High performance arithmetic for special hyperelliptic curve cryptosystems of genus two

International Conference on Information Technology: Coding Computing, ITCC

Volumn 2, Issue , 2004, Pages 513-517

  Pelzl, Jan ^a   Wollinger, Thomas ^a   Paar, Christof ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EMBEDDED ENVIRONMENTS; EMBEDDED PROCESSORS; HYPERELLIPTIC CURVES; NON-SUPERSINGULAR CURVES;

ALGORITHMS; APPROXIMATION THEORY; COMPUTER HARDWARE; OPTIMIZATION; PARAMETER ESTIMATION; POWER CONTROL;

CRYPTOGRAPHY;

EID: 3042668581     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ITCC.2004.1286706     Document Type: Conference Paper

References (34)

1. N. Boston, T. Clancy, Y. Liow, and J. Webster. Genus Two Hyperelliptic Curve Coprocessor. In Kaliski, Koç, Paar, editor, Workshop on Cryptographic Hardware and Embedded Systems - CHES 2002, New York, 2002. Springer Verlag. LNCS 2523.
2. D. Cantor. Computing in the Jacobian of a Hyperelliptic Curve. In Mathematics of Computation, volume 48(177), pages 95-101, 1987.
3. A. Enge. The extended Euclidean algorithm on polynomials, and the computational efficiency of hyperelliptic cryptosystems, November 1999. Preprint.
4. W. Fulton. Algebraic Curves - An Introduction to Algebraic Geometry. W. A. Benjamin, Inc., Reading, Massachusetts, 1969.
5. S. Galbraith. Supersingular curves in cryptography. LNCS 2248:495-517, 2001.
6. P. Gaudry. An algorithm for solving the discrete log problem on hyperelliptic curves. In B. Preneel, editor, Advances in Cryptology - EUROCRYPT 2000, pages 19-34, Berlin, Germany, 2000. Springer-Verlag. LNCS 1807.
7. P. Gaudry and R. Harley. Counting Points on Hyperelliptic Curves over Finite Fields. In W. Bosma, editor, The 4th Algorithmic Number Theory Symposium - ANTS IV, pages 297-312, Berlin, 2000. Springer Verlag. LNCS 1838.
8. R. Harley. Fast Arithmetic on Genus Two Curves. Available at http://cristal.inria.fr/~harley/hyper/, 2000.
9. N. Koblitz. A Family of Jacobians Suitable for Discrete Log Cryptosystems. In Shafi Goldwasser, editor, Advances in Cryptology - CRYPTO '88, pages 94 - 99, Berlin, 1988. Springer-Verlag. LNCS 403.
10. N. Koblitz, Hyperelliptic Cryptosystems. In Ernest F. Brickell, editor, Journal of Cryptology, pages 139 - 150, 1989.
11. N. Koblitz. Algebraic Aspects of Cryptography. Algorithms and Computation in Mathematics. Springer-Verlag, 1998.
12. J. Kuroki, M. Gonda, K. Matsuo, J. Chao, and S. Tsujii. Fast Genus Three Hyperelliptic Curve Cryptosystems. In The 2002 Symposium on Cryptography and Information Security, Japan - SCIS 2002, Jan.29-Feb.1 2002.
13. T. Lange. Efficient Arithmetic on Genus 2 Hyperelliptic Curves over Finite Fields via Explicit Formulae. Cryptology ePrint Archive, Report 2002/121, 2002. http: //eprint.iacr.org/.
14. T. Lange. Formulae for Arithmetic on Genus 2 Hyperelliptic Curves, 2003. Available at http://www.ruhr-uni-bochum.de/itsc/tanja/preprints.html.
15. K. Matsuo, J. Chao, and S. Tsujii. Fast Genus Two Hyperelliptic Curve Cryptosystems. In ISEC2001-31, IEICE, 2001.
16. A. Menezes, Y.-H. Wu, and R. Zuccherato. An elementary introduction to hyperelliptic curves. In N. Koblitz, editor, Algebraic Aspects of Cryptography, Berlin, Heidelberg, 1996. Springer Verlag.
17. Y. Miyamoto, H. Doi, K. Matsuo, J. Chao, and S. Tsuji. A Fast Addition Algorithm of Genus Two Hyperelliptic Curve. In SCIS, IEICE Japan, pages 497 - 502, 2002. in Japanese.
18. D. Mumford. Tata lectures on theta II. In Prog. Math., volume 43. Birkhäuser, 1984.
19. K. Nagao. Improving group law algorithms for Jacobians of hyperelliptic curves. In W. Bosma, editor, ANTS IV, volume LNCS 1838, pages 439 - 448, Berlin, 2000. Springer Verlag.
20. J. Pelzl. Hyperelliptic Cryptosystems on Embedded Microprocessors, September 2002. Diplomarbeit, Fakultät für Elektrotechnik und Informationstechnik, Ruhr-UniBochum.
21. J. Pelzl, T. Wollinger, J. Guajardo, and C. Paar. Hyperelliptic Curve CryptoSystems: Closing the Performance Gap to Elliptic Curves. In C. Walter, C. Koc, and C. Paar, editors, Workshop on Cryptographic Hardware and Embedded Systems - CHES 2003, pages 351-365, Berlin. Springer Verlag. LNCS 2779.
22. J. Pelzl, T. Wollinger, and C. Paar. High performance arithmetic for hyperelliptic curve cryptosystems of genus two. Cryptology ePrint Archive, Report 2003/212, 2003. http://eprint.iacr.org/.
23. J. Pelzl, T. Wollinger, and C. Paar. Low Cost Security: Explicit Formulae for Genus-4 Hyperelliptic Curves. In Tenth Annual Workshop on Selected Areas in Cryptography SAC 2003. Springer-Verlag, 2003. LNCS.
24. J. M. Pollard. Monte carlo methods for index computation modp. Mathematics of Computation, 32(143):918-924, July 1978.
25. 2n . In Advances in Cryptology - ASIACRYPT '98, pages 80-94, Berlin, 1998. Springer Verlag. LNCS 1514.
26. Y. Sakai and K. Sakurai. On the Practical Performance of Hyperelliptic Curve Cryptosystems in Software Implementation. In IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, volume E83-A N0.4, pages 692 - 703, April 2000. IEICE Trans.
27. Y. Sakai, K. Sakurai, and H. Ishizuka. Secure Hyperelliptic Cryptosystems and their Performance. In Public Key Cryptography, pages 164 - 181, Berlin, 1998. Springer-Verlag. LNCS 1431.
28. N. Smart. On the Performance of Hyperelliptic Cryptosystems. In Advances in Cryptology - EUROCRYPT '99, volume 1592, pages 165 - 175, Berlin, 1999. Springer-Verlag. LNCS 1592.
29. M. Takahashi. Improving Harley Algorithms for Jacobians of Genus 2 Hyperelliptic Curves. In SCIS, IEICE Japan, 2002. in Japanese.
30. N. Thériault. Index calculus attack for hyperelliptic curves of small genus. In Advances in Cryptology - ASIACRYPT '03, Berlin, 2003. Springer Verlag. LNCS.
31. P. C. van Oorschot and M. J. Wiener. Parallel collision search with cryptanalytic applications. Journal of Cryptology, 12(1): 1-28, Winter 1999.
32. T. Wollinger. Computer Architectures for Cryptosystems Based on Hyperelliptic Curves. Master's thesis, Worcester Polytechnic Institute, 2001.
33. T. Wollinger and C. Paar. Hardware Architectures proposed for Cryptosystems Based on Hyperelliptic Curves. In Proceedings of the 9th IEEE International Conference on Electronics, Circuits and Systems - ICECS 2002, volume III, pages 1159 - 1163, September 15-18 2002.
34. T. Wollinger, J. Pelzl, V. Wittelsberger, C. Paar, G. Saldamli, and Ç. K. Koç. Elliptic & hyperelliptic curves on embedded μp. ACM Transactions in Embedded Computing Systems (TECS), 2003. Special Issue on Embedded Systems and Security.