-
2
-
-
84863338116
-
Rethinking low genus hyperelliptic Jacobian arithmetic over binary fields: Interplay of field arithmetic and explicit formulæ
-
Avanzi, R., Thériault, N., Wang, Z.: Rethinking low genus hyperelliptic Jacobian arithmetic over binary fields: interplay of field arithmetic and explicit formulæ. J. Math. Crypt. 2(3), 227-255 (2008)
-
(2008)
J. Math. Crypt.
, vol.2
, Issue.3
, pp. 227-255
-
-
Avanzi, R.1
Thériault, N.2
Wang, Z.3
-
3
-
-
85057426796
-
-
CRC
-
Avanzi, R.M., Cohen, H., Doche, C., Frey, G., Lange, T., Nguyen, K., Vercauteren, F.: The Handbook of Elliptic and Hyperelliptic Curve Cryptography. CRC (2005)
-
(2005)
The Handbook of Elliptic and Hyperelliptic Curve Cryptography.
-
-
Avanzi, R.M.1
Cohen, H.2
Doche, C.3
Frey, G.4
Lange, T.5
Nguyen, K.6
Vercauteren, F.7
-
6
-
-
84968494137
-
Computing in the Jacobian of a hyperelliptic curve
-
Cantor, D.G.: Computing in the Jacobian of a hyperelliptic curve. Math. Comp. 48(177), 95-101 (1987)
-
(1987)
Math. Comp.
, vol.48
, Issue.177
, pp. 95-101
-
-
Cantor, D.G.1
-
7
-
-
33645106690
-
Trading inversions for multiplications in elliptic curve cryptography
-
Ciet, M., Joye, M., Lauter, K., Montgomery, P.L.: Trading inversions for multiplications in elliptic curve cryptography. Designs, Codes and Cryptography 39(2), 189-206 (2006)
-
(2006)
Designs, Codes and Cryptography
, vol.39
, Issue.2
, pp. 189-206
-
-
Ciet, M.1
Joye, M.2
Lauter, K.3
Montgomery, P.L.4
-
8
-
-
33746706217
-
An Index Calculus Algorithm for Plane Curves of Small Degree
-
Hess, F., Pauli, S., Pohst, M. (eds.) ANTS 2006. Springer, Heidelberg
-
Diem, C.: An Index Calculus Algorithm for Plane Curves of Small Degree. In: Hess, F., Pauli, S., Pohst, M. (eds.) ANTS 2006. LNCS, vol. 4076, pp. 543-557. Springer, Heidelberg (2006)
-
(2006)
LNCS
, vol.4076
, pp. 543-557
-
-
Diem, C.1
-
9
-
-
33745856887
-
Efficient scalar multiplication by isogeny decompositions
-
Doche, C., Icart, T., Kohel, D.R.: Efficient scalar multiplication by isogeny decompositions. In: PKC 2006 [54], pp. 191-206 (2006)
-
(2006)
PKC 2006
, Issue.54
, pp. 191-206
-
-
Doche, C.1
Icart, T.2
Kohel, D.R.3
-
10
-
-
35248862491
-
Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation
-
Joye, M. (ed.) CT-RSA 2003. Springer, Heidelberg
-
Eisenträger, K., Lauter, K., Montgomery, P.L.: Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 343-354. Springer, Heidelberg (2003)
-
(2003)
LNCS
, vol.2612
, pp. 343-354
-
-
Eisenträger, K.1
Lauter, K.2
Montgomery, P.L.3
-
11
-
-
38349058155
-
Explicit Formulas for Real Hyperelliptic Curves of Genus 2 in Affine Representation
-
Carlet, C., Sunar, B. (eds.) WAIFI 2007. Springer, Heidelberg
-
Erickson, S., Jacobson Jr., M.J., Shang, N., Shen, S., Stein, A.: Explicit Formulas for Real Hyperelliptic Curves of Genus 2 in Affine Representation. In: Carlet, C., Sunar, B. (eds.) WAIFI 2007. LNCS, vol. 4547, pp. 202-218. Springer, Heidelberg (2007)
-
(2007)
LNCS
, vol.4547
, pp. 202-218
-
-
Erickson, S.1
Jacobson Jr., M.J.2
Shang, N.3
Shen, S.4
Stein, A.5
-
12
-
-
70350657323
-
Efficient Pairing Computation on Genus 2 Curves in Projective Coordinates
-
Avanzi, R.M., Keliher, L., Sica, F. (eds.) SAC 2008. Springer, Heidelberg
-
Fan, X., Gong, G., Jao, D.: Efficient Pairing Computation on Genus 2 Curves in Projective Coordinates. In: Avanzi, R.M., Keliher, L., Sica, F. (eds.) SAC 2008. LNCS, vol. 5381, pp. 18-34. Springer, Heidelberg (2009)
-
(2009)
LNCS
, vol.5381
, pp. 18-34
-
-
Fan, X.1
Gong, G.2
Jao, D.3
-
13
-
-
79956334252
-
Fast addition on non-hyperelliptic genus 3 curves
-
Flon, S., Oyono, R., Ritzenthaler, a.C.: Fast addition on non-hyperelliptic genus 3 curves. Algebraic geometry and its applications 5(3), 227-256 (2008)
-
(2008)
Algebraic Geometry and Its Applications
, vol.5
, Issue.3
, pp. 227-256
-
-
Flon, S.1
Oyono, R.2
Ritzenthaler, A.C.3
-
14
-
-
21144431641
-
Fast Arithmetic on Jacobians of Picard Curves
-
Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. Springer, Heidelberg
-
Flon, S., Oyono, R.: Fast Arithmetic on Jacobians of Picard Curves. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 55-68. Springer, Heidelberg (2004)
-
(2004)
LNCS
, vol.2947
, pp. 55-68
-
-
Flon, S.1
Oyono, R.2
-
16
-
-
44649099054
-
Efficient hyperelliptic arithmetic using balanced representation for divisors
-
DOI 10.1007/978-3-540-79456-1-23, Algorithmic Number Theory - 8th International Symposium, ANTS-VIII, Proceedings
-
Galbraith, S.D., Harrison, M., Mireles Morales, D.J.: Efficient Hyperelliptic Arithmetic using Balanced Representation for Divisors. In: van der Poorten, A.J., Stein, A. (eds.) ANTS-VIII 2008. LNCS, vol. 5011, pp. 342-356. Springer, Heidelberg (2008) (Pubitemid 351775543)
-
(2008)
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
, vol.5011 LNCS
, pp. 342-356
-
-
Galbraith, S.D.1
Harrison, M.2
Morales, D.J.M.3
-
17
-
-
84948978775
-
An Algorithm for Solving the Discrete Log Problem on Hyperelliptic Curves
-
Preneel, B. (ed.) EUROCRYPT 2000. Springer, Heidelberg
-
Gaudry, P.: An Algorithm for Solving the Discrete Log Problem on Hyperelliptic Curves. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 19-34. Springer, Heidelberg (2000)
-
(2000)
LNCS
, vol.1807
, pp. 19-34
-
-
Gaudry, P.1
-
18
-
-
84921925742
-
Hyperelliptic curves and the HCDLP
-
ch. VII, . Cambridge University Press
-
Gaudry, P.: Hyperelliptic curves and the HCDLP. London Mathematical Society Lecture Notes, vol. 317, ch. VII, pp. 133-150. Cambridge University Press (2005)
-
(2005)
London Mathematical Society Lecture Notes
, vol.317
, pp. 133-150
-
-
Gaudry, P.1
-
19
-
-
49949100083
-
Fast genus 2 arithmetic based on Theta functions
-
Gaudry, P.: Fast genus 2 arithmetic based on Theta functions. J. Math. Crypt. 1(3), 243-265 (2007)
-
(2007)
J. Math. Crypt.
, vol.1
, Issue.3
, pp. 243-265
-
-
Gaudry, P.1
-
20
-
-
84946825131
-
Counting Points on Hyperelliptic Curves over Finite Fields
-
Bosma, W. (ed.) ANTS 2000. Springer, Heidelberg
-
Gaudry, P., Harley, R.: Counting Points on Hyperelliptic Curves Over Finite Fields. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 313-332. Springer, Heidelberg (2000)
-
(2000)
LNCS
, vol.1838
, pp. 313-332
-
-
Gaudry, P.1
Harley, R.2
-
21
-
-
38049124867
-
A double large prime variation for small genus hyperelliptic index calculus
-
Gaudry, P., Thomé, E., Thériault, N., Diem, C.: A double large prime variation for small genus hyperelliptic index calculus. Math. Comp. 76(257), 475-492 (2007)
-
(2007)
Math. Comp.
, vol.76
, Issue.257
, pp. 475-492
-
-
Gaudry, P.1
Thomé, E.2
Thériault, N.3
Diem, C.4
-
22
-
-
27544481767
-
Improvements of addition algorithm on genus 3 hyperelliptic curves and their implementation
-
Gonda, M., Matsuo, K., Aoki, K., Chao, J., Tsujii, S.: Improvements of addition algorithm on genus 3 hyperelliptic curves and their implementation. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, 89-96 (2005)
-
(2005)
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
, pp. 89-96
-
-
Gonda, M.1
Matsuo, K.2
Aoki, K.3
Chao, J.4
Tsujii, S.5
-
23
-
-
33646838892
-
Explicit algorithm for the arithmetic on the hyperelliptic Jacobians of genus 3
-
Gurot, C., Kaveh, K., Patankar, V.M.: Explicit algorithm for the arithmetic on the hyperelliptic Jacobians of genus 3. Journal of the Ramanujan Mathematical Society 19, 75-115 (2004)
-
(2004)
Journal of the Ramanujan Mathematical Society
, vol.19
, pp. 75-115
-
-
Gurot, C.1
Kaveh, K.2
Patankar, V.M.3
-
25
-
-
0036222252
-
Computing Riemann-Roch spaces in algebraic function fields and related topics
-
Hess, F.: Computing Riemann-Roch spaces in algebraic function fields and related topics. J. Symb. Comput. 33(4), 425-445 (2002)
-
(2002)
J. Symb. Comput.
, vol.33
, Issue.4
, pp. 425-445
-
-
Hess, F.1
-
27
-
-
0000266838
-
Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve
-
Huang, M.A., Ierardi, D.: Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve. J. Symb. Comput. 18(6), 519-539 (1994)
-
(1994)
J. Symb. Comput.
, vol.18
, Issue.6
, pp. 519-539
-
-
Huang, M.A.1
Ierardi, D.2
-
28
-
-
23944495554
-
Novel efficient implementations of hyperelliptic curve cryptosystems using degenerate divisors
-
Information Security Applications - 5th International Workshop, WISA 2004
-
Katagi, M., Kitamura, I., Akishita, T., Takagi, T.: Novel Efficient Implementations of Hyperelliptic Curve Cryptosystems using Degenerate Divisors. In: Lim, C.H., Yung, M. (eds.) WISA 2004. LNCS, vol. 3325, pp. 345-359. Springer, Heidelberg (2005) (Pubitemid 41190824)
-
(2005)
Lecture Notes in Computer Science
, vol.3325
, pp. 345-359
-
-
Katagi, M.1
Kitamura, I.2
Akishita, T.3
Takagi, T.4
-
29
-
-
0942300543
-
Linear algebra algorithms for divisors on an algebraic curve
-
Khuri-Makdisi, K.: Linear algebra algorithms for divisors on an algebraic curve. Math. Comp. 73(245), 333-357 (2004)
-
(2004)
Math. Comp.
, vol.73
, Issue.245
, pp. 333-357
-
-
Khuri-Makdisi, K.1
-
30
-
-
38849120595
-
Asymptotically fast group operations on jacobians of general curves
-
Khuri-Makdisi, K.: Asymptotically fast group operations on jacobians of general curves. Math. Comp. 76(260), 2213-2239 (2007)
-
(2007)
Math. Comp.
, vol.76
, Issue.260
, pp. 2213-2239
-
-
Khuri-Makdisi, K.1
-
31
-
-
84968503742
-
Elliptic curve cryptosystems
-
Koblitz, N.: Elliptic curve cryptosystems. Math. Comp. 48(177), 203-209 (1987)
-
(1987)
Math. Comp.
, vol.48
, Issue.177
, pp. 203-209
-
-
Koblitz, N.1
-
32
-
-
0024864204
-
Hyperelliptic cryptosystems
-
Koblitz, N.: Hyperelliptic cryptosystems. J. Cryptology 1(3), 139-150 (1989)
-
(1989)
J. Cryptology
, vol.1
, Issue.3
, pp. 139-150
-
-
Koblitz, N.1
-
35
-
-
21744445228
-
Efficient arithmetic on genus 2 hyperelliptic curves over finite fields via explicit formulae
-
ePrint Archive, Report 2002/121
-
Lange, T.: Efficient arithmetic on genus 2 hyperelliptic curves over finite fields via explicit formulae. Cryptology ePrint Archive, Report 2002/121 (2002), http://eprint.iacr.org/
-
(2002)
Cryptology
-
-
Lange, T.1
-
36
-
-
21444461295
-
Inversion-free arithmetic on genus 2 hyperelliptic curves
-
ePrint Archive, Report 2002/147
-
Lange, T.: Inversion-free arithmetic on genus 2 hyperelliptic curves. Cryptology ePrint Archive, Report 2002/147 (2002), http://eprint.iacr.org/
-
(2002)
Cryptology
-
-
Lange, T.1
-
37
-
-
23044490544
-
Weighted coordinates on genus 2 hyperelliptic curves
-
ePrint Archive, Report 2002/153
-
Lange, T.: Weighted coordinates on genus 2 hyperelliptic curves. Cryptology ePrint Archive, Report 2002/153 (2002), http://eprint.iacr.org/
-
(2002)
Cryptology
-
-
Lange, T.1
-
38
-
-
13644249451
-
Formulae for arithmetic on genus 2 hyperelliptic curves
-
Lange, T.: Formulae for arithmetic on genus 2 hyperelliptic curves. Appl. Algebra Eng. Commun. Comput. 15(5), 295-328 (2005)
-
(2005)
Appl. Algebra Eng. Commun. Comput.
, vol.15
, Issue.5
, pp. 295-328
-
-
Lange, T.1
-
40
-
-
23744507325
-
The equivalence of the geometric and algebraic group laws for Jacobians of genus 2 curves
-
Lauter, K.: The equivalence of the geometric and algebraic group laws for Jacobians of genus 2 curves. Topics in Algebraic and Noncommutative Geometry 324, 165-171 (2003)
-
(2003)
Topics in Algebraic and Noncommutative Geometry
, vol.324
, pp. 165-171
-
-
Lauter, K.1
-
41
-
-
78650290613
-
An Analysis of Affine Coordinates for Pairing Computation
-
Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. Springer, Heidelberg
-
Lauter, K., Montgomery, P.L., Naehrig, M.: An Analysis of Affine Coordinates for Pairing Computation. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 1-20. Springer, Heidelberg (2010)
-
(2010)
LNCS
, vol.6487
, pp. 1-20
-
-
Lauter, K.1
Montgomery, P.L.2
Naehrig, M.3
-
42
-
-
20844459001
-
About the group law for the Jacobi variety of a hyperelliptic curve
-
Leitenberger, F.: About the group law for the Jacobi variety of a hyperelliptic curve. Contributions to Algebra and Geometry 46(1), 125-130 (2005)
-
(2005)
Contributions to Algebra and Geometry
, vol.46
, Issue.1
, pp. 125-130
-
-
Leitenberger, F.1
-
43
-
-
0141911121
-
-
Technical Report 214, IEIC
-
Matsuo, K., Chao, J., Tsujii, S.: Fast genus two hyperelliptic curve cryptosystems. Technical Report 214, IEIC (2001)
-
(2001)
Fast Genus Two Hyperelliptic Curve Cryptosystems
-
-
Matsuo, K.1
Chao, J.2
Tsujii, S.3
-
44
-
-
85015402934
-
Use of Elliptic Curves in Cryptography
-
Williams, H.C. (ed.) CRYPTO 1985. Springer, Heidelberg
-
Miller, V.S.: Use of Elliptic Curves in Cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417-426. Springer, Heidelberg (1986)
-
(1986)
LNCS
, vol.218
, pp. 417-426
-
-
Miller, V.S.1
-
45
-
-
3042583179
-
A fast addition algorithm of genus two hyperelliptic curve
-
in Japanese
-
Miyamoto, Y., Doi, H., Matsuo, K., Chao, J., Tsujii, S.: A fast addition algorithm of genus two hyperelliptic curve. In: Symposium on Cryptography and Information Security - SCICS (2002) (in Japanese)
-
Symposium on Cryptography and Information Security - SCICS (2002)
-
-
Miyamoto, Y.1
Doi, H.2
Matsuo, K.3
Chao, J.4
Tsujii, S.5
-
46
-
-
0003358889
-
Tata lectures on theta II
-
Birkhiauser Boston Inc., Boston
-
Mumford, D.: Tata lectures on theta II. In: Progress in Mathematics, vol. 43. Birkhiauser Boston Inc., Boston (1984)
-
(1984)
Progress in Mathematics
, vol.43
-
-
Mumford, D.1
-
47
-
-
84966238549
-
Monte Carlo methods for index computation (mod p)
-
Pollard, J.M.: Monte Carlo methods for index computation (mod p). Math. Comp. 32(143), 918-924 (1978)
-
(1978)
Math. Comp.
, vol.32
, Issue.143
, pp. 918-924
-
-
Pollard, J.M.1
-
48
-
-
68549121006
-
Isogenies and the discrete logarithm problem in Jacobians of genus 3 hyperelliptic curves
-
Smith, B.: Isogenies and the discrete logarithm problem in Jacobians of genus 3 hyperelliptic curves. Journal of Cryptology 22(4), 505-529 (2009)
-
(2009)
Journal of Cryptology
, vol.22
, Issue.4
, pp. 505-529
-
-
Smith, B.1
-
49
-
-
23044484917
-
-
Technical Report ISEC2002-9(2002-5), IEICE
-
Sugizaki, H., Matsuo, K., Chao, J., Tsujii, S.: An extension of Harley addition algorithm for hyperelliptic curves over finite fields of characteristic two. Technical Report ISEC2002-9(2002-5), IEICE (2002)
-
(2002)
An Extension of Harley Addition Algorithm for Hyperelliptic Curves over Finite Fields of Characteristic Two.
-
-
Sugizaki, H.1
Matsuo, K.2
Chao, J.3
Tsujii, S.4
-
53
-
-
23044447217
-
Cantor versus Harley: Optimization and analysis of explicit formulae for hyperelliptic curve cryptosystems
-
Wollinger, T., Pelzl, J., Paar, C.: Cantor versus Harley: optimization and analysis of explicit formulae for hyperelliptic curve cryptosystems. IEEE Transactions on Computers, 861-872 (2005)
-
(2005)
IEEE Transactions on Computers
, pp. 861-872
-
-
Wollinger, T.1
Pelzl, J.2
Paar, C.3
-
54
-
-
49849094834
-
PKC 2006
-
Springer, Heidelberg
-
Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.): PKC 2006. LNCS, vol. 3958. Springer, Heidelberg (2006)
-
(2006)
LNCS
, vol.3958
-
-
Yung, M.1
Dodis, Y.2
Kiayias, A.3
Malkin, T.4
|