메뉴 건너뛰기




Volumn 20, Issue 1, 2000, Pages 5-40

The Xedni Calculus and the Elliptic Curve Discrete Logarithm Problem

Author keywords

Discrete logarithm; Elliptic curve; Xedni calculus

Indexed keywords


EID: 0012234171     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008319518035     Document Type: Article
Times cited : (44)

References (24)
  • 1
    • 0010893177 scopus 로고
    • Elliptic curves and modular functions
    • Antwerp IV: Springer Lecture Notes 476 (Birch and Kuyk, eds.), Springer-Verlag
    • B. Birch and H. P. F. Swinnerton-Dyer, Elliptic curves and modular functions, Modular Functions of One Variable, Antwerp IV: Springer Lecture Notes 476 (Birch and Kuyk, eds.), Springer-Verlag (1975) pp. 2-32.
    • (1975) Modular Functions of One Variable , pp. 2-32
    • Birch, B.1    Swinnerton-Dyer, H.P.F.2
  • 3
    • 0001033035 scopus 로고
    • Addendum to a paper of Harada and Lang
    • I. Connell, Addendum to a paper of Harada and Lang, J. Algebra, Vol. 145 (1992) pp. 463-467.
    • (1992) J. Algebra , vol.145 , pp. 463-467
    • Connell, I.1
  • 5
    • 0000626015 scopus 로고
    • L'ensemble exceptionnel dans la conjecture de Szpiro
    • E. Fouvry, M. Nair, and G. Tenenbaum, L'ensemble exceptionnel dans la conjecture de Szpiro, Bull. Soc. Math. France, Vol. 120 (1992) pp. 485-506.
    • (1992) Bull. Soc. Math. France , vol.120 , pp. 485-506
    • Fouvry, E.1    Nair, M.2    Tenenbaum, G.3
  • 6
    • 0032325491 scopus 로고    scopus 로고
    • Extended gcd and Hermite normal form algorithms via lattice basis reduction
    • G. Havas, B. S. Majewski, and K. R. Matthews, Extended gcd and Hermite normal form algorithms via lattice basis reduction, Experimental Math., Vol. 7 (1998) pp. 125-136
    • (1998) Experimental Math. , vol.7 , pp. 125-136
    • Havas, G.1    Majewski, B.S.2    Matthews, K.R.3
  • 7
    • 0042138791 scopus 로고
    • The canonical height and integral points on elliptic curves
    • M. Hindry and J. H. Silverman, The canonical height and integral points on elliptic curves, Invent. Math., Vol. 93, pp. 419-450 (1988).
    • (1988) Invent. Math. , vol.93 , pp. 419-450
    • Hindry, M.1    Silverman, J.H.2
  • 9
    • 84968503742 scopus 로고
    • Elliptic curve cryptosystems
    • N. Koblitz, Elliptic curve cryptosystems, Mathematics of Computation, Vol. 48, pp. 203-209 (1987).
    • (1987) Mathematics of Computation , vol.48 , pp. 203-209
    • Koblitz, N.1
  • 10
    • 0346760839 scopus 로고    scopus 로고
    • N. Koblitz, Private communications, September 1998
    • N. Koblitz, Private communications, September 1998.
  • 11
    • 0001258323 scopus 로고
    • Factoring integers with elliptic curves
    • H. Lenstra, Factoring integers with elliptic curves, Annals of Math, Vol. 126 (1987) pp. 649-673.
    • (1987) Annals of Math , vol.126 , pp. 649-673
    • Lenstra, H.1
  • 12
    • 84966225207 scopus 로고
    • Specializations of finitely generated subgroups of abelian varieties
    • D. W. Masser, Specializations of finitely generated subgroups of abelian varieties, Trans. AMS, Vol. 311 (1989) pp. 413-424.
    • (1989) Trans. AMS , vol.311 , pp. 413-424
    • Masser, D.W.1
  • 14
    • 0001543668 scopus 로고
    • Formules explicites et minoration de conducteurs de variétés algébriques
    • J. F. Mestre, Formules explicites et minoration de conducteurs de variétés algébriques, Compositio Math., Vol. 58 (1986) pp. 209-232.
    • (1986) Compositio Math. , vol.58 , pp. 209-232
    • Mestre, J.F.1
  • 16
    • 0000516903 scopus 로고
    • Propriétés arithmétiques et géométriques rattachés à la notion de rang d'une courbe algébrique dans un corps
    • A. Néron, Propriétés arithmétiques et géométriques rattachés à la notion de rang d'une courbe algébrique dans un corps, Bull. Soc. Math. France, Vol. 80 (1952) pp. 101-166.
    • (1952) Bull. Soc. Math. France , vol.80 , pp. 101-166
    • Néron, A.1
  • 17
    • 0000058131 scopus 로고
    • Variation of the root number in families of elliptic curves
    • D. Rohrlich, Variation of the root number in families of elliptic curves, Compositio Math, Vol. 87 (1993) pp. 119-151
    • (1993) Compositio Math , vol.87 , pp. 119-151
    • Rohrlich, D.1
  • 19
    • 0003474033 scopus 로고
    • Graduate Texts in Math., Springer-Verlag, Berlin and New York
    • J. H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Math., Vol. 106, Springer-Verlag, Berlin and New York (1986).
    • (1986) The Arithmetic of Elliptic Curves , vol.106
    • Silverman, J.H.1
  • 20
    • 84968504366 scopus 로고
    • Computing heights on elliptic curves
    • J. H. Silverman, Computing heights on elliptic curves, Math. Comp., Vol. 51 (1988) pp. 339-358.
    • (1988) Math. Comp. , vol.51 , pp. 339-358
    • Silverman, J.H.1
  • 21
    • 0031515260 scopus 로고    scopus 로고
    • Computing canonical heights with little (or no) factorization
    • J. H. Silverman, Computing canonical heights with little (or no) factorization, Math. Comp., Vol. 66 (1997) pp. 787-805.
    • (1997) Math. Comp. , vol.66 , pp. 787-805
    • Silverman, J.H.1
  • 22
    • 84947727672 scopus 로고    scopus 로고
    • Elliptic curve discrete logarithms and the index calculus
    • Springer-Verlag, Berlin
    • J. H. Silverman and J. Suzuki, Elliptic curve discrete logarithms and the index calculus, ASIACRYPT '98: Lecture Notes in Computer Science, Springer-Verlag, Berlin, 1998, pp. 110-125.
    • (1998) ASIACRYPT '98: Lecture Notes in Computer Science , pp. 110-125
    • Silverman, J.H.1    Suzuki, J.2
  • 24
    • 0000603921 scopus 로고
    • Modular elliptic curves and Fermat's last theorem
    • A. Wiles, Modular elliptic curves and Fermat's last theorem, Annals of Math, Vol. 141 (1995) pp. 443-551
    • (1995) Annals of Math , vol.141 , pp. 443-551
    • Wiles, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.