메뉴 건너뛰기




Volumn 5671 LNCS, Issue , 2009, Pages 52-65

On the security of Pairing-friendly abelian varieties over non-prime fields

Author keywords

[No Author keywords available]

Indexed keywords

ABELIAN VARIETIES; FINITE FIELDS; GENUS 2 CURVES; PAIRING-BASED CRYPTOSYSTEM; PRIME FIELD; SECURITY LEVEL; SUPERSINGULAR ELLIPTIC CURVE;

EID: 69949142052     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-03298-1_4     Document Type: Conference Paper
Times cited : (6)

References (17)
  • 1
    • 50049083123 scopus 로고    scopus 로고
    • Cardona, G., Nart, E.: Zeta function and cryptographic exponent of supersingular curves of genus 2. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds.) Pairing 2007. LNCS, 4575, pp. 132-151. Springer, Heidelberg (2007)
    • Cardona, G., Nart, E.: Zeta function and cryptographic exponent of supersingular curves of genus 2. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds.) Pairing 2007. LNCS, vol. 4575, pp. 132-151. Springer, Heidelberg (2007)
  • 2
    • 69949132329 scopus 로고    scopus 로고
    • Standard models for finite fields
    • de Smit, B., Lenstra, H.W.: Standard models for finite fields. Lecture notes (2008), http://www.math.leidenuniv.nl/~desmit/papers/standard-models.pdf
    • (2008) Lecture notes
    • de Smit, B.1    Lenstra, H.W.2
  • 5
    • 73849107877 scopus 로고    scopus 로고
    • A taxonomy of pairing-friendly elliptic curves
    • To appear in, preprint, 2009
    • Freeman, D., Scott, M., Teske, E.: A taxonomy of pairing-friendly elliptic curves. To appear in Journal of Cryptology (preprint, 2009), http://eprint.iacr.org/2006/372
    • Journal of Cryptology
    • Freeman, D.1    Scott, M.2    Teske, E.3
  • 6
    • 67650659199 scopus 로고    scopus 로고
    • Endomorphisms for faster elliptic curve cryptography on a large class of curves
    • EUROCRYPT, Springer, Heidelberg
    • Galbraith, S., Lin, X., Scott, M.: Endomorphisms for faster elliptic curve cryptography on a large class of curves. In: EUROCRYPT 2009. LNCS, vol. 5479, pp. 518-535. Springer, Heidelberg (2009)
    • (2009) LNCS , vol.5479 , pp. 518-535
    • Galbraith, S.1    Lin, X.2    Scott, M.3
  • 8
    • 65049090545 scopus 로고    scopus 로고
    • Index calculus for abelian varieties and the elliptic curve discrete logarithm problem
    • Preprint, http://www.loria.fr/~gaudry/publis/indexcalc.pdf, To appear in
    • Gaudry, P.: Index calculus for abelian varieties and the elliptic curve discrete logarithm problem. To appear in J. Symbolic Computation. Preprint, http://www.loria.fr/~gaudry/publis/indexcalc.pdf
    • J. Symbolic Computation
    • 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.P.: Constructive and destructive facets of Weil descent on elliptic curves. J. Cryptology 15, 19-46 (2002)
    • (2002) J. Cryptology , vol.15 , pp. 19-46
    • Gaudry, P.1    Hess, F.2    Smart, N.P.3
  • 10
    • 47849110765 scopus 로고    scopus 로고
    • Hitt, L.: On the minimal embedding field. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds.) Pairing 2007. LNCS, 4575, pp. 294-301. Springer, Heidelberg (2007)
    • Hitt, L.: On the minimal embedding field. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds.) Pairing 2007. LNCS, vol. 4575, pp. 294-301. Springer, Heidelberg (2007)
  • 11
    • 69949178175 scopus 로고    scopus 로고
    • Hitt O'Connor, L., McGuire, G., Naehrig, M., Streng, M.: CM construction of genus 2 curves with p-rank 1. Cryptology ePrint Archive, Report 2008/491 (2008), http://eprint.iacr.org/2008/491
    • Hitt O'Connor, L., McGuire, G., Naehrig, M., Streng, M.: CM construction of genus 2 curves with p-rank 1. Cryptology ePrint Archive, Report 2008/491 (2008), http://eprint.iacr.org/2008/491
  • 12
    • 69949133194 scopus 로고    scopus 로고
    • Lang, S.: Algebra, revised third edn. Graduate Texts in Mathematics, 211. Springer, New York (2002)
    • Lang, S.: Algebra, revised third edn. Graduate Texts in Mathematics, vol. 211. Springer, New York (2002)
  • 14
    • 0002627221 scopus 로고
    • Abelian varieties
    • Gornell, G, Silverman, J, eds, Springer, New York
    • Milne, J.S.: Abelian varieties. In: Gornell, G., Silverman, J. (eds.) Arithmetic Geometry, pp. 103-150. Springer, New York (1986)
    • (1986) Arithmetic Geometry , pp. 103-150
    • Milne, J.S.1
  • 15
    • 84937426999 scopus 로고    scopus 로고
    • Supersingular abelian varieties in cryptology
    • Yung, M, ed, CRYPTO 2002, Springer, Heidelberg
    • Rubin, K., Silverberg, A.: Supersingular abelian varieties in cryptology. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 336-353. Springer, Heidelberg (2002)
    • (2002) LNCS , vol.2442 , pp. 336-353
    • Rubin, K.1    Silverberg, A.2
  • 16
    • 65049089121 scopus 로고    scopus 로고
    • Using abelian varieties to improve pairing-based cryp-tography
    • Rubin, K., Silverberg, A.: Using abelian varieties to improve pairing-based cryp-tography. Journal of Cryptology 22, 330-364 (2009)
    • (2009) Journal of Cryptology , vol.22 , pp. 330-364
    • Rubin, K.1    Silverberg, A.2
  • 17
    • 0003357475 scopus 로고
    • The Arithmetic of Elliptic Curves
    • Springer, New York
    • Silverman, J.: The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, vol. 106. Springer, New York (1986)
    • (1986) Graduate Texts in Mathematics , vol.106
    • Silverman, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.