CALCULATION OF GF (P) ELLIPTIC CURVES IN FPGA

Authors

  • Marek Aleksander
  • Mykola Karpinskyy
  • Grzegorz Litawa

DOI:

https://doi.org/10.47839/ijc.10.2.739

Keywords:

Elliptic curve, rho-Pollard, Rademacher-Krestenson’s bases, FPGA, GF(p), ECDLP.

Abstract

The paper describes a hardware system carrying out point summation on elliptic curves. The implementation of basic function, which is modulo multiplication of huge integrals, is based on Krestenson’s basis. Such a summing unit has been used for hardware implementation of Pollard rho-algorithm. The paper also presents the performance of the mentioned unit.

References

Majkowski P., Wojciechowski T., Wojdynski M., Rawski M. Implementation of module for cryptanalysis of elliptic curve ciphers in reprogrammable structures. Measurements, Automation and Monitoring, (53) 7 (2007). pp. 24-26. (in Polish)

Blade I., Seroussi G., Smart N. Elliptic curves in cryptography. TAO, Warsaw, 2004. (in Polish)

Fichtenholz G.M. Differential and integral calculation. Vol. 2, Polish Scientific Publishers PWN, Warsaw 2011. – 696 p. (in Polish)

Chocianowicz W.: Cryptology and advanced methods of cryptography (http://uznam.net.pl/~blondasek/iuz/materialy/Krypto-2007-2008-2MUDZ.pdf) (in Polish)

IEEE PI363. Standard Specyfications for Public Key, Cryptography. Draft 13. 1999.

Hankerson D., Menezes A., Vanstone S. Guide to elliptic curve cryptography. Springer, NY 2004. – 332 p. (http://math.boisestate.edu/~liljanab/Crypto2 Spring10/GuideToECC.pdf)

Bulens P., Meurice G., Quisquater J.-J. Collision Search for Elliptic Curve Discrete Logarithm over GF(2m) with FPGA, 2007 (http://www.springerlink.com/content/p274683181434n28/)

Yakymenko I., Kasyanchuk M., Nykolajchuk Y. Matrix algorithms of processing of the information flow in computer systems based on theoretical and numerical Krestenson’s basis, TCSET’2010, February 23-27, 2010, Lviv-Slavske, Ukraine. – P. 241.

Маkоhа А.Н., Zuj B.U. Arithmetic of very large integers in parallel computer systems, 20.03.2007 (http://revolution.allbest.ru/mathematics/00011260_0.html) (in Russian)

Downloads

Published

2011-12-20

How to Cite

Aleksander, M., Karpinskyy, M., & Litawa, G. (2011). CALCULATION OF GF (P) ELLIPTIC CURVES IN FPGA. International Journal of Computing, 10(2), 91-96. https://doi.org/10.47839/ijc.10.2.739

Issue

2011, Volume 10, Issue 2

Section

Articles

License

International Journal of Computing is an open access journal. Authors who publish with this journal agree to the following terms:
•    Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
•    Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
•    Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.