Efficient doubling on genus 3 curves over binary fields

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3960 LNCS, Issue , 2006, Pages 64-81

  Fan, Xinxin ^a   Wollinger, Thomas ^b   Wang, Yumin ^a  

^a XIDIAN UNIVERSITY   (China)

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Binary Fields; Explicit Doubling Formulae; Fast Arithmetic; Genus 3 Hyperelliptic Curve

Indexed keywords

ALGORITHMS; COSTS; INTEGER PROGRAMMING; MATHEMATICAL TRANSFORMATIONS; PROGRAM PROCESSORS; VECTORS; BINS; GEOMETRY;

BINARY FIELDS; EXPLICIT DOUBLING FORMULAE; FAST ARITHMETICS; GENUS 3 HYPERELLIPTIC CURVE;

CRYPTOGRAPHY;

BINARY FIELDS; EXPLICIT DOUBLING FORMULAE; FAST ARITHMETIC; GENUS 3 HYPERELLIPTIC CURVES; HYPERELLIPTIC CURVE CRYPTOSYSTEMS; PENTIUM-M PROCESSORS; SCALAR MULTIPLICATION; TRANSFORMATION OF VARIABLES;

EID: 33745578231     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11605805_5     Document Type: Conference Paper

References (31)

1. [Ava04] R. M. Avarizi. Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations. In M. Joye and J.-J. Quisquater, editors, Workshop on Cryptographic Hardware and Embedded Systems - CUES "2004, volume LNCS 3156, pp. 148-1(12, Springer-Verlag, 2004.
2. [BCLW02] N. Boston, T. Clancy, Y. Liow, and J. Webster. Genus Two Hyperelliptic Curve Coprocessor. In B. S. Kaliski, Ç. K. Koç, and C. Paar, editors, Cryptographic Hardware and Embedded Systems - CUES 2002, volume LNCS 2523, pp. 529 - 539. Springer-Verlag, 2002. Updated version available at http://www.cs.umd.edu/clancy/docs/hec-ches2002.pdf.
3. 2n and optimazation of their arithmetic. Cryptology ePrint Archieve, Report 2004/107, 2004. http://eprint.iacr.org/.
4. [Can87] D.G.Cantor. Computing In The Jacobian Of A Hyperelliptic Curve. Math. Comp. 48:95-101, 1987.
5. +05] H.Cohen, G.Frey, R.Avanzi, C.Doche, T.Lange, K. Nguyen and F.vercauteren. Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman Hall/CRC, 2005.
6. [Cla02] T. Clancy. Analysis of FPGA-bascd Hyperelliptic Curve Cryptosystems. Master's thesis, University of Illinois Urbana-Champnign, December 2002.
7. [EMY04] G. Elias, A. Miri and T.H. Yeap. High-Performance, FPGA-Based Hyperelliptic Curve Cryptosystems. In The Proceeding of the 22nd Biennial Symposium on Communications, May 2004, Queen's University, Kingston, Ontario, Canada.
8. [FWW05] X. Fan, T. Wollinger, and Y. Wang. Inversion-Free Arithmetic on Genus 3 Hyperelliptic Curves and Its Implementations. International Conference on Information Technology: Coding and Computing - ITCC, pp. 642-647, IEEE Computer Society, 2005.
9. [Gal01] S. D. Galbraith. Supersingular Curves in Cryptography. In Advance in Cryptograpy - Asiacrypt 2001, LNCS 2248, Springer-Verlag, pp. 495-513, 2001.
10. [GH00] P. Gaudry and R. Harley. Counting Points on Hyperelliptic Curves over Finite Fields. In ANTS-IV, ser. LNCS 1838, W.Bosma, Ed. Berlin: Springer-Verlag, pp. 297-312, 2000.
11. [GKP04] C. Guyot, K. Kaveh, V.M. Patankar. Explicit Algorithm for The Arithmetic on The Hyperelliptic Jacobians of Genus 3. Journal of Ramanujan Mathematical Society, 19 (2004), No.2, 119-159.
12. [GLS00] C. Günther, T. Lange, and A. Stein. Speeding up the Arithmetic on Koblitz Curves of Genus Two. In Selected Areas in Cryptography - SAC 2000, Volume 2012, Lecture Notes in Computer Science, pp. 106-117, Springer-Verlag, 2000.
13. +04] M. Gonda, K. Matsuo, K. Aoki, J. Chao and S. Tsujii. Improvements Of Addition Algorithm On Genus 3 Hyperelliptic Curves And Their Implementations. In Proc. of SCIS 2004, Japan, 2004.
14. [Kob87] N. Koblitz. Elliptic curve cryptosystems. Mathematics of Computation, 48:203-209, 1987.
15. [Kob88] N. Koblitz. A Family of Jacobians Suitable for Discrete Log Cryptosystems. In Shafi Goldwasser, editor, Advances in Cryptology - Crypto '88, LNCS 403, pp. 94-99, Berlin, 1988. Springer-Verlag.
16. [Kob89] N. Koblitz. Hyperelliptic Cryptosystems. In Ernest F.Brickell, editor, Journal of Cryptology, pp. 139-150, 1989.
17. +04] H. Kim, T. Wollinger, Y. Choi, K. Chung and C. Paar. Hyperelliptic Curve Coprocessors on a FPGA, In Workshop on Information Security Applications - WISA, volume LNCS 3325, pp. 360-374, Springer-Verlag, 2004.
18. [Lan03] T. Lange. Formulae for Arithmetic on Genus 2 Hyperelliptic Curves. Jounal of AAECC, Septemper 2003.
19. [Lan04] T. Lange. Koblitz Curve Cryptosystems. Finite Fields and Their Applications, 2004. to appear.
20. [Loc94] P. Lockhart. On the discriminant of a hyperelliptic curve. In Tran. Amer. Math. Soc. 342, 2, pp. 729-752, 1994.
21. [LS04] T. Lange and M. Stevens. Efficient Doubling on Genus Two Curves over Binary Fields. In H.Handschuh and A.Hasan, editors, Eleventh Annual Workshop on Selected Areas in Cryptography - SAC 2004, volume LNCS 3357, pp. 170-181, Springer-Verlag, 2005.
22. [Mil86] V. Miller. Uses of Elliptic Curves in Cryptography. In H. C. Williams, editor, Advances in Cryptology - CRYPTO '85, LNCS 218, pp. 417-426, Berlin, Germany, Springer-Verlag, 1986.
23. [MWZ96] A. Menezes, Y. Wu and R. Zuccherato. An Elementary Introduction to Hyperelliptic Curve. Technical Report CORR 96-19, University of Waterloo, 1996, Canada. Available at http://www.cacr.math.uwaterloo.ca
24. [Mum84] D. Mumford. Tata Lectures on Thcta II, Progress in Mathematics 43, Birkhäuser, 1984.
25. [Pel02] J. Pelzl. Hyperelliptic Cryptosystemt on Embedded Microprocessor. Master's thesis, Department of Electronical Engineering and Information Sciences, Ruhr-Universitaet Bochum, Bochum, Germany, September 2002.
26. [PWGP03] J. Pelzl, T. Wollinger, J. Guajardo and G. Paar. Hyperelliptic Curve Cryptosystems: Closing The Performance Gap To elliptic Curve (Update), Cryptology ePrint Archieve, Report 2003/026, http://eprint.iacr.org/, 2003
27. [PWP03] J. Pelzl, T. Wollinger, and C. Paar. Low Cost Security: Explicit Formulae for Genus-4 Hyperelliptic Curves. In M. Matsui and R. Zuccherato, editors, Tenth Annual Workshop on Selected Areas in Cryptography - SAC 2003, volume LNCS 3006, pp. 1-16, Springer-Verlag, 2003.
28. [RS02] K. Rubin and A. Silverberg. Supersingular abelian varieties in cryptology. In Advance in cryptology - Crypto'8002, volume 2442 of Lecture Notes in Computer Science, pp. 336-353, Springer-Verlag, 2002.
29. [Thé03] N.Thériault. Index calculus attack fcr hyperelliptic curves of small genus. Advances in Cryptology - ASIACRYPT'03, G.Goos, J.Hartmanis, and J.van Leeuwen, Eds. Berlin: Springer Verlag, 2003, pp. 79 - 92, LNCS 2894.
30. [Wol04] T. Wollinger. Software and Hardware Implementation of Hyperelliptic Curve Cryptosystems. Europäischer Universitätsverlag, 3-86515-025-X, 2004.
31. +03] 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.