메뉴 건너뛰기




Volumn 16, Issue 6, 2006, Pages 439-460

Cryptographic implications of Hess' generalized GHS attack

Author keywords

Elliptic curve cryptography; Isogenies; Weil descent

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DISCRETE TIME CONTROL SYSTEMS; PROBLEM SOLVING;

EID: 31444432696     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00200-005-0186-8     Document Type: Article
Times cited : (15)

References (25)
  • 1
    • 84929727140 scopus 로고
    • A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fields
    • Algorithmic Number Theory
    • Adleman, L., DeMarrais, J., Huang, M.: A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fields. Algorithmic Number Theory, Lecture Notes in Computer Science, 877, 28-40 (1994)
    • (1994) Lecture Notes in Computer Science , vol.877 , pp. 28-40
    • Adleman, L.1    Demarrais, J.2    Huang, M.3
  • 2
    • 0042833029 scopus 로고    scopus 로고
    • A general framework for subexponential discrete logarithm algorithms
    • Enge, A., Gaudry, P.: A general framework for subexponential discrete logarithm algorithms. Acta Arithmetica 102, 83-103 (2002)
    • (2002) Acta Arithmetica , vol.102 , pp. 83-103
    • Enge, A.1    Gaudry, P.2
  • 4
    • 84968502759 scopus 로고
    • A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
    • Frey, G., Rück, H.: A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves. Mathematics of Computation 62, 865-874 (1994)
    • (1994) Mathematics of Computation , vol.62 , pp. 865-874
    • Frey, G.1    Rück, H.2
  • 5
    • 23044503196 scopus 로고    scopus 로고
    • Constructing isogenies between elliptic curves over finite fields
    • Galbraith, S.: Constructing isogenies between elliptic curves over finite fields. LMS Journal of Computation and Mathematics 2, 118-138 (1999)
    • (1999) LMS Journal of Computation and Mathematics , vol.2 , pp. 118-138
    • Galbraith, S.1
  • 6
    • 84947261826 scopus 로고    scopus 로고
    • Extending the GHS weil descent attack. Advances in cryptology
    • EUROCRYPT 2002
    • Galbraith, S., Hess, F., Smart, N.: Extending the GHS Weil descent attack. Advances in Cryptology - EUROCRYPT 2002 Lecture Notes in Computer Science, 2332, 29-44 (2002)
    • (2002) Lecture Notes in Computer Science , vol.2332 , pp. 29-44
    • Galbraith, S.1    Hess, F.2    Smart, N.3
  • 7
    • 84948978775 scopus 로고    scopus 로고
    • An algorithm for solving the discrete log problem in hyperelliptic curves. Advances in Cryptology
    • EUROCRYPT 2000
    • Gaudry, P.: An algorithm for solving the discrete log problem in hyperelliptic curves. Advances in Cryptology - EUROCRYPT 2000, Lecture Notes in Computer Science, 1807, 19-34 (2000)
    • (2000) Lecture Notes in Computer Science , vol.1807 , pp. 19-34
    • Gaudry, P.1
  • 8
    • 33745142755 scopus 로고    scopus 로고
    • Index calculus for abelian varieties and the elliptic curve discrete logarithm problem
    • Gaudry, P.: Index calculus for abelian varieties and the elliptic curve discrete logarithm problem. Cryptology ePrint Archive: Report 2004/073, 2004 Available from http://eprint.iacr.org/2004/073/
    • (2004) Cryptology EPrint Archive: Report , vol.2004 , Issue.73
    • Gaudry, P.1
  • 9
    • 0001788567 scopus 로고    scopus 로고
    • Constructive and destructive facets of Weil descent on elliptic curves
    • Gaudry, P., Hess, F., Smart, N.: Constructive and destructive facets of Weil descent on elliptic curves. J. Cryptol. 15, 19-46 (2002)
    • (2002) J. Cryptol. , vol.15 , pp. 19-46
    • Gaudry, P.1    Hess, F.2    Smart, N.3
  • 10
    • 24144479320 scopus 로고    scopus 로고
    • A double large prime variation for small genus hyper-elliptic index calculus
    • Gaudry, P., Thériault, N., Thomé, E.: A double large prime variation for small genus hyper-elliptic index calculus. Cryptology ePrint Archive: Report 2004/153, 2004 Available from http://eprint.iacr.org/2004/153/
    • (2004) Cryptology EPrint Archive: Report , vol.2004 , Issue.153
    • Gaudry, P.1    Thériault, N.2    Thomé, E.3
  • 11
    • 0036222252 scopus 로고    scopus 로고
    • Computing Riemann-Roch spaces in algebraic function fields and related topics
    • Hess, F.: Computing Riemann-Roch spaces in algebraic function fields and related topics. J. Symbol. Comput. 33, 425-445 (2002)
    • (2002) J. Symbol. Comput. , vol.33 , pp. 425-445
    • Hess, F.1
  • 13
    • 23044512900 scopus 로고    scopus 로고
    • Generalising the GHS attack on the elliptic curve discrete logarithm problem
    • Hess, F.: Generalising the GHS attack on the elliptic curve discrete logarithm problem. LMS J. Comput. Math. 7, 167-192 (2004)
    • (2004) LMS J. Comput. Math. , vol.7 , pp. 167-192
    • Hess, F.1
  • 14
    • 31444453853 scopus 로고    scopus 로고
    • Weil descent attacks
    • Blake, I., Seroussi, G., Smart, N. (eds.) Cambridge University Press
    • Hess, F.: Weil descent attacks. In: Blake, I., Seroussi, G., Smart, N. (eds.) Advances in elliptic curve cryptography, Cambridge University Press, 2005
    • (2005) Advances in Elliptic Curve Cryptography
    • Hess, F.1
  • 16
    • 11344252143 scopus 로고    scopus 로고
    • Analysis of the GHS Weil descent attack on the ECDLP over characteristic two finite fields of composite degree
    • Maurer, M., Menezes, A., Teske, E.: Analysis of the GHS Weil descent attack on the ECDLP over characteristic two finite fields of composite degree. LMS J. Comput. Math. 5, 127-174 (2002)
    • (2002) LMS J. Comput. Math. , vol.5 , pp. 127-174
    • Maurer, M.1    Menezes, A.2    Teske, E.3
  • 17
    • 0027662341 scopus 로고
    • Reducing elliptic curve logarithms to logarithms in a finite field
    • Menezes, A., Okamoto, T., Vanstone, S.: Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Trans. Inform. Theory 39, 1639-1646 (1993)
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 1639-1646
    • Menezes, A.1    Okamoto, T.2    Vanstone, S.3
  • 18
    • 33847320580 scopus 로고    scopus 로고
    • Analysis of the weil descent attack of gaudry, hess and smart
    • Topics in Cryptology - CT-RSA 2001
    • Menezes, A., Qu, M.: Analysis of the weil descent attack of gaudry, hess and smart. Topics in Cryptology - CT-RSA 2001, Lecture Notes in Computer Science, 2020, 308-318 (2001)
    • (2001) Lecture Notes in Computer Science , vol.2020 , pp. 308-318
    • Menezes, A.1    Qu, M.2
  • 19
    • 35048833769 scopus 로고    scopus 로고
    • Weak fields for ECC
    • Topics in Cryptology - CT-RSA 2004
    • Menezes, A., Teske, E., Weng, A.: Weak fields for ECC. Topics in Cryptology - CT-RSA 2004, Lecture Notes in Computer Science, 2964, 366-386 (2004)
    • (2004) Lecture Notes in Computer Science , vol.2964 , pp. 366-386
    • Menezes, A.1    Teske, E.2    Weng, A.3
  • 20
    • 17444376558 scopus 로고    scopus 로고
    • Parallel collision search with cryptanalytic applications
    • van Oorschot, P., Wiener, M.: Parallel collision search with cryptanalytic applications. J. Cryptol. 12, 1-28 (1999)
    • (1999) J. Cryptol. , vol.12 , pp. 1-28
    • Van Oorschot, P.1    Wiener, M.2
  • 21
    • 84966238549 scopus 로고
    • Monte Carlo methods for index computation mod p
    • Pollard, J.: Monte Carlo methods for index computation mod p. Math. Comput. 32, 918-924 (1978)
    • (1978) Math. Comput. , vol.32 , pp. 918-924
    • Pollard, J.1
  • 22
    • 0343623059 scopus 로고    scopus 로고
    • Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves
    • Satoh, T., Araki, K.: Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves. Commentarii Mathematici Universitatis Sancti Pauli 47, 81-92 (1998)
    • (1998) Commentarii Mathematici Universitatis Sancti Pauli , vol.47 , pp. 81-92
    • Satoh, T.1    Araki, K.2
  • 23
    • 0032352723 scopus 로고    scopus 로고
    • Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p
    • Semaev, I.: Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p. Math. Comput. 67, 353-356 (1998)
    • (1998) Math. Comput. , vol.67 , pp. 353-356
    • Semaev, I.1
  • 24
    • 0003539458 scopus 로고    scopus 로고
    • The discrete logarithm problem on elliptic curves of trace one
    • Smart, N.: The discrete logarithm problem on elliptic curves of trace one. J. Cryptol. 12, 193-196 (1999)
    • (1999) J. Cryptol. , vol.12 , pp. 193-196
    • Smart, N.1
  • 25
    • 0035531397 scopus 로고    scopus 로고
    • On random walks for Pollard's rho method
    • Teske, E.: On random walks for Pollard's rho method. Math. Comput. 70, 809-825 (2001)
    • (2001) Math. Comput. , vol.70 , pp. 809-825
    • Teske, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.