-
1
-
-
84966236672
-
A subexponential algorithm for discrete logarithms over all finite fields
-
L. Adleman J. DeMarrais A subexponential algorithm for discrete logarithms over all finite fields Math. Comput. 61 1993 1-15
-
(1993)
Math. Comput.
, vol.61
, pp. 1-15
-
-
Adleman, L.1
DeMarrais, J.2
-
2
-
-
23044482179
-
On the optimal parameter choice for elliptic curve cryptosystems using isogeny
-
Lecture Notes in Computer Science
-
T. Akishita, T. Takagi, On the optimal parameter choice for elliptic curve cryptosystems using isogeny, Public Key Cryptography-PKC 2004, Lecture Notes in Computer Science, vol. 2947, 2004, pp. 346-359.
-
(2004)
Public Key Cryptography-PKC 2004
, vol.2947
, pp. 346-359
-
-
Akishita, T.1
Takagi, T.2
-
6
-
-
23044522661
-
Weil descent of elliptic curves over finite fields of characteristic three
-
Lecture Notes in Computer Science
-
S. Arita, Weil descent of elliptic curves over finite fields of characteristic three, Advances in Cryptology-ASIACRYPT 2000, Lecture Notes in Computer Science, vol. 1976, 2000, pp. 248-259.
-
(2000)
Advances in Cryptology-ASIACRYPT 2000
, vol.1976
, pp. 248-259
-
-
Arita, S.1
-
7
-
-
35048858891
-
Aspects of hyperelliptic curves over large prime fields in software implementations
-
Lecture Notes in Computer Science
-
R. Avanzi, Aspects of hyperelliptic curves over large prime fields in software implementations, Cryptographic Hardware and Embedded Systems-CHES 2004, Lecture Notes in Computer Science, vol. 3156, 2004, pp. 148-162.
-
(2004)
Cryptographic Hardware and Embedded Systems-CHES 2004
, vol.3156
, pp. 148-162
-
-
Avanzi, R.1
-
9
-
-
0343736058
-
The improbability that an elliptic curve has sub-exponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm
-
R. Balasubramanian N. Koblitz The improbability that an elliptic curve has sub-exponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm J. Cryptol. 11 1998 141-145
-
(1998)
J. Cryptol.
, vol.11
, pp. 141-145
-
-
Balasubramanian, R.1
Koblitz, N.2
-
10
-
-
11244342973
-
Efficient reduction on the jacobian variety of Picard curves
-
Springer, Berlin
-
E. Barreiro, J. Sarlabous, J. Cherdieu, Efficient reduction on the jacobian variety of Picard curves, Coding Theory, Cryptography and Related Areas, Springer, Berlin, 2000, pp. 13-28.
-
(2000)
Coding Theory, Cryptography and Related Areas
, pp. 13-28
-
-
Barreiro, E.1
Sarlabous, J.2
Cherdieu, J.3
-
11
-
-
84937428623
-
Efficient implementation of pairing-based cryptosystems
-
Lecture Notes in Computer Science
-
P. Barreto, H. Kim, B. Lynn, M. Scott, Efficient implementation of pairing-based cryptosystems, Advances in Cryptology-CRYPTO 2002, Lecture Notes in Computer Science, vol. 2442, 2002, pp. 354-368.
-
(2002)
Advances in Cryptology-CRYPTO 2002
, vol.2442
, pp. 354-368
-
-
Barreto, P.1
Kim, H.2
Lynn, B.3
Scott, M.4
-
12
-
-
35248835023
-
Constructing elliptic curves with prescribed embedding degrees
-
Lecture Notes in Computer Science
-
P. Barreto, B. Lynn, M. Scott, Constructing elliptic curves with prescribed embedding degrees, Security in Communication Networks-SCN 2002, Lecture Notes in Computer Science, vol. 2576, 2003, pp. 257-267.
-
(2003)
Security in Communication Networks-SCN 2002
, vol.2576
, pp. 257-267
-
-
Barreto, P.1
Lynn, B.2
Scott, M.3
-
13
-
-
23044435243
-
Efficient implementation of pairing-based cryptosystems
-
P. Barreto B. Lynn M. Scott Efficient implementation of pairing-based cryptosystems J. Cryptol. 17 2004 321-334
-
(2004)
J. Cryptol.
, vol.17
, pp. 321-334
-
-
Barreto, P.1
Lynn, B.2
Scott, M.3
-
14
-
-
0344196670
-
On class group computations using the number field sieve
-
Lecture Notes in Computer Science
-
M. Bauer, S. Hamdy, On class group computations using the number field sieve, Advances in Cryptology-ASIACRYPT 2003, Lecture Notes in Computer Science, vol. 2894, 2003, pp. 311-325.
-
(2003)
Advances in Cryptology-ASIACRYPT 2003
, vol.2894
, pp. 311-325
-
-
Bauer, M.1
Hamdy, S.2
-
17
-
-
77649118700
-
Diffie-Hellman is as strong as discrete log for certain primes
-
Lecture Notes in Computer Science
-
B. den Boer, Diffie-Hellman is as strong as discrete log for certain primes, Advances in Cryptology-CRYPTO '88, Lecture Notes in Computer Science, vol. 403, 1996, pp. 530-539.
-
(1996)
Advances in Cryptology-CRYPTO '88
, vol.403
, pp. 530-539
-
-
den Boer, B.1
-
18
-
-
35048887476
-
Short group signatures
-
Lecture Notes in Computer Science
-
D. Boneh, X. Boyen, H. Shacham, Short group signatures, Advances in Cryptology-CRYPTO 2004, Lecture Notes in Computer Science, vol. 3152, 2004, pp. 41-55.
-
(2004)
Advances in Cryptology-CRYPTO 2004
, vol.3152
, pp. 41-55
-
-
Boneh, D.1
Boyen, X.2
Shacham, H.3
-
19
-
-
0037623983
-
Identity-based encryption from the Weil pairing
-
D. Boneh M. Franklin Identity-based encryption from the Weil pairing SIAM J. Comput. 32 2003 586-615
-
(2003)
SIAM J. Comput.
, vol.32
, pp. 586-615
-
-
Boneh, D.1
Franklin, M.2
-
20
-
-
84955604812
-
Algorithms for black-box fields and their application to cryptography
-
Lecture Notes in Computer Science
-
D. Boneh, R. Lipton, Algorithms for black-box fields and their application to cryptography, Advances in Cryptology-CRYPTO '96, Lecture Notes in Computer Science, vol. 109, 1996, pp. 283-297.
-
(1996)
Advances in Cryptology-CRYPTO '96
, vol.109
, pp. 283-297
-
-
Boneh, D.1
Lipton, R.2
-
21
-
-
23044435711
-
Short signatures from the Weil pairing
-
D. Boneh B. Lynn H. Shacham Short signatures from the Weil pairing J. Cryptol. 7 2004 297-319
-
(2004)
J. Cryptol.
, vol.7
, pp. 297-319
-
-
Boneh, D.1
Lynn, B.2
Shacham, H.3
-
22
-
-
5644266059
-
Applications of multilinear forms to cryptography
-
D. Boneh A. Silverberg Applications of multilinear forms to cryptography Contemp. Math. 324 2003 71-90
-
(2003)
Contemp. Math.
, vol.324
, pp. 71-90
-
-
Boneh, D.1
Silverberg, A.2
-
23
-
-
23044454162
-
Elliptic curves suitable for pairing based cryptography
-
to appear
-
F. Brezing, A. Weng, Elliptic curves suitable for pairing based cryptography, Designs, Codes Cryptogr., to appear.
-
Designs, Codes Cryptogr.
-
-
Brezing, F.1
Weng, A.2
-
24
-
-
27544448878
-
Fast point multiplication on elliptic curves through isogenies
-
Lecture Notes in Computer Science
-
E. Brier, M. Joye, Fast point multiplication on elliptic curves through isogenies, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium, AAECC-15, Lecture Notes in Computer Science, vol. 2643, 2003, pp. 43-50.
-
(2003)
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium AAECC-15
, vol.2643
, pp. 43-50
-
-
Brier, E.1
Joye, M.2
-
25
-
-
84968494137
-
Computing in the jacobian of a hyperelliptic curve
-
D. Cantor Computing in the jacobian of a hyperelliptic curve Math. Comput. 48 1987 95-101
-
(1987)
Math. Comput.
, vol.48
, pp. 95-101
-
-
Cantor, D.1
-
26
-
-
0001494997
-
Small solutions to polynomial equations, with low exponent RSA vulnerabilities
-
D. Coppersmith Small solutions to polynomial equations, with low exponent RSA vulnerabilities J. Cryptol. 10 1997 233-260
-
(1997)
J. Cryptol.
, vol.10
, pp. 233-260
-
-
Coppersmith, D.1
-
27
-
-
52449142539
-
Die Typen der Multiplikatorenringe elliptischer Funktionenkörper
-
M. Deuring Die Typen der Multiplikatorenringe elliptischer Funktionenkörper Abh. Math. Sem. Hansischen Univ. 14 1941 197-272
-
(1941)
Abh. Math. Sem. Hansischen Univ.
, vol.14
, pp. 197-272
-
-
Deuring, M.1
-
28
-
-
4544381452
-
The GHS attack in odd characteristic
-
C. Diem The GHS attack in odd characteristic J. Ramanujan Math. Soc. 18 2003 1-32
-
(2003)
J. Ramanujan Math. Soc.
, vol.18
, pp. 1-32
-
-
Diem, C.1
-
29
-
-
23044469351
-
On the discrete logarithm problem in elliptic curves over non-prime finite fields
-
presentation at ECC 2004, Bochum, Germany
-
C. Diem, On the discrete logarithm problem in elliptic curves over non-prime finite fields, presentation at ECC 2004, Bochum, Germany, 2004.
-
(2004)
-
-
Diem, C.1
-
31
-
-
17444391606
-
Building curves with arbitrary small MOV degree over finite prime fields
-
R. Dupont A. Enge F. Morain Building curves with arbitrary small MOV degree over finite prime fields J. Cryptol. 18 2005 79-89
-
(2005)
J. Cryptol.
, vol.18
, pp. 79-89
-
-
Dupont, R.1
Enge, A.2
Morain, F.3
-
33
-
-
23044508350
-
Sur les couplages de Weil et de Tate
-
University of Rennes Seminar 15 February Available from
-
S. Edixhoven, Sur les couplages de Weil et de Tate, University of Rennes Seminar 15 February 2002. Available from http://www.math.univ-rennes1.fr/ crypto/seminaire0.html.
-
(2002)
-
-
Edixhoven, S.1
-
34
-
-
35048886487
-
Improved Weil and Tate pairings for elliptic and hyperelliptic curves
-
Lecture Notes in Computer Science
-
K. Eisenträger, K. Lauter, P. Montgomery, Improved Weil and Tate pairings for elliptic and hyperelliptic curves, Algorithmic Number Theory: 6th International Symposium, Lecture Notes in Computer Science, vol. 3076, 2004, pp. 169-183.
-
(2004)
Algorithmic Number Theory: 6th International Symposium
, vol.3076
, pp. 169-183
-
-
Eisenträger, K.1
Lauter, K.2
Montgomery, P.3
-
35
-
-
84874800178
-
A public key cryptosystem and a signature scheme based on discrete logarithms
-
T. ElGamal A public key cryptosystem and a signature scheme based on discrete logarithms IEEE Trans. Inform. Theory 31 1985 469-472
-
(1985)
IEEE Trans. Inform. Theory
, vol.31
, pp. 469-472
-
-
ElGamal, T.1
-
36
-
-
0042833029
-
A general framework for subexponential discrete logarithm algorithms
-
A. Enge P. Gaudry A general framework for subexponential discrete logarithm algorithms Acta Arith. 102 2002 83-103
-
(2002)
Acta Arith.
, vol.102
, pp. 83-103
-
-
Enge, A.1
Gaudry, P.2
-
37
-
-
0003508564
-
-
FIPS 186 Federal Information Processing Standards Publication 186, National Institute of Standards and Technology
-
FIPS 186, Digital Signature Standard (DSS), Federal Information Processing Standards Publication 186, National Institute of Standards and Technology, 1994.
-
(1994)
Digital Signature Standard (DSS)
-
-
-
38
-
-
0003508562
-
-
FIPS 186-2 Federal Information Processing Standards Publication 186-2, National Institute of Standards and Technology
-
FIPS 186-2, Digital Signature Standard (DSS), Federal Information Processing Standards Publication 186-2, National Institute of Standards and Technology, 2000.
-
(2000)
Digital Signature Standard (DSS)
-
-
-
39
-
-
21144431641
-
Fast arithmetic on jacobians of Picard curves
-
Lecture Notes in Computer Science
-
S. Flon, R. Oyono, Fast arithmetic on jacobians of Picard curves, Public Key Cryptography-PKC 2004, Lecture Notes in Computer Science, vol. 2947, 2004, pp. 55-68.
-
(2004)
Public Key Cryptography-PKC 2004
, vol.2947
, pp. 55-68
-
-
Flon, S.1
Oyono, R.2
-
40
-
-
0001113371
-
An extension of Satoh's algorithm and its implementation
-
M. Fouquet P. Gaudry R. Harley An extension of Satoh's algorithm and its implementation J. Ramanujan Math. Soc. 15 2000 281-318
-
(2000)
J. Ramanujan Math. Soc.
, vol.15
, pp. 281-318
-
-
Fouquet, M.1
Gaudry, P.2
Harley, R.3
-
42
-
-
84968502759
-
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
-
G. Frey H. Rück A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves Math. Comput. 62 1994 865-874
-
(1994)
Math. Comput.
, vol.62
, pp. 865-874
-
-
Frey, G.1
Rück, H.2
-
44
-
-
23044503196
-
Constructing isogenies between elliptic curves over finite fields
-
S. Galbraith Constructing isogenies between elliptic curves over finite fields LMS J. Comput. Math. 2 1999 118-138
-
(1999)
LMS J. Comput. Math.
, vol.2
, pp. 118-138
-
-
Galbraith, S.1
-
45
-
-
84946832010
-
Supersingular curves in cryptography
-
Lecture Notes in Computer Science
-
S. Galbraith, Supersingular curves in cryptography, Advances in Cryptology-ASIACRYPT 2001, Lecture Notes in Computer Science, vol. 2248, 2001, pp. 495-513.
-
(2001)
Advances in Cryptology-ASIACRYPT 2001
, vol.2248
, pp. 495-513
-
-
Galbraith, S.1
-
46
-
-
0038060517
-
Weil descent of Jacobians
-
S. Galbraith Weil descent of Jacobians Discrete Appl. Math. 128 2003 165-180
-
(2003)
Discrete Appl. Math.
, vol.128
, pp. 165-180
-
-
Galbraith, S.1
-
47
-
-
23044437033
-
Pairings
-
Chapter IX of [16]
-
S. Galbraith, Pairings, Chapter IX of [16], 2005.
-
(2005)
-
-
Galbraith, S.1
-
48
-
-
82955246861
-
Implementing the Tate pairing
-
Lecture Notes in Computer Science
-
S. Galbraith, K. Harrison, D. Soldera, Implementing the Tate pairing, Algorithmic Number Theory: 5th International Symposium, Lecture Notes in Computer Science, vol. 2369, 2002, pp. 324-337.
-
(2002)
Algorithmic Number Theory: 5th International Symposium
, vol.2369
, pp. 324-337
-
-
Galbraith, S.1
Harrison, K.2
Soldera, D.3
-
49
-
-
84947261826
-
Extending the GHS Weil descent attack
-
Lecture Notes in Computer Science
-
S. Galbraith, F. Hess, N. Smart, Extending the GHS Weil descent attack, Advances in Cryptology-EUROCRYPT 2002, Lecture Notes in Computer Science, vol. 2332, 2002, pp. 29-44.
-
(2002)
Advances in Cryptology-EUROCRYPT 2002
, vol.2332
, pp. 29-44
-
-
Galbraith, S.1
Hess, F.2
Smart, N.3
-
50
-
-
23044445566
-
Ordinary abelian varieties having small embedding degree Cryptology ePrint Archive: Report 2004/365
-
Available from
-
S. Galbraith, J. McKee, P. Valença, Ordinary abelian varieties having small embedding degree Cryptology ePrint Archive: Report 2004/ 365, 2004. Available from http://eprint.iacr.org/2004/365/.
-
(2004)
-
-
Galbraith, S.1
McKee, J.2
Valença, P.3
-
53
-
-
84948978775
-
An algorithm for solving the discrete log problem in hyperelliptic curves
-
Lecture Notes in Computer Science
-
P. Gaudry, An algorithm for solving the discrete log problem in hyperelliptic curves, Advances in Cryptology-EUROCRYPT 2000, Lecture Notes in Computer Science, vol. 1807, 2000, pp. 19-34.
-
(2000)
Advances in Cryptology-EUROCRYPT 2000
, vol.1807
, pp. 19-34
-
-
Gaudry, P.1
-
54
-
-
84958773354
-
A comparison and a combination of SST and AGM algorithms for counting points of elliptic curve in characteristic 2
-
Lecture Notes in Computer Science
-
P. Gaudry, A comparison and a combination of SST and AGM algorithms for counting points of elliptic curve in characteristic 2, Advances in Cryptology-ASIACRYPT 2002, Lecture Notes in Computer Science, vol. 2501, 2002, pp. 311-327.
-
(2002)
Advances in Cryptology-ASIACRYPT 2002
, vol.2501
, pp. 311-327
-
-
Gaudry, P.1
-
55
-
-
23044465981
-
Index calculus for abelian varieties and the elliptic curve discrete logarithm problem
-
Available from
-
P. Gaudry, Index calculus for abelian varieties and the elliptic curve discrete logarithm problem, Cryptology ePrint Archive: Report 2004/073, 2004. Available from http://eprint.iacr.org/2004/073/.
-
(2004)
Cryptology EPrint Archive: Report 2004/073
-
-
Gaudry, P.1
-
56
-
-
0001788567
-
Constructive and destructive facets of Weil descent on elliptic curves
-
P. Gaudry F. Hess N. Smart Constructive and destructive facets of Weil descent on elliptic curves J. Cryptol. 15 2002 19-46
-
(2002)
J. Cryptol.
, vol.15
, pp. 19-46
-
-
Gaudry, P.1
Hess, F.2
Smart, N.3
-
57
-
-
35048820123
-
Construction of secure random curves of genus 2 over prime fields
-
Lecture Notes in Computer Science
-
P. Gaudry, É. Schost, Construction of secure random curves of genus 2 over prime fields, Advances in Cryptology-EUROCRYPT 2004, Lecture Notes in Computer Science, vol. 3027, 2004, pp. 239-256.
-
(2004)
Advances in Cryptology-EUROCRYPT 2004
, vol.3027
, pp. 239-256
-
-
Gaudry, P.1
Schost, É.2
-
58
-
-
23044495111
-
A double large prime variation for small genus hyperelliptic index calculus
-
Available from
-
P. Gaudry, N. Thériault, E. Thomé, A double large prime variation for small genus hyperelliptic index calculus, Cryptology ePrint Archive: Report 2004/153, 2004. Available from http://eprint. iacr.org/2004/153/
-
(2004)
Cryptology EPrint Archive: Report 2004/153
-
-
Gaudry, P.1
Thériault, N.2
Thomé, E.3
-
59
-
-
0000303380
-
Discrete logarithms in GF(p) using the number field sieve
-
D. Gordon Discrete logarithms in GF (p) using the number field sieve SIAM J. Discrete Math. 6 1993 124-138
-
(1993)
SIAM J. Discrete Math.
, vol.6
, pp. 124-138
-
-
Gordon, D.1
-
61
-
-
0036222252
-
Computing Riemann-Roch spaces in algebraic function fields and related topics
-
F. Hess Computing Riemann-Roch spaces in algebraic function fields and related topics J. Symbolic Comput. 33 2002 425-445
-
(2002)
J. Symbolic Comput.
, vol.33
, pp. 425-445
-
-
Hess, F.1
-
62
-
-
23044512900
-
Generalising the GHS attack on the elliptic curve discrete logarithm problem
-
F. Hess Generalising the GHS attack on the elliptic curve discrete logarithm problem LMS J. Comput. Math. 7 2004 167-192
-
(2004)
LMS J. Comput. Math.
, vol.7
, pp. 167-192
-
-
Hess, F.1
-
63
-
-
23044507498
-
Weil descent attacks
-
Chapter VIII of [16]
-
F. Hess, Weil descent attacks, Chapter VIII of [16], 2005.
-
(2005)
-
-
Hess, F.1
-
64
-
-
0000266838
-
Efficient algorithms for the Riemann-Roch problem and for addition in the jacobian of a curve
-
M. Huang D. Ierardi Efficient algorithms for the Riemann-Roch problem and for addition in the jacobian of a curve J. Symbolic Comput. 18 1994 519-539
-
(1994)
J. Symbolic Comput.
, vol.18
, pp. 519-539
-
-
Huang, M.1
Ierardi, D.2
-
66
-
-
23044507497
-
-
ISO/IEC 15946 Part 1: General (2002), Part2: Digital Signatures (2002), Part3: Key Establishment (2002), Part4: Digital Signatures Giving Message Recovery
-
ISO/IEC 15946, Information Technology-Security Techniques-Cryptography Techniques Based on Elliptic Curves, Part 1: General (2002), Part 2: Digital Signatures (2002), Part 3: Key Establishment (2002), Part 4: Digital Signatures Giving Message Recovery (2004).
-
(2004)
Information Technology-Security Techniques-Cryptography Techniques Based on Elliptic Curves
-
-
-
67
-
-
84947711740
-
Efficient implementation of Schoof's algorithm
-
Lecture Notes in Computer Science
-
T. Izu, J. Kogure, M. Noro, K. Yokoyama, Efficient implementation of Schoof's algorithm, Advances in Cryptology-ASIACRYPT '98, Lecture Notes in Computer Science, vol. 1514, 1998, pp. 66-79.
-
(1998)
Advances in Cryptology-ASIACRYPT '98
, vol.1514
, pp. 66-79
-
-
Izu, T.1
Kogure, J.2
Noro, M.3
Yokoyama, K.4
-
69
-
-
11344293445
-
Solving elliptic curve discrete logarithm problems using Weil descent
-
M. Jacobson A. Menezes A. Stein Solving elliptic curve discrete logarithm problems using Weil descent J. Ramanujan Math. Soc. 16 2001 231-260
-
(2001)
J. Ramanujan Math. Soc.
, vol.16
, pp. 231-260
-
-
Jacobson, M.1
Menezes, A.2
Stein, A.3
-
70
-
-
23044438304
-
Ramanujan graphs and the random reducibility of discrete log on isogenous elliptic curves
-
Available from
-
D. Jao, S.D. Miller, R. Venkatesan, Ramanujan graphs and the random reducibility of discrete log on isogenous elliptic curves, Cryptology ePrint Archive: Report 2004/312, 2004. Available from http://eprint. iacr.org/2004/312/.
-
(2004)
Cryptology EPrint Archive: Report 2004/312
-
-
Jao, D.1
Miller, S.D.2
Venkatesan, R.3
-
71
-
-
84946844750
-
A one round protocol for tripartite Diffie-Hellman
-
Lecture Notes in Computer Science
-
A. Joux, A one round protocol for tripartite Diffie-Hellman, Algorithmic Number Theory: Fourth International Symposium, Lecture Notes in Computer Science, vol. 1838, 2000, pp. 385-393.
-
(2000)
Algorithmic Number Theory: Fourth International Symposium
, vol.1838
, pp. 385-393
-
-
Joux, A.1
-
72
-
-
84958545035
-
The function field sieve is quite special
-
Lecture Notes in Computer Science
-
A. Joux, R. Lercier, The function field sieve is quite special, Algorithmic Number Theory: 5th International Symposium, Lecture Notes in Computer Science, vol. 2369, 2002, pp. 431-445.
-
(2002)
Algorithmic Number Theory: 5th International Symposium
, vol.2369
, pp. 431-445
-
-
Joux, A.1
Lercier, R.2
-
73
-
-
0013266180
-
Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology
-
K. Kedlaya Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology J. Ramanujan Math. Soc. 16 2001 323-338
-
(2001)
J. Ramanujan Math. Soc.
, vol.16
, pp. 323-338
-
-
Kedlaya, K.1
-
74
-
-
84968503742
-
Elliptic curve cryptosystems
-
N. Koblitz Elliptic curve cryptosystems Math. Comput. 48 1987 203-209
-
(1987)
Math. Comput.
, vol.48
, pp. 203-209
-
-
Koblitz, N.1
-
75
-
-
0024864204
-
Hyperelliptic cryptosystems
-
N. Koblitz Hyperelliptic cryptosystems J. Cryptol. 1 1989 139-150
-
(1989)
J. Cryptol.
, vol.1
, pp. 139-150
-
-
Koblitz, N.1
-
77
-
-
13644249451
-
Formulae for arithmetic on genus 2 hyperelliptic curves
-
T. Lange Formulae for arithmetic on genus 2 hyperelliptic curves Appl. Algebra Eng. Commun. Comput. 15 2005 295-328
-
(2005)
Appl. Algebra Eng. Commun. Comput.
, vol.15
, pp. 295-328
-
-
Lange, T.1
-
78
-
-
84968499118
-
Factoring with two large primes
-
A. Lenstra M. Manasse Factoring with two large primes Math. Comput. 63 1994 785-798
-
(1994)
Math. Comput.
, vol.63
, pp. 785-798
-
-
Lenstra, A.1
Manasse, M.2
-
79
-
-
84957648431
-
Counting the number of points on elliptic curves over finite fields: Strategies and performances
-
Lecture Notes in Computer Science
-
R. Lercier, F. Morain, Counting the number of points on elliptic curves over finite fields: Strategies and performances, Advances in Cryptology-EUROCRYPT '95, Lecture Notes in Computer Science, vol. 921, 1995, pp. 79-94.
-
(1995)
Advances in Cryptology-EUROCRYPT '95
, vol.921
, pp. 79-94
-
-
Lercier, R.1
Morain, F.2
-
81
-
-
11344252143
-
Analysis of the GHS Weil descent attack on the ECDLP over characteristic two finite fields of composite degree
-
M. Maurer A. Menezes E. Teske Analysis of the GHS Weil descent attack on the ECDLP over characteristic two finite fields of composite degree LMS J. Comput. Math. 5 2002 127-174
-
(2002)
LMS J. Comput. Math.
, vol.5
, pp. 127-174
-
-
Maurer, M.1
Menezes, A.2
Teske, E.3
-
82
-
-
0032621240
-
The relationship between breaking the Diffie-Hellman protocol and computing discrete logarithms
-
U. Maurer S. Wolf The relationship between breaking the Diffie-Hellman protocol and computing discrete logarithms SIAM J. Comput. 28 1999 1689-1731
-
(1999)
SIAM J. Comput.
, vol.28
, pp. 1689-1731
-
-
Maurer, U.1
Wolf, S.2
-
83
-
-
0027662341
-
Reducing elliptic curve logarithms to logarithms in a finite field
-
A. Menezes T. Okamoto S. Vanstone Reducing elliptic curve logarithms to logarithms in a finite field IEEE Trans. Inform. Theory 39 1993 1639-1646
-
(1993)
IEEE Trans. Inform. Theory
, vol.39
, pp. 1639-1646
-
-
Menezes, A.1
Okamoto, T.2
Vanstone, S.3
-
84
-
-
33847320580
-
Analysis of the Weil descent attack of Gaudry, Hess and Smart
-
Lecture Notes in Computer Science
-
A. Menezes, M. Qu, Analysis of the Weil descent attack of Gaudry, Hess and Smart, Topics in Cryptology-CT-RSA 2001, Lecture Notes in Computer Science, vol. 2020, 2001, pp. 308-318.
-
(2001)
Topics in Cryptology-CT-RSA 2001
, vol.2020
, pp. 308-318
-
-
Menezes, A.1
Qu, M.2
-
86
-
-
35048833769
-
Weak fields for ECC
-
Lecture Notes in Computer Science
-
A. Menezes, E. Teske, A. Weng, Weak fields for ECC, Topics in Cryptology-CT-RSA 2004, Lecture Notes in Computer Science, vol. 2964, 2004, pp. 366-386.
-
(2004)
Topics in Cryptology-CT-RSA 2004
, vol.2964
, pp. 366-386
-
-
Menezes, A.1
Teske, E.2
Weng, A.3
-
87
-
-
3042619844
-
An elementary introduction to hyperelliptic curves
-
appendix in [76]
-
A. Menezes, Y. Wu, R. Zuccherato, An elementary introduction to hyperelliptic curves, appendix in [76], 1998, 155-178.
-
(1998)
, pp. 155-178
-
-
Menezes, A.1
Wu, Y.2
Zuccherato, R.3
-
88
-
-
85015402934
-
Uses of elliptic curves in cryptography
-
Lecture Notes in Computer Science
-
V. Miller, Uses of elliptic curves in cryptography, Advances in Cryptology-CRYPTO '85, Lecture Notes in Computer Science, vol. 218, 1986, pp. 417-426.
-
(1986)
Advances in Cryptology-CRYPTO '85
, vol.218
, pp. 417-426
-
-
Miller, V.1
-
89
-
-
22144445920
-
The Weil pairing, and its efficient calculation
-
V. Miller The Weil pairing, and its efficient calculation J. Cryptol. 17 2004 235-261
-
(2004)
J. Cryptol.
, vol.17
, pp. 235-261
-
-
Miller, V.1
-
90
-
-
0035336179
-
New explicit conditions of elliptic curve traces for FR-reduction
-
A. Miyaji, M. Nakabayashi, S. Takano, New explicit conditions of elliptic curve traces for FR-reduction, IEICE-Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E84-A (2001), pp. 1234-1243.
-
(2001)
IEICE-Transactions on Fundamentals of Electronics Communications and Computer Sciences
, vol.E84-A
, pp. 1234-1243
-
-
Miyaji, A.1
Nakabayashi, M.2
Takano, S.3
-
91
-
-
23044514913
-
-
Birkhäuser, Basel
-
D. Mumford, Tata Lectures on Theta II, Progress in Mathematics, vol. 43, Birkhäuser, Basel, 1984.
-
(1984)
Tata Lectures on Theta II, Progress in Mathematics
, vol.43
-
-
Mumford, D.1
-
92
-
-
84941637905
-
Signing on a postcard
-
Lecture Notes in Computer Science
-
D. Naccache, J. Stern, Signing on a postcard, Financial Cryptography-FC 2000, Lecture Notes in Computer Science, vol. 1962, 2001, pp. 121-135.
-
(2001)
Financial Cryptography-FC 2000
, vol.1962
, pp. 121-135
-
-
Naccache, D.1
Stern, J.2
-
93
-
-
0010227312
-
Complexity of a determinate algorithm for the discrete logarithm problem
-
V. Nechaev Complexity of a determinate algorithm for the discrete logarithm problem Math. Notes 55 1994 165-172
-
(1994)
Math. Notes
, vol.55
, pp. 165-172
-
-
Nechaev, V.1
-
94
-
-
0040575045
-
Real and imaginary quadratic representations of hyperelliptic function fields
-
S. Paulus H.-G. Rück Real and imaginary quadratic representations of hyperelliptic function fields Math. Comput. 68 1999 1233-1241
-
(1999)
Math. Comput.
, vol.68
, pp. 1233-1241
-
-
Paulus, S.1
Rück, H.-G.2
-
95
-
-
35248899925
-
Hyperelliptic curve cryptosystems: Closing the performance gap to elliptic curves
-
Lecture Notes in Computer Science
-
J. Pelzl, T. Wollinger, J. Guajardo, C. Paar, Hyperelliptic curve cryptosystems: Closing the performance gap to elliptic curves, Cryptographic Hardware and Embedded Systems-CHES 2003, Lecture Notes in Computer Science, vol. 2779, 2003, pp. 351-365.
-
(2003)
Cryptographic Hardware and Embedded Systems-CHES 2003
, vol.2779
, pp. 351-365
-
-
Pelzl, J.1
Wollinger, T.2
Guajardo, J.3
Paar, C.4
-
96
-
-
84944319191
-
Postal revenue collection in the digital age
-
Lecture Notes in Computer Science
-
L. Pintsov, S. Vanstone, Postal revenue collection in the digital age, Financial Cryptography-FC 2000, Lecture Notes in Computer Science, vol. 1962, 2001, pp. 105-120.
-
(2001)
Financial Cryptography-FC 2000
, vol.1962
, pp. 105-120
-
-
Pintsov, L.1
Vanstone, S.2
-
97
-
-
84919085619
-
An improved algorithm for computing logarithms over GF(p) and its cryptographic significance
-
S. Pohlig M. Hellman An improved algorithm for computing logarithms over GF (p) and its cryptographic significance IEEE Trans. Inform. Theory 24 1978 106-110
-
(1978)
IEEE Trans. Inform. Theory
, vol.24
, pp. 106-110
-
-
Pohlig, S.1
Hellman, M.2
-
98
-
-
84966238549
-
Monte Carlo methods for index computation mod p
-
J. Pollard Monte Carlo methods for index computation mod p Math. Comput. 32 1978 918-924
-
(1978)
Math. Comput.
, vol.32
, pp. 918-924
-
-
Pollard, J.1
-
99
-
-
84937426999
-
Supersingular abelian varieties in cryptology
-
Lecture Notes in Computer Science
-
K. Rubin, A. Silverberg, Supersingular abelian varieties in cryptology, Advances in Cryptology-CRYPTO 2002, Lecture Notes in Computer Science, vol. 2442, 2002, pp. 336-353.
-
(2002)
Advances in Cryptology-CRYPTO 2002
, vol.2442
, pp. 336-353
-
-
Rubin, K.1
Silverberg, A.2
-
100
-
-
0040712692
-
On the discrete logarithm in the divisor class group of curves
-
H. Rück On the discrete logarithm in the divisor class group of curves Math. Comput. 68 1999 805-806
-
(1999)
Math. Comput.
, vol.68
, pp. 805-806
-
-
Rück, H.1
-
101
-
-
2642549675
-
Cryptosystems based on pairings
-
Okinawa, Japan
-
R. Sakai, K. Ohgishi, M. Kasahara, Cryptosystems based on pairings, Proceedings of the 2000 Symposium on Cryptography and Information Security, Okinawa, Japan, 2000.
-
(2000)
Proceedings of the 2000 Symposium on Cryptography and Information Security
-
-
Sakai, R.1
Ohgishi, K.2
Kasahara, M.3
-
102
-
-
0001100056
-
The canonical lift of an ordinary elliptic curve over a prime field and its point counting
-
T. Satoh The canonical lift of an ordinary elliptic curve over a prime field and its point counting J. Ramanujan Math. Soc. 15 2000 247-270
-
(2000)
J. Ramanujan Math. Soc.
, vol.15
, pp. 247-270
-
-
Satoh, T.1
-
103
-
-
0343623059
-
Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves
-
T. Satoh K. Araki Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves Comment. Math. Univ. Sancti Pauli 47 1998 81-92
-
(1998)
Comment. Math. Univ. Sancti Pauli
, vol.47
, pp. 81-92
-
-
Satoh, T.1
Araki, K.2
-
104
-
-
12344258539
-
Efficient signature generation for smart cards
-
C. Schnorr Efficient signature generation for smart cards J. Cryptol. 4 1991 161-174
-
(1991)
J. Cryptol.
, vol.4
, pp. 161-174
-
-
Schnorr, C.1
-
105
-
-
84966233278
-
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. Comput. 44 1985 483-494
-
(1985)
Math. Comput.
, vol.44
, pp. 483-494
-
-
Schoof, R.1
-
106
-
-
38249034734
-
Nonsingular plane cubic curves over finite fields
-
R. Schoof Nonsingular plane cubic curves over finite fields J. Combin. Theory, A 46 1987 183-211
-
(1987)
J. Combin. Theory, A
, vol.46
, pp. 183-211
-
-
Schoof, R.1
-
108
-
-
0032352723
-
Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p
-
I. Semaev Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p Math. Comput. 67 1998 353-356
-
(1998)
Math. Comput.
, vol.67
, pp. 353-356
-
-
Semaev, I.1
-
109
-
-
23044515783
-
Summation polynomial and the discrete logarithm problem on elliptic curves
-
Available from
-
I. Semaev, Summation polynomial and the discrete logarithm problem on elliptic curves, Cryptology ePrint Archive: Report 2004/031, 2004. Available from http://eprint.iacr.org/2004/031/.
-
(2004)
Cryptology EPrint Archive: Report 2004/031
-
-
Semaev, I.1
-
110
-
-
85020598353
-
Identity-based cryptosystems and signature schemes
-
Lecture Notes in Computer Science
-
A. Shamir, Identity-based cryptosystems and signature schemes, Advances in Cryptology-Proceedings of CRYPTO 84, Lecture Notes in Computer Science, vol. 196, 1985, pp. 47-53.
-
(1985)
Advances in Cryptology-Proceedings of CRYPTO 84
, vol.196
, pp. 47-53
-
-
Shamir, A.1
-
111
-
-
84942550160
-
Lower bounds for discrete logarithms and related problems
-
Lecture Notes in Computer Science
-
V. Shoup, Lower bounds for discrete logarithms and related problems, Advances in Cryptology-EUROCRYPT '97, Lecture Notes in Computer Science, vol. 1233, 1997, pp. 256-266.
-
(1997)
Advances in Cryptology-EUROCRYPT '97
, vol.1233
, pp. 256-266
-
-
Shoup, V.1
-
113
-
-
0012234171
-
The xedni calculus and the elliptic curve discrete logarithm problem
-
J. Silverman The xedni calculus and the elliptic curve discrete logarithm problem Designs, Codes Cryptogr. 20 2000 5-40
-
(2000)
Designs, Codes Cryptogr.
, vol.20
, pp. 5-40
-
-
Silverman, J.1
-
114
-
-
84947727672
-
Elliptic curve discrete logarithms and the index calculus
-
Lecture Notes in Computer Science
-
J. Silverman, J. Suzuki, Elliptic curve discrete logarithms and the index calculus, Advances in Cryptology-ASIACRYPT '98, Lecture Notes in Computer Science, vol. 1514, 1998, pp. 110-125.
-
(1998)
Advances in Cryptology-ASIACRYPT '98
, vol.1514
, pp. 110-125
-
-
Silverman, J.1
Suzuki, J.2
-
115
-
-
0003539458
-
The discrete logarithm problem on elliptic curves of trace one
-
N. Smart The discrete logarithm problem on elliptic curves of trace one J. Cryptol. 12 1999 193-196
-
(1999)
J. Cryptol.
, vol.12
, pp. 193-196
-
-
Smart, N.1
-
116
-
-
35248821153
-
An analysis of Goubin's refined power analysis attack
-
Lecture Notes in Computer Science
-
N. Smart, An analysis of Goubin's refined power analysis attack, Cryptographic Hardware and Embedded Systems-CHES 2003, Lecture Notes in Computer Science, vol. 2779, 2003, pp. 281-290.
-
(2003)
Cryptographic Hardware and Embedded Systems-CHES 2003
, vol.2779
, pp. 281-290
-
-
Smart, N.1
-
117
-
-
4244162562
-
Sharp upper bounds for arithmetics in hyperelliptic function fields
-
A. Stein Sharp upper bounds for arithmetics in hyperelliptic function fields J. Ramanujan Math. Soc. 16 2001 1-86
-
(2001)
J. Ramanujan Math. Soc.
, vol.16
, pp. 1-86
-
-
Stein, A.1
-
118
-
-
23044501623
-
Efficient doubling on genus two curves over binary fields
-
Lecture Notes in Computer Science
-
M. Stevens, T. Lange, Efficient doubling on genus two curves over binary fields, Selected Areas in Cryptography-SAC 2004, Lecture Notes in Computer Science, vol. 3357, 2005, pp. 170-181.
-
(2005)
Selected Areas in Cryptography-SAC 2004
, vol.3357
, pp. 170-181
-
-
Stevens, M.1
Lange, T.2
-
119
-
-
0345058968
-
Index calculus attack for hyperelliptic curves of small genus
-
Lecture Notes in Computer Science
-
N. Thériault, Index calculus attack for hyperelliptic curves of small genus, Advances in Cryptology-ASIACRYPT 2003, Lecture Notes in Computer Science, vol. 2894, 2003, pp. 75-92.
-
(2003)
Advances in Cryptology-ASIACRYPT 2003
, vol.2894
, pp. 75-92
-
-
Thériault, N.1
-
120
-
-
23044510745
-
Weil descent attack for Kummer extensions
-
N. Thériault Weil descent attack for Kummer extensions J. Ramanujan Math. Soc. 18 2003 281-312
-
(2003)
J. Ramanujan Math. Soc.
, vol.18
, pp. 281-312
-
-
Thériault, N.1
-
121
-
-
84937390605
-
Computing zeta functions of hyperelliptic curves over finite fields of characteristic 2
-
Lecture Notes in Computer Science
-
F. Vercauteren, Computing zeta functions of hyperelliptic curves over finite fields of characteristic 2, Advances in Cryptology-CRYPTO 2002, Lecture Notes in Computer Science, vol. 2442, 2002, pp. 369-384.
-
(2002)
Advances in Cryptology-CRYPTO 2002
, vol.2442
, pp. 369-384
-
-
Vercauteren, F.1
-
122
-
-
23044474013
-
Evidence that XTR is more secure than supersingular elliptic curve cryptosystems
-
E. Verheul Evidence that XTR is more secure than supersingular elliptic curve cryptosystems J. Cryptol. 17 2004 277-296
-
(2004)
J. Cryptol.
, vol.17
, pp. 277-296
-
-
Verheul, E.1
-
123
-
-
85028812500
-
Computing in the jacobian of a plane algebraic curve
-
Lecture Notes in Computer Science
-
E. Volcheck, Computing in the jacobian of a plane algebraic curve, Algorithmic Number Theory, Lecture Notes in Computer Science, 1994, pp. 221-233.
-
(1994)
Algorithmic Number Theory
, pp. 221-233
-
-
Volcheck, E.1
-
125
-
-
0037235338
-
Constructing hyperelliptic curves of genus 2 suitable for cryptography
-
A. Weng Constructing hyperelliptic curves of genus 2 suitable for cryptography Math. Comput. 72 2003 435-458
-
(2003)
Math. Comput.
, vol.72
, pp. 435-458
-
-
Weng, A.1
|