-
1
-
-
84968498708
-
Two theorems on Riemann surfaces with noncyclic automorphism groups
-
R. D. Accola. Two theorems on Riemann surfaces with noncyclic automorphism groups. Proc. Amer. Math. Soc., 25:598–602, 1970.
-
(1970)
Proc. Amer. Math. Soc
, vol.25
, pp. 598-602
-
-
Accola, R.D.1
-
2
-
-
84929727140
-
A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fields
-
L. M. Adleman, J. DeMarrais, and M.-D. Huang. A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fields. In L. Adleman and M.-D. Huang, editors, ANTS-I, volume 877 of Lecture Notes in Comput. Sci., pages 28–40. Springer-Verlag, 1994. 1st Algorithmic Number Theory Symposium - Cornell University, May 6-9, 1994.
-
(1994)
Lecture Notes in Comput
, vol.877
, pp. 28-40
-
-
Adleman, L.M.1
Demarrais, J.2
Huang, M.-D.3
Adleman, L.4
Huang, M.-D.5
-
3
-
-
0032147416
-
Lattice basis reduction, Jacobi sums and hyperellitic cryptosystems
-
J. Buhler and N. Koblitz. Lattice basis reduction, Jacobi sums and hyperellitic cryptosystems. Bull. Austral. Math. Soc., 58:147–154, 1998.
-
(1998)
Bull. Austral. Math. Soc
, vol.58
, pp. 147-154
-
-
Buhler, J.1
Koblitz, N.2
-
4
-
-
84968494137
-
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
-
7
-
-
84956853573
-
-
Elliptic curve discrete logarithms and Wieferich primes
-
J. H. Cheon, D. H. Lee, and S. G. Hahn. Elliptic curve discrete logarithms and Wieferich primes. Preprint, September 1998.
-
(1998)
Preprint
-
-
Cheon, J.H.1
Lee, D.H.2
Hahn, S.G.3
-
8
-
-
0004171569
-
-
Presses Universitaires de France
-
L. Comtet. Analyse combinatoire. Presses Universitaires de France, 1970.
-
(1970)
Analyse Combinatoire
-
-
Comtet, L.1
-
9
-
-
85086948514
-
Efficient algorithms for the jacobian variety of hy-perelliptic curves y
-
p− x + 1 over a finite field of odd characteristic p. In H. Tapia-Recillas, editor, Proceedings of the”International Conference on Coding Theory, Cryptography and Related Areas”, volume yyy of Lecture Notes in Comput. Sci., 1999. Guanajuato, Mexico on April, 1998.
-
(1999)
Volume Yyy of Lecture Notes in Comput. Sci.
-
-
Duursma, I.1
Sakurai, K.2
Tapia-Recillas, H.3
-
10
-
-
84915939958
-
-
Random mapping statistics
-
P. Flajolet and A. M. Odlyzko. Random mapping statistics. In J.-J. Quisquater, editor, Advances in Cryptology, volume 434 of Lecture Notes in Comput. Sci., pages 329–354. Springer-Verlag, 1990. Proc. Eurocrypt’89, Houthalen, April 10–13.
-
(1990)
Advances in Cryptology
, vol.434
, pp. 329-354
-
-
Flajolet, P.1
Odlyzko, A.M.2
Quisquater, J.-J.3
-
11
-
-
84968502759
-
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. Comp., 62(206):865–874, April 1994.
-
(1994)
Math. Comp.
, vol.62
, Issue.206
, pp. 865-874
-
-
Frey, G.1
Rück, H.-G.2
-
15
-
-
84956855135
-
-
Analysis of the Xedni calculus attack
-
M. J. Jacobson, N. Koblitz, J. H. Silverman, A. Stein, and E. Teske. Analysis of the Xedni calculus attack. Preprint, February 1999.
-
(1999)
Preprint
-
-
Jacobson, M.J.1
Koblitz, N.2
Silverman, J.H.3
Stein, A.4
Teske, E.5
-
16
-
-
0000119243
-
Idempotent relations and factors of Jacobians
-
E. Kani and M. Rosen. Idempotent relations and factors of Jacobians. Math. Ann., 298:307–327, 1989.
-
(1989)
Math. Ann.
, vol.298
, pp. 307-327
-
-
Kani, E.1
Rosen, M.2
-
18
-
-
0042981058
-
A course in number theory and cryptography
-
N. Koblitz. A course in number theory and cryptography, volume 114 of Graduate Texts in Mathematics. Springer–Verlag, 1987.
-
(1987)
Graduate Texts in Mathematics
, vol.114
-
-
Koblitz, N.1
-
19
-
-
84968503742
-
Elliptic curve cryptosystems
-
N. Koblitz. Elliptic curve cryptosystems. Math. Comp., 48(177):203–209, January 1987.
-
(1987)
Math. Comp.
, vol.48
, Issue.177
, pp. 203-209
-
-
Koblitz, N.1
-
20
-
-
0024864204
-
-
Hyperelliptic cryptosystems
-
N. Koblitz. Hyperelliptic cryptosystems. J. of Cryptology, 1:139–150, 1989.
-
(1989)
Cryptology
, vol.1
, pp. 139-150
-
-
Koblitz, N.1
-
21
-
-
85031798246
-
-
A family of jacobians suitable for discrete log cryptosystems, Proceedings of a conference on the theory and application of cryptography held at the University of California, Santa Barbara
-
N. Koblitz. A family of jacobians suitable for discrete log cryptosystems. In S. Goldwasser, editor, Advances in Cryptology – CRYPTO’88, volume 403 of Lecture Notes in Comput. Sci., pages 94–99. Springer–Verlag, 1990. Proceedings of a conference on the theory and application of cryptography held at the University of California, Santa Barbara, August 21-25, 1988.
-
(1990)
Advances in Cryptology – CRYPTO’88
, vol.403
, pp. 94-99
-
-
Koblitz, N.1
Goldwasser, S.2
-
22
-
-
85024567680
-
-
CM-curves with good cryptographic properties Advances in Cryptology – CRYPTO’91
-
N. Koblitz. CM-curves with good cryptographic properties. In Joan Feigenbaum, editor, Advances in Cryptology – CRYPTO’91, volume 576 of Lecture Notes in Comput. Sci., pages 279–287. Springer-Verlag, 1992. Santa Barbara, August 12–15.
-
(1992)
Lecture Notes in Comput. Sci
, vol.576
, pp. 279-287
-
-
Koblitz, N.1
-
23
-
-
0001258323
-
-
Factoring integers with elliptic curves
-
H. W. Lenstra, Jr. Factoring integers with elliptic curves. Ann. of Math. (2), 126:649–673, 1987.
-
(1987)
Ann.
, vol.126
, Issue.2
, pp. 649-673
-
-
Lenstra, H.W.1
-
24
-
-
84957363701
-
-
Finding good random elliptic curves for cryptosystems defined over, Advances in Cryptology – EUROCRYPT’97, International Conference on the Theory and Application of Cryptographic Techniques, Konstanz, Germany
-
R. Lercier. Finding good random elliptic curves for cryptosystems defined over F2n. In W. Fumy, editor, Advances in Cryptology – EUROCRYPT’97, volume 1233 of Lecture Notes in Comput. Sci., pages 379–392. Springer-Verlag, 1997. International Conference on the Theory and Application of Cryptographic Techniques, Konstanz, Germany, May 1997, Proceedings.
-
(1997)
Lecture Notes in Comput. Sci
, vol.1233
, pp. 379-392
-
-
Lercier, R.1
Fumy, W.2
-
25
-
-
84957648431
-
-
Counting the number of points on elliptic curves over finite fields: strategies and performances, advances in cryptology – eurocrypt’95, international conference on the theory and application of cryptographic techniques, saint-malo, france
-
R. Lercier and F. Morain. Counting the number of points on elliptic curves over finite fields: strategies and performances. In L. C. Guillou and J.-J. Quisquater, editors, Advances in Cryptology – EUROCRYPT’95, volume 921 of Lecture Notes in Comput. Sci., pages 79–94, 1995. International Conference on the Theory and Application of Cryptographic Techniques, Saint-Malo, France, May 1995, Proceedings.
-
(1995)
Lecture Notes in Comput. Sci
, vol.921
, pp. 79-94
-
-
Lercier, R.1
Morain, F.2
Guillou, L.C.3
Quisquater, J.-J.4
-
26
-
-
0027662341
-
-
Reducing elliptic curves logarithms to logarithms in a finite field
-
A. Menezes, T. Okamoto, and S. A. Vanstone. Reducing elliptic curves logarithms to logarithms in a finite field. IEEE Trans. Inform. Theory, IT–39(5):1639–1646, September 1993.
-
(1993)
IEEE Trans. Inform. Theory
, vol.39
, Issue.5
, pp. 1639-1646
-
-
Menezes, A.1
Okamoto, T.2
Vanstone, S.A.3
-
28
-
-
85015402934
-
-
Use of elliptic curves in cryptography, Advances in Cryptology – CRYPTO’86
-
V. Miller. Use of elliptic curves in cryptography. In A. M. Odlyzko, editor, Advances in Cryptology – CRYPTO’86, volume 263 of Lecture Notes in Comput. Sci., pages 417–426. Springer-Verlag, 1987. Proceedings, Santa Barbara (USA), August 11–15, 1986.
-
(1987)
Lecture Notes in Comput. Sci
, vol.263
, pp. 417-426
-
-
Miller, V.1
Odlyzko, A.M.2
-
30
-
-
0011918550
-
-
Fast multiplication on elliptic curves over small fields of characteristic two
-
V. M¨uller. Fast multiplication on elliptic curves over small fields of characteristic two. J. of Cryptology, 11(4):219–234, 1998.
-
(1998)
Cryptology
, vol.11
, Issue.4
, pp. 219-234
-
-
M¨Uller, V.1
-
32
-
-
0001572749
-
-
S. Nakajima. p-ranks and automorphism groups of algebraic curves. Trans. Amer. Math. Soc., 303(2):595–607, October 1987.
-
(1987)
Trans. Amer. Math. Soc.
, vol.303
, Issue.2
, pp. 595-607
-
-
Nakajima, S.1
-
33
-
-
84919085619
-
-
An improved algorithm for computing logarithms over GF(
-
S. Pohlig and M. Hellman. An improved algorithm for computing logarithms over GF(p) and its cryptographic significance. IEEE Trans. Inform. Theory, IT–24:106– 110, 1978.
-
(1978)
IEEE Trans. Inform. Theory
, vol.24
-
-
Pohlig, S.1
Hellman, M.2
-
34
-
-
84966238549
-
-
Monte Carlo methods for index computation (mod
-
J. M. Pollard. Monte Carlo methods for index computation (mod p). Math. Comp., 32(143):918–924, July 1978.
-
(1978)
Math. Comp.
, vol.32
, Issue.143
, pp. 918-924
-
-
Pollard, J.M.1
-
35
-
-
0042715199
-
-
How easy is collision search? application to des
-
J.-J. Quisquater and J.-P. Delescaille. How easy is collision search? application to DES. In J.-J. Quisquater, editor, Advances in Cryptology, volume 434 of Lecture Notes in Comput. Sci., pages 429–434. Springer-Verlag, 1990. Proc. Eurocrypt’89, Houthalen, April 10–13.
-
(1990)
Advances in Cryptology
, vol.434
, pp. 429-434
-
-
Quisquater, J.-J.1
Delescaille, J.-P.2
Quisquater, J.-J.3
-
36
-
-
0000617256
-
-
Abschätzung der Automorphismenanzahl von Funktionenkörpern bei Primzahlcharakteristik
-
P. Roquette. Abschätzung der Automorphismenanzahl von Funktionenkörpern bei Primzahlcharakteristik. Math. Z., 117:157–163, 1970.
-
(1970)
Math. Z.
, vol.117
, pp. 157-163
-
-
Roquette, P.1
-
37
-
-
84947769343
-
-
Design of hyperelliptic cryptosystems in small charatc-teristic and a software implementation over
-
Y. Sakai and K. Sakurai. Design of hyperelliptic cryptosystems in small charatc-teristic and a software implementation over T'2n. In K. Ohta and D. Pei, editors, Advances in Cryptology, volume 1514 of Lecture Notes in Comput. Sci., pages 80– 94. Springer-Verlag, 1998. Proc. Asiacrypt’98, Beijing, October, 1998.
-
(1998)
Advances in Cryptology
, vol.1514
-
-
Sakai, Y.1
Sakurai, K.2
Ohta, K.3
Pei, D.4
-
38
-
-
0343623059
-
-
Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves
-
T. Satoh and K. Araki. Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves. Comment. Math. Helv., 47(1):81–92, 1998.
-
(1998)
Comment. Math. Helv.
, vol.47
, Issue.1
, pp. 81-92
-
-
Satoh, T.1
Araki, K.2
-
40
-
-
0032352723
-
-
Evaluation of discrete logarithms in a group of
-
I. A. Semaev. Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curves in characteristic p. Math. Comp., 67(221):353–356, January 1998.
-
(1998)
Math. Comp
, vol.67
, Issue.221
, pp. 353-356
-
-
Semaev, I.A.1
-
41
-
-
0000211152
-
-
Class number, a theory of factorization, and genera
-
D. Shanks. Class number, a theory of factorization, and genera. In Proc. Symp. Pure Math. vol. 20, pages 415–440. AMS, 1971.
-
(1971)
Proc. Symp. Pure Math
, vol.20
, pp. 415-440
-
-
Shanks, D.1
-
43
-
-
84956867810
-
-
The XEDNI calculus and the elliptic curve discrete logarithm problem
-
J. H. Silverman. The XEDNI calculus and the elliptic curve discrete logarithm problem. Preprint, August 1998.
-
(1998)
Preprint
-
-
Silverman, J.H.1
-
44
-
-
17644430597
-
-
The discrete logarithm problem on elliptic curves of trace one. Preprint HP-LABS Technical Report (Number HPL-97-128)
-
N. Smart. The discrete logarithm problem on elliptic curves of trace one. Preprint HP-LABS Technical Report (Number HPL-97-128). To appear in J. Cryptology, 1997.
-
(1997)
J. Cryptology
-
-
Smart, N.1
-
45
-
-
0000702044
-
-
Elliptic curve cryptosystems over small fields of odd characteristic
-
N. P. Smart. Elliptic curve cryptosystems over small fields of odd characteristic. J. of Cryptology, 12(2):141–151, 1999.
-
(1999)
J.
, vol.12
, Issue.2
, pp. 141-151
-
-
Smart, N.P.1
-
47
-
-
84956862651
-
-
Catching kangaroos in function fields
-
A. Stein and E. Teske. Catching kangaroos in function fields. Preprint, March 1999.
-
(1999)
Preprint
-
-
Stein, A.1
Teske, E.2
-
48
-
-
34250432668
-
-
¨, Uber die Automorphismengruppe eines algebraischen Funktio-nenkörpers von Primzahlcharakteristik. I. Eine Abschätzung der Ordnung der Au-tomorphismengruppe
-
¨Uber die Automorphismengruppe eines algebraischen Funktio-nenkörpers von Primzahlcharakteristik. I. Eine Abschätzung der Ordnung der Au-tomorphismengruppe. Arch. Math. (Basel), 24:527–544, 1973.
-
(1973)
Arch. Math. (Basel)
, vol.24
, pp. 527-544
-
-
Stichtenoth, H.1
-
49
-
-
84947761194
-
-
Speeding up Pollard’s rho method for computing discrete logarithms
-
E. Teske. Speeding up Pollard’s rho method for computing discrete logarithms. In J. P. Buhler, editor, Algorithmic Number Theory, volume 1423 of Lecture Notes in Comput. Sci., pages 541–554. Springer-Verlag, 1998. Third International Symposium, ANTS-III, Portland, Oregon, june 1998, Proceedings. 106
-
(1998)
Algorithmic Number Theory
, vol.1423
, pp. 541-554
-
-
Teske, E.1
Buhler, J.P.2
-
50
-
-
17444376558
-
-
Parallel collision search with cryptanalytic applications
-
P. C. van Oorschot and M. J. Wiener. Parallel collision search with cryptanalytic applications. J. of Cryptology, 12:1–28, 1999.
-
(1999)
Cryptology
, vol.12
, pp. 1-28
-
-
Van Oorschot, P.C.1
Wiener, M.J.2
-
51
-
-
0033480564
-
-
Examples of genus two CM curves defined over the rationals
-
P. van Wamelen. Examples of genus two CM curves defined over the rationals. Math. Comp., 68(225):307–320, January 1999.
-
(1999)
Math. Comp.
, vol.68
, Issue.225
, pp. 307-320
-
-
Van Wamelen, P.1
-
52
-
-
84956855910
-
-
Faster attacks on elliptic curve cryptosys-tems, Selected Areas in Cryptography’98, 5th Annual International Workshop, SAC’98, Kingston, Ontario, Canada
-
M. J. Wiener and R. J. Zuccherato. Faster attacks on elliptic curve cryptosys-tems. In S. Tavares and H. Meijer, editors, Selected Areas in Cryptography’98, volume 1556 of Lecture Notes in Comput. Sci. Springer-Verlag, 1999. 5th Annual International Workshop, SAC’98, Kingston, Ontario, Canada, August 17-18, 1998, Proceedings.
-
(1999)
Lecture Notes in Comput. Sci.
, vol.1556
-
-
Wiener, M.J.1
Zuccherato, R.J.2
Tavares, S.3
Meijer, H.4
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