Fast explicit formulae for genus 2 hyperelliptic curves using projective coordinates

Proceedings - International Conference on Information Technology-New Generations, ITNG 2007

Volumn , Issue , 2007, Pages 893-897

  Wollinger, Thomas ^a   Kovtun, Vladyslav ^b  

^a ESCRYPT GMBH   (Germany)

^b IVAN KOZHEDUB KHARKIV NATIONAL AIR FORCE UNIVERSITY   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

COMMUNICATION SYSTEMS; GRAPH THEORY; JACOBIAN MATRICES;

CRYPTOGRAPHIC SECURITY; HYPERELLIPTIC CURVES;

CRYPTOGRAPHY;

EID: 34548135324     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ITNG.2007.94     Document Type: Conference Paper

References (15)

1. IEEE P1363-2000. Standard Specifications for Public Key Cryptography. Available at: http://www.ieee.org.
2. N. Koblitz Hyperelliptic cryptosystems. Journal of cryptology, No 1, 1989, pp. 139-150.
3. A. M. Spallek, "Kurven vom geschlecht 2 und ihre anwendung in public-key-kryptosystemen", PhD thesis, Universitat Gesamthochschule Essen, 1994.
4. U. Kriger, "Anwendung hyperellipischer kurven in der kryptographie", Master's thesis, Universitat Gesamthochschule, Essen, 2001.
5. R. Harley, "Fast arithmetic on genus 2 curves", available at: http://cristal.infra.fr/~harley/hyper. 2000.
6. T. Wollinger, "Software and hardware implementation of hyperelliptic curve cryptosystems", PhD dissertation. Bochum, Germany, May 2004.
7. Y. Miyamoto, H. Doi, K. Matsuo, J. Chao, S. Tsujii, "A fast addition algorithm of genus two hyperelliptic curve", In the 2002 Symposium on cryptography and information security - SCIS 2002, IEICE Japan, pp. 497-502, 2002. In Japanese.
8. M. Takahashi, "Improving Harley algorithms for Jacobians of genus 2 Hyperelliptic curves", In Proc. of SCIS2002, IEICE Japan, 2002. In Japanese.
9. T. Lange, "Efficient arithmetic on genus 2 hyperelliptic curves over finite fields via explicit formulae", Cryptology ePrint Archive, report 2002/121, 2002. Available http://eprint.iacr.org.
10. H. Suguzaki, K. Matsuo, J. Chao, S. Tsujii, "An extension of Harley algorithm addition algorithm for hyperelliptic curves over finite fields of characteristic two", Technical report ISEC2002-9, IEICE Japan, 2002. pp. 49-56.
11. D. Hankerson, J. Lopez Hernandez, A. Menezes, "Software implementation of elliptic curve cryptography over binary fields", Cryptographic Hardware and Embedded Systems, CHES'2000, Springer-Verlag, LNCS 1965, 2001, pp 1-24.
12. T. Lange, "Inversion-free arithmetic on genus 2 hyperelliptic curves", Cryptology ePrint Archive, report 2002/147, 2002. Available http://eprint.iacr.org.
13. T. Lange, "Weighted coordinates on genus 2 hyperelliptic curves", Cryptology ePrint Archive, Report 2002/153, 2002. Available http://eprint.iacr.org.
14. 2 and optimization of their arithmetic", Cryptology ePrint Archive, Report 2004/107, 2002. Available http://eprint.iacr.org.
15. T. Lange, M. Stevens, "Efficient Doubling on Genus Two Curves over Binary Fields", Selected Areas in Cryptography, Springer-Verlag, LNCS 3357, 2004, pp. 170-181.