-
1
-
-
84966219173
-
Elliptic curves and primality proving
-
Atkin A., Morain F. Elliptic curves and primality proving. Math. Comp. 1993, 61:29-68.
-
(1993)
Math. Comp.
, vol.61
, pp. 29-68
-
-
Atkin, A.1
Morain, F.2
-
2
-
-
84968508650
-
A heuristic asymptotic formula concerning the distribution of prime numbers
-
Bateman P., Horn R. A heuristic asymptotic formula concerning the distribution of prime numbers. Math. Comp. 1962, 16:363-367.
-
(1962)
Math. Comp.
, vol.16
, pp. 363-367
-
-
Bateman, P.1
Horn, R.2
-
3
-
-
69949142052
-
On the security of pairing-friendly abelian varieties over non-prime fields
-
Springer, Pairing-Based Cryptography - Pairing 2009
-
Benger N., Charlemagne M., Freeman D. On the security of pairing-friendly abelian varieties over non-prime fields. Lecture Notes in Comput. Sci. 2009, vol. 5671:52-65. Springer.
-
(2009)
Lecture Notes in Comput. Sci.
, vol.5671
, pp. 52-65
-
-
Benger, N.1
Charlemagne, M.2
Freeman, D.3
-
5
-
-
23944463638
-
Elliptic curves suitable for pairing based cryptography
-
Brezing F., Weng A. Elliptic curves suitable for pairing based cryptography. Des. Codes Cryptogr. 2005, 37:133-141.
-
(2005)
Des. Codes Cryptogr.
, vol.37
, pp. 133-141
-
-
Brezing, F.1
Weng, A.2
-
6
-
-
38849170047
-
-
PhD dissertation, Universiteit Leiden, 2006, available at
-
Bröker R. Constructing elliptic curves of prescribed order PhD dissertation, Universiteit Leiden, 2006, available at. http://math.leidenuniv.nl/~reinier/thesis.pdf.
-
Constructing elliptic curves of prescribed order
-
-
Bröker, R.1
-
7
-
-
0003272622
-
Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2
-
Cambridge Univ. Press, Cambridge
-
Cassels J.W.S., Flynn E.V. Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2. London Math. Soc. Lecture Note Ser. 1996, vol. 230. Cambridge Univ. Press, Cambridge.
-
(1996)
London Math. Soc. Lecture Note Ser.
, vol.230
-
-
Cassels, J.W.S.1
Flynn, E.V.2
-
8
-
-
79551601110
-
-
Identity-based cryptosystems based on the Weil pairing, unpublished manuscript, while this manuscript is generally unavailable, the main result appears as Theorem 4.1 of [13].
-
C. Cocks, R. Pinch, Identity-based cryptosystems based on the Weil pairing, unpublished manuscript, 2001, while this manuscript is generally unavailable, the main result appears as Theorem 4.1 of [13].
-
(2001)
-
-
Cocks, C.1
Pinch, R.2
-
10
-
-
40249109433
-
The vector decomposition problem for elliptic and hyperelliptic curves
-
Duursma I., Kiyavash N. The vector decomposition problem for elliptic and hyperelliptic curves. J. Ramanujan Math. Soc. 2005, 20:59-76.
-
(2005)
J. Ramanujan Math. Soc.
, vol.20
, pp. 59-76
-
-
Duursma, I.1
Kiyavash, N.2
-
11
-
-
52149096501
-
A generalized Brezing-Weng algorithm for constructing pairing-friendly ordinary abelian varieties
-
Springer, Pairing-Based Cryptography - Pairing 2008
-
Freeman D. A generalized Brezing-Weng algorithm for constructing pairing-friendly ordinary abelian varieties. Lecture Notes in Comput. Sci. 2008, vol. 5209:146-163. Springer.
-
(2008)
Lecture Notes in Comput. Sci.
, vol.5209
, pp. 146-163
-
-
Freeman, D.1
-
13
-
-
73849107877
-
A taxonomy of pairing-friendly elliptic curves
-
Freeman D., Scott M., Teske E. A taxonomy of pairing-friendly elliptic curves. J. Cryptology 2010, 23:224-280.
-
(2010)
J. Cryptology
, vol.23
, pp. 224-280
-
-
Freeman, D.1
Scott, M.2
Teske, E.3
-
14
-
-
44649167142
-
Abelian varieties with prescribed embedding degree
-
Springer, Algorithmic Number Theory - ANTS-VIII
-
Freeman D., Stevenhagen P., Streng M. Abelian varieties with prescribed embedding degree. Lecture Notes in Comput. Sci. 2008, vol. 5011:60-73. Springer.
-
(2008)
Lecture Notes in Comput. Sci.
, vol.5011
, pp. 60-73
-
-
Freeman, D.1
Stevenhagen, P.2
Streng, M.3
-
15
-
-
0001923968
-
Curves with infinite K-rational geometric fundamental group
-
Cambridge Univ. Press, Cambridge, Aspects of Galois Theory
-
Frey G., Kani E., Völklein H. Curves with infinite K-rational geometric fundamental group. London Math. Soc. Lecture Note Ser. 1999, vol. 256:85-118. Cambridge Univ. Press, Cambridge.
-
(1999)
London Math. Soc. Lecture Note Ser.
, vol.256
, pp. 85-118
-
-
Frey, G.1
Kani, E.2
Völklein, H.3
-
16
-
-
35048824357
-
Counting points for hyperelliptic curves of type y2=x5+ax over finite prime fields
-
Springer, Selected Areas in Cryptography - SAC 2003
-
Furukawa E., Kawazoe M., Takahashi T. Counting points for hyperelliptic curves of type y2=x5+ax over finite prime fields. Lecture Notes in Comput. Sci. 2004, vol. 3006:26-41. Springer.
-
(2004)
Lecture Notes in Comput. Sci.
, vol.3006
, pp. 26-41
-
-
Furukawa, E.1
Kawazoe, M.2
Takahashi, T.3
-
17
-
-
44649099054
-
Efficient hyperelliptic arithmetic using balanced representation for divisors
-
Springer, Algorithmic Number Theory Symposium - ANTS-VIII
-
Galbraith S.D., Harrison M., Morales D.J.M. Efficient hyperelliptic arithmetic using balanced representation for divisors. Lecture Notes in Comput. Sci. 2008, vol. 5011:342-356. Springer.
-
(2008)
Lecture Notes in Comput. Sci.
, vol.5011
, pp. 342-356
-
-
Galbraith, S.D.1
Harrison, M.2
Morales, D.J.M.3
-
18
-
-
52149120956
-
Pairings on hyperelliptic curves with a real model
-
Springer, Pairing-Based Cryptography - Pairing 2008
-
Galbraith S.D., Lin X., Morales D.J.M. Pairings on hyperelliptic curves with a real model. Lecture Notes in Comput. Sci. 2008, vol. 5209:265-281. Springer.
-
(2008)
Lecture Notes in Comput. Sci.
, vol.5209
, pp. 265-281
-
-
Galbraith, S.D.1
Lin, X.2
Morales, D.J.M.3
-
19
-
-
67650659199
-
Endomorphisms for faster elliptic curve cryptography on a large class of curves
-
Springer, Advances in Cryptology - EUROCRYPT 2009
-
Galbraith S., Lin X., Scott M. Endomorphisms for faster elliptic curve cryptography on a large class of curves. Lecture Notes in Comput. Sci. 2009, vol. 5479:518-535. Springer.
-
(2009)
Lecture Notes in Comput. Sci.
, vol.5479
, pp. 518-535
-
-
Galbraith, S.1
Lin, X.2
Scott, M.3
-
20
-
-
84867079019
-
On the invariants of the quotients of the Jacobian of a curve of genus 2
-
Springer, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - AAECC-14
-
Gaudry P., Schost É. On the invariants of the quotients of the Jacobian of a curve of genus 2. Lecture Notes in Comput. Sci. 2001, vol. 2227:373-386. Springer.
-
(2001)
Lecture Notes in Comput. Sci.
, vol.2227
, pp. 373-386
-
-
Gaudry, P.1
Schost, É.2
-
21
-
-
35048820123
-
Construction of secure random curves of genus 2 over prime fields
-
Springer, Advances in Cryptology - EUROCRYPT 2004
-
Gaudry P., Schost É. Construction of secure random curves of genus 2 over prime fields. Lecture Notes in Comput. Sci. 2004, vol. 3027:239-256. Springer.
-
(2004)
Lecture Notes in Comput. Sci.
, vol.3027
, pp. 239-256
-
-
Gaudry, P.1
Schost, É.2
-
22
-
-
47849110765
-
On the minimal embedding field
-
Springer, Pairing-Based Cryptography - Pairing 2007
-
Hitt L. On the minimal embedding field. Lecture Notes in Comput. Sci. 2007, vol. 4575:294-301. Springer.
-
(2007)
Lecture Notes in Comput. Sci.
, vol.4575
, pp. 294-301
-
-
Hitt, L.1
-
23
-
-
52149118038
-
Pairing-friendly hyperelliptic curves with ordinary Jacobians of type y2=x5+ax
-
Springer, Pairing-Based Cryptography - Pairing 2008
-
Kawazoe M., Takahashi T. Pairing-friendly hyperelliptic curves with ordinary Jacobians of type y2=x5+ax. Lecture Notes in Comput. Sci. 2008, vol. 5209:164-177. Springer.
-
(2008)
Lecture Notes in Comput. Sci.
, vol.5209
, pp. 164-177
-
-
Kawazoe, M.1
Takahashi, T.2
-
24
-
-
0003352579
-
Elliptic Functions
-
Springer-Verlag, New York
-
Lang S. Elliptic Functions. Grad. Texts in Math. 1987, vol. 112. Springer-Verlag, New York. second ed.
-
(1987)
Grad. Texts in Math.
, vol.112
-
-
Lang, S.1
-
25
-
-
0036934634
-
Abelian surfaces over finite fields as Jacobians
-
with an appendix by Everett W. Howe
-
Maisner D., Nart E. Abelian surfaces over finite fields as Jacobians. Experiment. Math. 2002, 11:321-337. with an appendix by Everett W. Howe.
-
(2002)
Experiment. Math.
, vol.11
, pp. 321-337
-
-
Maisner, D.1
Nart, E.2
-
26
-
-
34249004685
-
Twisting commutative algebraic groups
-
Mazur B., Rubin K., Silverberg A. Twisting commutative algebraic groups. J. Algebra 2007, 314:419-438.
-
(2007)
J. Algebra
, vol.314
, pp. 419-438
-
-
Mazur, B.1
Rubin, K.2
Silverberg, A.3
-
27
-
-
33746100516
-
Cryptography from pairings
-
Cambridge Univ. Press, I.F. Blake, G. Seroussi, N.P. Smart (Eds.)
-
Paterson K. Cryptography from pairings. Advances in Elliptic Curve Cryptography 2005, 215-251. Cambridge Univ. Press. I.F. Blake, G. Seroussi, N.P. Smart (Eds.).
-
(2005)
Advances in Elliptic Curve Cryptography
, pp. 215-251
-
-
Paterson, K.1
-
28
-
-
24944518198
-
Using primitive subgroups to do more with fewer bits
-
Springer, Algorithmic Number Theory - ANTS VI
-
Rubin K., Silverberg A. Using primitive subgroups to do more with fewer bits. Lecture Notes in Comput. Sci. 2004, vol. 3076:18-41. Springer.
-
(2004)
Lecture Notes in Comput. Sci.
, vol.3076
, pp. 18-41
-
-
Rubin, K.1
Silverberg, A.2
-
29
-
-
65049089121
-
Using abelian varieties to improve pairing-based cryptography
-
Rubin K., Silverberg A. Using abelian varieties to improve pairing-based cryptography. J. Cryptology 2009, 22:330-364.
-
(2009)
J. Cryptology
, vol.22
, pp. 330-364
-
-
Rubin, K.1
Silverberg, A.2
-
30
-
-
77950188914
-
Choosing the correct elliptic curve in the CM method
-
Rubin K., Silverberg A. Choosing the correct elliptic curve in the CM method. Math. Comp. 2010, 79:545-561.
-
(2010)
Math. Comp.
, vol.79
, pp. 545-561
-
-
Rubin, K.1
Silverberg, A.2
-
31
-
-
67650679681
-
Generating genus two hyperelliptic curves over large characteristic finite fields
-
Springer, Advances in Cryptology - EUROCRYPT 2009
-
Satoh T. Generating genus two hyperelliptic curves over large characteristic finite fields. Lecture Notes in Comput. Sci. 2009, vol. 5479:536-553. Springer.
-
(2009)
Lecture Notes in Comput. Sci.
, vol.5479
, pp. 536-553
-
-
Satoh, T.1
-
32
-
-
0003236499
-
Advanced Topics in the Arithmetic of Elliptic Curves
-
Springer-Verlag, New York
-
Silverman J. Advanced Topics in the Arithmetic of Elliptic Curves. Grad. Texts in Math. 1994, vol. 151. Springer-Verlag, New York.
-
(1994)
Grad. Texts in Math.
, vol.151
-
-
Silverman, J.1
-
34
-
-
34250541896
-
Endomorphisms of abelian varieties over finite fields
-
Tate J. Endomorphisms of abelian varieties over finite fields. Invent. Math. 1966, 2:134-144.
-
(1966)
Invent. Math.
, vol.2
, pp. 134-144
-
-
Tate, J.1
-
35
-
-
0003201529
-
Classes d'isogénie des variétés abéliennes sur un corps fini (d'après T. Honda)
-
Springer, Séminaire Bourbaki 1968/69
-
Tate J. Classes d'isogénie des variétés abéliennes sur un corps fini (d'après T. Honda). Lecture Notes in Math. 1971, vol. 179:95-110. Springer.
-
(1971)
Lecture Notes in Math.
, vol.179
, pp. 95-110
-
-
Tate, J.1
-
36
-
-
0033480564
-
Examples of genus two CM curves defined over the rationals
-
van Wamelen P. Examples of genus two CM curves defined over the rationals. Math. Comp. 1999, 68:307-320.
-
(1999)
Math. Comp.
, vol.68
, pp. 307-320
-
-
van Wamelen, P.1
-
38
-
-
0003361966
-
Adèles and Algebraic Groups
-
Birkhäuser, Boston, with appendices by M. Demazure and Takashi Ono
-
Weil A. Adèles and Algebraic Groups. Progr. Math. 1982, vol. 23. Birkhäuser, Boston, with appendices by M. Demazure and Takashi Ono.
-
(1982)
Progr. Math.
, vol.23
-
-
Weil, A.1
|