메뉴 건너뛰기




Volumn 3027, Issue , 2004, Pages 239-256

Construction of secure random curves of genus 2 over prime fields

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTERS;

EID: 35048820123     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24676-3_15     Document Type: Article
Times cited : (46)

References (34)
  • 1
    • 0035204351 scopus 로고    scopus 로고
    • Counting points on curves and abelian varieties over finite fields
    • L. Adleman and M.-D. Huang. Counting points on curves and abelian varieties over finite fields. J. Symbolic Comput., 32:171-189, 2001.
    • (2001) J. Symbolic Comput. , vol.32 , pp. 171-189
    • Adleman, L.1    Huang, M.-D.2
  • 2
    • 0001761077 scopus 로고
    • Evaluating polynomials at fixed sets of points
    • A. Aho, K. Steiglitz, and J. D. Ullman. Evaluating polynomials at fixed sets of points. SIAM J. Comput., 4(4):533-539, 1975.
    • (1975) SIAM J. Comput. , vol.4 , Issue.4 , pp. 533-539
    • Aho, A.1    Steiglitz, K.2    Ullman, J.D.3
  • 5
    • 35048894070 scopus 로고    scopus 로고
    • Linear recurrences with polynomial coefficients and computation of the Cartier-Manin operator on hyperelliptic curves
    • A. Bostan, P. Gaudry, and E. Schost. Linear recurrences with polynomial coefficients and computation of the Cartier-Manin operator on hyperelliptic curves. 2003. To appear in Proceedings Fq'7.
    • (2003) Proceedings Fq'7
    • Bostan, A.1    Gaudry, P.2    Schost, E.3
  • 6
    • 0018019849 scopus 로고
    • Fast algorithms for manipulating formal power series
    • R. Brent and H. Kung. Fast algorithms for manipulating formal power series. J. ACM, 25:581-595, 1978.
    • (1978) J. ACM , vol.25 , pp. 581-595
    • Brent, R.1    Kung, H.2
  • 7
    • 84968494137 scopus 로고
    • Computing in the Jacobian of an hyperelliptic curve
    • D. G. Cantor. Computing in the Jacobian of an hyperelliptic curve. Math. Comp., 48(177):95-101, 1987.
    • (1987) Math. Comp. , vol.48 , Issue.177 , pp. 95-101
    • Cantor, D.G.1
  • 8
    • 84941611264 scopus 로고
    • On the analogue of the division polynomials for hyperelliptic curves
    • D. G. Cantor. On the analogue of the division polynomials for hyperelliptic curves. J. Reine Angew. Math., 447:91-145, 1994.
    • (1994) J. Reine Angew. Math. , vol.447 , pp. 91-145
    • Cantor, D.G.1
  • 10
    • 35048827592 scopus 로고    scopus 로고
    • Counting points in medium characteristic using Kedlaya's algorithm
    • P. Gaudry and N. Gürel. Counting points in medium characteristic using Kedlaya's algorithm. To appear in Experiment. Math.
    • Experiment. Math.
    • Gaudry, P.1    Gürel, N.2
  • 11
    • 84946825131 scopus 로고    scopus 로고
    • Counting points on hyperelliptic curves over finite fields
    • W. Bosma, editor, ANTS-IV, Springer-Verlag
    • P. Gaudry and R. Harley. Counting points on hyperelliptic curves over finite fields. In W. Bosma, editor, ANTS-IV, volume 1838 of Lecture Notes in Comput. Sci., pages 313-332. Springer-Verlag, 2000.
    • (2000) Lecture Notes in Comput. Sci. , vol.1838 , pp. 313-332
    • Gaudry, P.1    Harley, R.2
  • 12
    • 84948124573 scopus 로고    scopus 로고
    • Modular equations for hyperelliptic curves
    • P. Gaudry and É. Schost. Modular equations for hyperelliptic curves. To appear in Math. Comp.
    • Math. Comp.
    • Gaudry, P.1    Schost, É.2
  • 13
    • 35048885274 scopus 로고    scopus 로고
    • A low-memory parallel version of Matsuo, Chao and Tsujii's algorithm
    • P. Gaudry and Eric Schost. A low-memory parallel version of Matsuo, Chao and Tsujii's algorithm. To appear in ANTS VI.
    • ANTS VI.
    • Gaudry, P.1    Schost, E.2
  • 14
    • 0034782089 scopus 로고    scopus 로고
    • Solvability of radicals from an algorithmic point of view
    • ACM Press
    • G. Hanrot and F. Morain. Solvability of radicals from an algorithmic point of view. In ISSAC'0l, pages 175-182. ACM Press, 2001.
    • (2001) ISSAC'0l , pp. 175-182
    • Hanrot, G.1    Morain, F.2
  • 15
    • 0009327846 scopus 로고    scopus 로고
    • Diophantine geometry. An introduction
    • Springer-Verlag
    • M. Hindry and J. Silverman. Diophantine geometry. An introduction, volume 201 of Graduate Texts in Mathematics. Springer-Verlag, 2000.
    • (2000) Graduate Texts in Mathematics , vol.201
    • Hindry, M.1    Silverman, J.2
  • 16
    • 0031616738 scopus 로고    scopus 로고
    • Counting points on curves over finite fields
    • M.-D. Huang and D. lerardi. Counting points on curves over finite fields. J. Symbolic Comput, 25:1-21, 1998.
    • (1998) J. Symbolic Comput , vol.25 , pp. 1-21
    • Huang, M.-D.1    Lerardi, D.2
  • 17
    • 0030674617 scopus 로고    scopus 로고
    • Fast polynomial factorization over high algebraic extensions of finite fields
    • W. Kuchlin, editor, ACM Press
    • E. Kaltofen and V. Shoup. Fast polynomial factorization over high algebraic extensions of finite fields. In W. Kuchlin, editor, ISSAC-97, pages 184-188. ACM Press, 1997.
    • (1997) ISSAC-97 , pp. 184-188
    • Kaltofen, E.1    Shoup, V.2
  • 21
    • 84958532498 scopus 로고    scopus 로고
    • An improved baby step giant step algorithm for point counting of hyperelliptic curves over finite fields
    • C. Fiecker and D. Kohel, editors, ANTS-V, Springer-Verlag
    • K. Matsuo, J. Chao, and S. Tsujii. An improved baby step giant step algorithm for point counting of hyperelliptic curves over finite fields. In C. Fiecker and D. Kohel, editors, ANTS-V, volume 2369 of Lecture Notes in Comput. Sci., pages 461-474. Springer-Verlag, 2002.
    • (2002) Lecture Notes in Comput. Sci. , vol.2369 , pp. 461-474
    • Matsuo, K.1    Chao, J.2    Tsujii, S.3
  • 22
    • 15544368414 scopus 로고    scopus 로고
    • An elementary introduction to hyperelliptic curves
    • by N. Koblitz, Springer-Verlag
    • A. Menezes, Y.-H. Wu, and R. Zuccherato. An elementary introduction to hyperelliptic curves. In Algebraic aspects of cryptography, by N. Koblitz, pages 155-178, Springer-Verlag, 1997.
    • (1997) Algebraic Aspects of Cryptography , pp. 155-178
    • Menezes, A.1    Wu, Y.-H.2    Zuccherato, R.3
  • 23
    • 35048895034 scopus 로고    scopus 로고
    • Letter to Gaudry and Harley, December
    • 2n). Letter to Gaudry and Harley, December 2000.
    • (2000) 2n)
    • Mestre, J.-F.1
  • 24
    • 0002627221 scopus 로고
    • Abelian varieties
    • G. Cornell and J. H. Silverman, editors, Springer-Verlag
    • J. S. Milne. Abelian varieties. In G. Cornell and J. H. Silverman, editors, Arithmetic Geometry, pages 103-150. Springer-Verlag, 1986.
    • (1986) Arithmetic Geometry , pp. 103-150
    • Milne, J.S.1
  • 26
    • 84966216845 scopus 로고
    • Frobenius maps of abelian varieties and finding roots of unity in finite fields
    • October
    • J. Pila. Frobenius maps of abelian varieties and finding roots of unity in finite fields. Math. Comp., 55 (192):745-763, October 1990.
    • (1990) Math. Comp. , vol.55 , Issue.192 , pp. 745-763
    • Pila, J.1
  • 27
    • 84966233278 scopus 로고
    • Elliptic curves over finite fields and the computation of square roots mod p
    • R. Schoof. Elliptic curves over finite fields and the computation of square roots mod p. Math. Comp., 44:483-494, 1985.
    • (1985) Math. Comp. , vol.44 , pp. 483-494
    • Schoof, R.1
  • 28
    • 0042205179 scopus 로고    scopus 로고
    • Complexity results for triangular sets
    • É. Schost. Complexity results for triangular sets. J. Symbolic Comput., 36:555-594, 2003.
    • (2003) J. Symbolic Comput. , vol.36 , pp. 555-594
    • Schost, É.1
  • 30
    • 0001465210 scopus 로고
    • A new polynomial factorization algorithm and its implementation
    • V. Shoup. A new polynomial factorization algorithm and its implementation. J. Symbolic Comput, 20:363-397, 1995.
    • (1995) J. Symbolic Comput , vol.20 , pp. 363-397
    • Shoup, V.1
  • 31
    • 84937390605 scopus 로고    scopus 로고
    • Computing Zeta functions of hyperelliptic curves over finite fields of characteristic 2
    • M. Yung, editor, Advances in Cryptology - CRYPTO 2002, Springer-Verlag
    • F. Vercauteren. Computing Zeta functions of hyperelliptic curves over finite fields of characteristic 2. In M. Yung, editor, Advances in Cryptology - CRYPTO 2002, volume 2442 of Lecture Notes in Comput. Sci., pages 369-384. Springer-Verlag, 2002.
    • (2002) Lecture Notes in Comput. Sci. , vol.2442 , pp. 369-384
    • Vercauteren, F.1
  • 33
    • 0001605828 scopus 로고
    • Computing Frobenius maps and factoring polynomials
    • J. von zur Gathen and V. Shoup. Computing Frobenius maps and factoring polynomials. Comput. Complexity, 2:187-224, 1992.
    • (1992) Comput. Complexity , vol.2 , pp. 187-224
    • Von Zur Gathen, J.1    Shoup, V.2
  • 34
    • 0037235338 scopus 로고    scopus 로고
    • Constructing hyperelliptic curves of genus 2 suitable for cryptography
    • A. Weng. Constructing hyperelliptic curves of genus 2 suitable for cryptography. Math. Comp., 72:435-458, 2003.
    • (2003) Math. Comp. , vol.72 , pp. 435-458
    • Weng, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.