Novel efficient implementations of hyperelliptic curve cryptosystems using degenerate divisors

Lecture Notes in Computer Science

Volumn 3325, Issue , 2005, Pages 345-359

  Katagi, Masanobu ^a   Kitamura, Izuru ^a   Akishita, Toru ^a   Takagi, Tsuyoshi ^b  

^a SONY CORPORATION   (Japan)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Degenerate divisor; Efficient computation; Hyperelliptic curve cryptosystem; Scalar multiplication; SSL; Timing attack

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; CURVE FITTING; MICROPROCESSOR CHIPS; VIRUSES;

HYPERELLIPTIC CURVE CRYPTOSYSTEMS (HECC); MATHEMATICAL STRUCTURE; SECRET KEY; XEON PROCESSORS;

CRYPTOGRAPHY;

EID: 23944495554     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-31815-6_28     Document Type: Conference Paper

References (32)

1. [AT03] T. Akishita and T. Takagi, "Zero-Value Point Attacks on Elliptic Curve Cryptosystem," ISC 2002, LNCS 2851, Springer-Verlag, pp.218-233, 2003.
2. [Ava03a] R. Avanzi, "Countermeasures against Differential Power Analysis for Hyperelliptic Curve Cryptosystems," CHES 2003, LNCS 2779, Springer-Verlag, pp.366-381, 2003.
3. [Ava03b] R. Avanzi, "Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations", Cryptology ePrint Archive, 2003/253, IACR, 2003.
4. [Can87] D. Cantor, "Computing in the Jacobian of a Hyperelliptic Curve," Mathematics of Computation, 48, 177, pp.95-101, 1987.
5. [CMO98] H. Cohen, A. Miyaji, and T. Ono, "Efficient Elliptic Curve Exponentiation Using Mixed Coordinates," ASIACRYPT'98, LNCS1514, pp.51-65, 1998.
6. [Cor99] J.-S. Coron, "Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems," CHES'99, LNCS 1717, Springer-Verlag, pp.292-302, 1999.
7. +98] J.F. Dhem, F. Koeune, P.A. Leroux, P. Mestré, J.J Quisquater and J.L. Willems, "A Practical Implementation of the Timing Attack," UCL Crypto Group Technical Report CG-1998/1, 1998.
8. [GMP] GMP, GNU MP Library GMP. http://www.swox.com/gmp
9. [Gou03] L. Goubin, "A Refined Power-Analysis Attack on Elliptic Curve Cryptosystem," PKC2003, LNCS 2567, Springer-Verlag, pp. 199-211, 2003.
10. [Har00a] R. Harley, "Adding.text," 2000. http://cristal.inria. fr/~harley/hyper/
11. [Har00b] R. Harley, "Doubling.c," 2000. http://cristal.inria. fr/~harley/hyper/
12. [HSS00] F. Hess, G. Seroussi and N. Smart, "Two Topics in Hyperelliptic Cryptography," CSTR-00-008, Depart. of Computer Science, University of Bristol, 2000.
13. [IT03] T. Izu and T. Takagi, "Exceptional Procedure Attack on Elliptic Curve Cryptosystems," PKC2003, LNCS 2567, Springer-Verlag, pp.224-239, 2003.
14. [JT01] M. Joye and C. Tymen, "Protection against Differential Analysis for Elliptic Curve Cryptography," CHES 2001, LNCS 2162, Springer-Verlag, pp.377-390, 2001.
15. +04] M. Katagi, I. Kitamura, T. Akishita, and T. Takagi, "Novel Efficient Implementations of Hyperelliptic Curve CryptoSystems using Degenerate Divisors," Cryptology ePrint Archive, IACR, 2004. http://eprint.iacr.org/
16. [Kob89] N. Koblitz, "Hyperelliptic Cryptosystems," Journal of Cryptology, Vol.1, Springer-Verlag, pp. 139-150, 1989.
17. [Koc96] C. Kocher, "Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems," CRYPTO'96, LNCS 1109, pp.104-113, 1996.
18. [KJJ99] C. Kocher, J. Jaffe, and B. Jun, "Differential Power Analysis," CRYPTO'99, LNCS 1666, pp.388-397, 1999.
19. +02] J. Kuroki, M. Gonda, K. Matsuo, J. Chao and S. Tsujii, "Fast Genus Three Hyperelliptic Curve Cryptosystems," Proc. of SCIS2002, 2002.
20. [Lan02a] T. Lange, "Efficient Arithmetic on Genus 2 Hyperelliptic Curves over Finite Fields via Explicit Formulae," Cryptology ePrint Archive, 2002/121, IACR, 2002.
21. [Lan02b] T. Lange, "Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves," Cryptology ePrint Archive, 2002/147, IACR, 2002.
22. [Lan02c] T. Lange, "Weighed Coordinate on Genus 2 Hyperellipitc Curve," Cryptology ePrint Archive, 2002/153, IACR, 2002.
23. [Mum84] D. Mumford, Tata Lectures on Theta II, Progress in Mathematics 43, Birkhäuser, 1984.
24. [MCT01] K. Matsuo, J. Chao and S. Tsuji, "Fast Genus Two Hyperelliptic Curve Cryptosystems," Technical Report ISEC2001-31, IEICE Japan, pp.89-96, 2001.
25. [Nag00] N. Nagao, "Improving Group Law Algorithms for Jacobians of Hyperelliptic Curves," ANTS-IV, LNCS 1838, Springer-Verlag, pp.439-448, 2000.
26. [NTL] NTL: A Library for Doing Number Theory, http://www.shoup.net/ntl
27. [Pel02] J. Pelzl, "Hyperelliptic Cryptosystems on Embedded Microprocessors," Diploma Thesis, Rühr-Universität Bochum, 2002.
28. +03] J. Pelzl, T. Wollinger, J. Guajardo and C. Paar, "Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves," CHES 2003, LNCS 2779, Springer-Verlag, pp.351-365, 2003.
29. +02] T. Sugizaki, K. Matsuo, J. Chao, and S. Tsujii, "An Extension of Harley Addition Algorithm for Hyperelliptic Curves over Finite Fields of Characteristic Two," Technical Report ISEC2002-9, IEICE Japan, pp.49-56, 2002.
30. [Sch00] W. Schindler, "A Timing Attack against RSA with the Chinese Remainder Theorem," CHES 2000, LNCS 1965, pp.109-124, 2000.
31. [Sch02] W. Schindler, "A Combined Timing and Power Attack," PKC 2002, LNCS 2274, pp.263-279, 2002.
32. [SKQ01] W. Schindler, F. Koeune, J.-J. Quisquater, "Improving Divide and Conquer Attacks against Cryptosystems by Better Error Detection/Correction Strategies," Cryptography and Coding, 8th IMA Int. Conf., LNCS 2260, pp.245-267, 2001.