Computation , vol.68 , Issue.226 , pp. 859-867
    • Jacobson Jr., M.J.1
  • 13
    • 0034405017 scopus 로고    scopus 로고
    • Using number fields to compute logarithms in finite fields
    • SCHIROKAUER, O. Using number fields to compute logarithms in finite fields. Mathematics of Computation 69, 231 (2000), 1267-1283.
    • (2000) Mathematics of Computation , vol.69 , Issue.231 , pp. 1267-1283
    • Schirokauer, O.1
  • 14
    • 84958036387 scopus 로고    scopus 로고
    • Discrete logarithms: The effectiveness of the index calculus method
    • Algorithmic Number Theory, ANTS-II H. Cohen, Ed., Springer-Verlag
    • SCHIROKAUER, O., WEBER, D., AND DENNY, T. Discrete logarithms: The effectiveness of the index calculus method. In Algorithmic Number Theory, ANTS-II (1996), H. Cohen, Ed., vol. 1122 of LNCS, Springer-Verlag, pp. 337-361.
    • (1996) LNCS , vol.1122 , pp. 337-361
    • Schirokauer, O.1    Weber, D.2    Denny, T.3
  • 15
    • 84958033848 scopus 로고    scopus 로고
    • Computing discrete logarithms with the general number field sieve
    • Algorithmic Number Theory, ANTS-II H. Cohen, Ed., Springer-Verlag
    • WEBER, D. Computing discrete logarithms with the general number field sieve. In Algorithmic Number Theory, ANTS-II (1996), H. Cohen, Ed., vol. 1122 of LNCS, Springer-Verlag, pp. 391-403.
    • (1996) LNCS , vol.1122 , pp. 391-403
    • Weber, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.