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Volumn 12, Issue 1, 2006, Pages 78-102

Counting points on Cab curves using Monsky-Washnitzer cohomology

Author keywords

Cab curves; Cryptography; Kedlaya's algorithm; Monsky Washnitzer cohomology; Zeta function

Indexed keywords

APPROXIMATION THEORY; COMPUTATION THEORY; CRYPTOGRAPHY; FINITE DIFFERENCE METHOD; FUNCTIONS; POLYNOMIALS;

EID: 28444451233     PISSN: 10715797     EISSN: 10902465     Source Type: Journal    
DOI: 10.1016/j.ffa.2005.01.003     Document Type: Article
Times cited : (28)

References (36)
  • 1
    • 84958035958 scopus 로고    scopus 로고
    • Counting rational points on curves and abelian varieties over finite fields
    • H. Cohen (Ed.), Algorithmic Number Theory Symposium, Proceedings ANTS-II Springer, Berlin
    • L.M. Adleman, M.-D. Huang, Counting rational points on curves and abelian varieties over finite fields, in: H. Cohen (Ed.), Algorithmic Number Theory Symposium, Proceedings ANTS-II, Lecture Notes in Computer Science, vol. 1122, Springer, Berlin, 1996, pp. 1-16.
    • (1996) Lecture Notes in Computer Science , vol.1122 , pp. 1-16
    • Adleman, L.M.1    Huang, M.-D.2
  • 2
    • 0035204351 scopus 로고    scopus 로고
    • Counting points on curves and abelian varieties over finite fields
    • L.M. Adleman, and M.-D. Huang Counting points on curves and abelian varieties over finite fields J. Symbolic Comput. 32 3 2001 171 189
    • (2001) J. Symbolic Comput. , vol.32 , Issue.3 , pp. 171-189
    • Adleman, L.M.1    Huang, M.-D.2
  • 3
    • 0003076215 scopus 로고
    • A rigid analytic version of M. Artin's theorem on analytic equations
    • S. Bosch A rigid analytic version of M. Artin's theorem on analytic equations Math. Ann. 255 3 1981 395 404
    • (1981) Math. Ann. , vol.255 , Issue.3 , pp. 395-404
    • Bosch, S.1
  • 4
    • 0002522928 scopus 로고
    • A theoretical basis for the reduction of polynomials to canonical forms
    • B. Buchberger A theoretical basis for the reduction of polynomials to canonical forms ACM SIGSAM Bull. 10 3 1976 19 29
    • (1976) ACM SIGSAM Bull. , vol.10 , Issue.3 , pp. 19-29
    • Buchberger, B.1
  • 6
    • 28444488476 scopus 로고    scopus 로고
    • An extension of Kedlaya's algorithm to hyperelliptic curves in characteristic 2
    • February in press
    • J. Denef, F. Vercauteren, An extension of Kedlaya's algorithm to hyperelliptic curves in characteristic 2, J. Cryptology, February 2005, in press.
    • (2005) J. Cryptology
    • Denef, J.1    Vercauteren, F.2
  • 7
    • 0001376121 scopus 로고
    • Solutions d'équations à coefficients dans un anneau hensélien
    • R. Elkik, Solutions d'équations à coefficients dans un anneau hensélien, Ann. Sci. École Norm. Sup. (4) 6 (1973) 553-603 (1974).
    • (1973) Ann. Sci. École Norm. Sup. (4) , vol.6 , pp. 553-603
    • Elkik, R.1
  • 8
    • 84968502759 scopus 로고
    • A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
    • G. Frey, and H.-G. Rück A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves Math. Comput. 62 206 1994 865 874
    • (1994) Math. Comput. , vol.62 , Issue.206 , pp. 865-874
    • Frey, G.1    Rück, H.-G.2
  • 10
    • 84946832010 scopus 로고    scopus 로고
    • Supersingular curves in cryptography
    • C. Boyd (Ed.), Advances in Cryptology, Proceedings Asiacrypt 2001 Springer, Berlin
    • S.D. Galbraith, Supersingular curves in cryptography, in: C. Boyd (Ed.), Advances in Cryptology, Proceedings Asiacrypt 2001, Lecture Notes in Computer Science, vol. 2248, Springer, Berlin, 2001, pp. 495-513.
    • (2001) Lecture Notes in Computer Science , vol.2248 , pp. 495-513
    • Galbraith, S.D.1
  • 11
    • 84946847285 scopus 로고    scopus 로고
    • An extension of Kedlaya's point-counting algorithm to superelliptic curves
    • C. Boyd (Ed.), Advances in Cryptology, Proceedings Asiacrypt 2001 Springer, Berlin
    • P. Gaudry, N. Gürel, An extension of Kedlaya's point-counting algorithm to superelliptic curves, in: C. Boyd (Ed.), Advances in Cryptology, Proceedings Asiacrypt 2001, Lecture Notes in Computer Science, vol. 2248, Springer, Berlin, 2001, pp. 80-494.
    • (2001) Lecture Notes in Computer Science , vol.2248 , pp. 80-494
    • Gaudry, P.1    Gürel, N.2
  • 12
    • 0031616738 scopus 로고    scopus 로고
    • Counting points on curves over finite fields
    • M.-D. Huang, and D. Ierardi Counting points on curves over finite fields J. Symbolic Comput. 25 1 1998 1 21
    • (1998) J. Symbolic Comput. , vol.25 , Issue.1 , pp. 1-21
    • Huang, M.-D.1    Ierardi, D.2
  • 13
    • 0001464763 scopus 로고
    • Multiplication of multidigit numbers on automata
    • A.A. Karatsuba, and Y. Ofman Multiplication of multidigit numbers on automata Sov. Phys. Dokl. 7 1963 595 596
    • (1963) Sov. Phys. Dokl. , vol.7 , pp. 595-596
    • Karatsuba, A.A.1    Ofman, Y.2
  • 14
    • 0013266180 scopus 로고    scopus 로고
    • Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology
    • K.S. Kedlaya Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology J. Ramanujan Math. Soc. 16 4 2001 323 338
    • (2001) J. Ramanujan Math. Soc. , vol.16 , Issue.4 , pp. 323-338
    • Kedlaya, K.S.1
  • 15
    • 84968503742 scopus 로고
    • Elliptic curve cryptosystems
    • N. Koblitz Elliptic curve cryptosystems Math. Comput. 48 177 1987 203 209
    • (1987) Math. Comput. , vol.48 , Issue.177 , pp. 203-209
    • Koblitz, N.1
  • 16
    • 0024864204 scopus 로고
    • Hyperelliptic cryptosystems
    • N. Koblitz Hyperelliptic cryptosystems J. Cryptology 1 3 1989 139 150
    • (1989) J. Cryptology , vol.1 , Issue.3 , pp. 139-150
    • Koblitz, N.1
  • 17
    • 84876602865 scopus 로고    scopus 로고
    • Counting points on varieties over finite fields of small characteristic
    • J.P. Buhler, P. Stevenhagen (Eds.) Mathematical Sciences Research Institute Publications, Cambridge University Press
    • A. Lauder, D. Wan, Counting points on varieties over finite fields of small characteristic, in: J.P. Buhler, P. Stevenhagen (Eds.), Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography, Vol. 44, Mathematical Sciences Research Institute Publications, Cambridge University Press.
    • Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography , vol.44
    • Lauder, A.1    Wan, D.2
  • 18
    • 0141911120 scopus 로고    scopus 로고
    • Computing zeta functions of Artin-Schreier curves over finite fields
    • A.G.B. Lauder, and D. Wan Computing zeta functions of Artin-Schreier curves over finite fields LMS J. Comput. Math. 5 2002 34 55 (electronic)
    • (2002) LMS J. Comput. Math. , vol.5 , pp. 34-55
    • Lauder, A.G.B.1    Wan, D.2
  • 19
    • 1942443626 scopus 로고    scopus 로고
    • Computing zeta functions of Artin-Schreier curves over finite fields II
    • A.G.B. Lauder, D. Wan, Computing zeta functions of Artin-Schreier curves over finite fields II, special issue of the J. Complexity 20 (2004) 331-349.
    • (2004) J. Complexity , vol.20 , Issue.SPEC. ISSUE , pp. 331-349
    • Lauder, A.G.B.1    Wan, D.2
  • 20
    • 84960556527 scopus 로고
    • On some formulas in elimination
    • F. Macaulay On some formulas in elimination Proc. London Math. Soc. 3 1902 3 27
    • (1902) Proc. London Math. Soc. , vol.3 , pp. 3-27
    • MacAulay, F.1
  • 22
    • 0027662341 scopus 로고
    • Reducing elliptic curve logarithms to logarithms in a finite field
    • A.J. Menezes, T. Okamoto, and S.A. Vanstone Reducing elliptic curve logarithms to logarithms in a finite field IEEE Trans. Inform. Theory 39 5 1993 1639 1646
    • (1993) IEEE Trans. Inform. Theory , vol.39 , Issue.5 , pp. 1639-1646
    • Menezes, A.J.1    Okamoto, T.2    Vanstone, S.A.3
  • 24
    • 85015402934 scopus 로고
    • Use of elliptic curves in cryptography
    • H.C. Williams (Ed.), Advances in Cryptology, Proceedings Crypto 1985 Springer, Berlin
    • V.S. Miller, Use of elliptic curves in cryptography, in: H.C. Williams (Ed.), Advances in Cryptology, Proceedings Crypto 1985, Lecture Notes in Computer Science, vol. 218, Springer, Berlin, 1986, pp. 417-426.
    • (1986) Lecture Notes in Computer Science , vol.218 , pp. 417-426
    • Miller, V.S.1
  • 25
    • 0001330096 scopus 로고
    • Formal cohomology. II. the cohomology sequence of a pair
    • P. Monsky Formal cohomology. II. The cohomology sequence of a pair Ann. of Math. (2) 88 1968 218 238
    • (1968) Ann. of Math. (2) , vol.88 , pp. 218-238
    • Monsky, P.1
  • 27
    • 0000699776 scopus 로고
    • Formal cohomology. III. Fixed point theorems
    • P. Monsky Formal cohomology. III. Fixed point theorems Ann. of Math. (2) 93 1971 315 343
    • (1971) Ann. of Math. (2) , vol.93 , pp. 315-343
    • Monsky, P.1
  • 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. Comput. 55 192 1990 745 763
    • (1990) Math. Comput. , vol.55 , Issue.192 , pp. 745-763
    • Pila, J.1
  • 30
    • 28444481978 scopus 로고    scopus 로고
    • 2N, available at http://arxiv.org/abs/math. NT/0303072, 2003.
    • (2003) 2N
    • Ritzenthaler, C.1
  • 31
    • 0001100056 scopus 로고    scopus 로고
    • The canonical lift of an ordinary elliptic curve over a finite field and its point counting
    • T. Satoh The canonical lift of an ordinary elliptic curve over a finite field and its point counting J. Ramanujan Math. Soc. 15 4 2000 247 270
    • (2000) J. Ramanujan Math. Soc. , vol.15 , Issue.4 , pp. 247-270
    • Satoh, T.1
  • 32
    • 0001219865 scopus 로고
    • Counting points on elliptic curves over finite fields
    • R. Schoof Counting points on elliptic curves over finite fields J. Théor. Nombres Bordeaux 7 1 1995 219 254 Les Dix-huitièmes Journées Arithmétiques (Bordeaux, 1993)
    • (1995) J. Théor. Nombres Bordeaux , vol.7 , Issue.1 , pp. 219-254
    • Schoof, R.1
  • 33
    • 0011937834 scopus 로고
    • The complexity of a scheme of functional elements simulating the multiplication of integers
    • A.L. Toom The complexity of a scheme of functional elements simulating the multiplication of integers Dokl. Akad. Nauk SSSR 150 1963 496 498
    • (1963) Dokl. Akad. Nauk SSSR , vol.150 , pp. 496-498
    • Toom, A.L.1
  • 34
    • 0003036437 scopus 로고
    • The cohomology of Monsky and Washnitzer
    • M. van der Put The cohomology of Monsky and Washnitzer Mém. Soc. Math. France (N.S.) 23 4 1986 33 59 Introductions aux cohomologies p-adiques (Luminy, 1984)
    • (1986) Mém. Soc. Math. France (N.S.) , vol.23 , Issue.4 , pp. 33-59
    • Van Der Put, M.1
  • 36
    • 84938487185 scopus 로고
    • Numbers of solutions of equations in finite fields
    • A. Weil Numbers of solutions of equations in finite fields Bull. Amer. Math. Soc. 55 1949 497 508
    • (1949) Bull. Amer. Math. Soc. , vol.55 , pp. 497-508
    • Weil, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.