메뉴 건너뛰기




Volumn 1976, Issue , 2000, Pages 259-273

Construction of hyperelliptic curves with CM and its application to cryptosystems

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; EXPONENTIAL FUNCTIONS; POLYNOMIAL APPROXIMATION; SECURITY OF DATA;

EID: 0142200497     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44448-3_20     Document Type: Conference Paper
Times cited : (4)

References (40)
  • 2
    • 84937443786 scopus 로고
    • A Subexponential Algorithms for Discrete Logarithms over the Rational Subgroup of the Jacobians of Large Genus Hyperelliptic Curves over Finite Fields
    • L.M. Adleman, J. DeMarrais, M.D. Huang, “A Subexponential Algorithms for Discrete Logarithms over the Rational Subgroup of the Jacobians of Large Genus Hyperelliptic Curves over Finite Fields,” Proc. of ANTS95, Springer, (1995)
    • (1995) Proc. Of ANTS95
    • Adleman, L.M.1    Demarrais, J.2    Huang, M.D.3
  • 3
    • 84958035958 scopus 로고    scopus 로고
    • Counting rational points on curves and Abelian varieties over finite fields Henri Cohen (Ed)“Algorithmic number theory
    • Lecture Notes in Computer Science, 1122
    • L.M. Adleman, M.D. Huang, “Counting rational points on curves and Abelian varieties over finite fields” Henri Cohen (Ed)“Algorithmic number theory” Lecture Notes in Computer Science, 1122, Second International Symposium, ANTS-II, Proceedings, p.1-16. 1996
    • (1996) Second International Symposium, ANTS-II, Proceedings , pp. 1-16
    • Adleman, L.M.1    Huang, M.D.2
  • 6
    • 84968494137 scopus 로고
    • Computing in the jacobian of hyperelliptic curve
    • D. Cantor, “Computing in the jacobian of hyperelliptic curve,” Math. Comp., vol.48, p.95-101, (1987)
    • (1987) Math. Comp. , vol.48 , pp. 95-101
    • Cantor, D.1
  • 7
    • 0141879191 scopus 로고    scopus 로고
    • Efficient construction of secure hyperelliptic discrete logarithm problems
    • Springer-Verlag Lecture Notes on Computer Science, Y. Han, T. Okamoto, S. Qing (Eds.), Beijing, China, Nov
    • J. Chao, N. Matsuda, S. Tsujii, “Efficient construction of secure hyperelliptic discrete logarithm problems” Springer-Verlag Lecture Notes on Computer Science, Vol.1334, pp.292-301, “Information and Communication Security” Y. Han, T. Okamoto, S. Qing (Eds.) Proceedings of First International Conference ICICS’97, Beijing, China, Nov. 1997.
    • (1997) Information and Communication Security , vol.1334 , pp. 292-301
    • Chao, J.1    Matsuda, N.2    Tsujii, S.3
  • 11
    • 84937443789 scopus 로고    scopus 로고
    • Speeding up the discrete log computation on curves with automorphism
    • Duursma, Gaudry, O Morain, “Speeding up the discrete log computation on curves with automorphism”, Proceeding. Asiacrypt-99, 1999.
    • (1999) Proceeding. Asiacrypt-99
    • Duursma, G.1    Morain, O.2
  • 12
    • 84968502759 scopus 로고
    • A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
    • G. Frey, H.G. Rück, “A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves,” Math. Comp., 62, 865-874, 1994.
    • (1994) Math. Comp. , vol.62 , pp. 865-874
    • Frey, G.1    Rück, H.G.2
  • 14
    • 84937443790 scopus 로고    scopus 로고
    • A variant of the Adelman-DeMarrais-Huang algorithm and its application to small genera
    • June
    • P. Gaudry “A variant of the Adelman-DeMarrais-Huang algorithm and its application to small genera,” Preliminary version, June 1999.
    • (1999) Preliminary Version
    • Gaudry, P.1
  • 16
    • 84937443791 scopus 로고    scopus 로고
    • Construction of CM hyperelliptic curves using ordinary lifting
    • IEICE Japan
    • T. Haga, K. Matsuo, J. Chao, S. Tsujii, “Construction of CM hyperelliptic curves using ordinary lifting,” Proc. of SCIS’2000, IEICE Japan, 2000.
    • (2000) Proc. Of SCIS’2000
    • Haga, T.1    Matsuo, K.2    Chao, J.3    Tsujii, S.4
  • 18
    • 0000160903 scopus 로고
    • Arithmetic variety of for genus two
    • J. Igusa, “Arithmetic variety of for genus two,” Ann. of Math., vol.72, No.3, p.612-649, (1960)
    • (1960) Ann. Of Math. , vol.72 , Issue.3 , pp. 612-649
    • Igusa, J.1
  • 20
    • 0024864204 scopus 로고
    • Hyperelliptic cryptosystems
    • N. Koblitz, “Hyperelliptic cryptosystems,” J. of Cryptology, vol.1, p.139-150, (1989)
    • (1989) J. Of Cryptology , vol.1 , pp. 139-150
    • Koblitz, N.1
  • 23
    • 85030330304 scopus 로고
    • Reducing Elliptic Curve Logarithms to Logarithms in a Finite Fields
    • A. Menezes, S. Vanstone, T. Okamoto, “Reducing Elliptic Curve Logarithms to Logarithms in a Finite Fields,” Proc. of STOC, p.80-89, (1991).
    • (1991) Proc. Of STOC , pp. 80-89
    • Menezes, A.1    Vanstone, S.2    Okamoto, T.3
  • 29
    • 84966216845 scopus 로고
    • Frobenius maps of abelian varieties and finding roots of unity in finite fields
    • J. Pila, “Frobenius maps of abelian varieties and finding roots of unity in finite fields,” Math. Comp., vol.55, p. 745-763, (1990)
    • (1990) Math. Comp. , vol.55 , pp. 745-763
    • Pila, J.1
  • 31
    • 0000794868 scopus 로고
    • Good reduction of abelian varieties
    • J.P. Serre, J. Tate, “Good reduction of abelian varieties,” Ann. of Math. (2), 88 (1968), page 492-517.
    • (1968) Ann. Of Math , vol.88 , Issue.2 , pp. 492-517
    • Serre, J.P.1    Tate, J.2
  • 34
    • 34250541896 scopus 로고
    • Endomorphisms of Abelian varieties over finite fields
    • J. Tate, “Endomorphisms of Abelian varieties over finite fields,” Invent. Math. 2, p.134-144, (1966)
    • (1966) Invent. Math. , vol.2 , pp. 134-144
    • Tate, J.1
  • 35
    • 85028812500 scopus 로고
    • Computing in the Jacobian of a plane algebraic curve
    • LNCS-877
    • E.J. Volcheck, “Computing in the Jacobian of a plane algebraic curve,” Proc. of ANT-1, p.221-233, LNCS-877, (1994).
    • (1994) Proc. Of ANT-1 , pp. 221-233
    • Volcheck, E.J.1
  • 36
    • 0033480564 scopus 로고    scopus 로고
    • Examples of genus two CM curves defined over the rationals
    • P.V. Wamelen, “Examples of genus two CM curves defined over the rationals,” Math. Comp., 68(225), pp. 308-320, 1999.
    • (1999) Math. Comp. , vol.68 , Issue.225 , pp. 308-320
    • Wamelen, P.V.1
  • 37
    • 85034427792 scopus 로고
    • A p-adic algorithm for univariate partial fractions
    • P.S. Wang, “A p-adic algorithm for univariate partial fractions,” Proc. of ACM SYMSAC’81, ACM, 212-217, 1981.
    • (1981) Proc. Of ACM SYMSAC’81, ACM , pp. 212-217
    • Wang, P.S.1
  • 39
    • 0031283967 scopus 로고    scopus 로고
    • 0 (N) with dimension at least 3
    • 0(N) with dimension at least 3,” Experimental Math. vol. 6, No.4, 273-287, 1997.
    • (1997) Experimental Math , vol.6 , Issue.4 , pp. 273-287
    • Weber, H.J.1
  • 40
    • 84937439630 scopus 로고
    • Hecke characters and models of abelian varieties with complex multiplication
    • H. Yoshida, “Hecke characters and models of abelian varieties with complex multiplication,” J. Fac. Sci. Univ. of Tokyo, Sec. IA, 28, 633-649(1982).
    • (1982) J. Fac. Sci. Univ. Of Tokyo, Sec. IA , vol.28 , pp. 633-649
    • Yoshida, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.