A METHOD FOR FLEXIBLE REDUCTION OVER BINARY FIELDS USING A FIELD MULTIPLIER

Saptarsi Das, Keshavan Varadarajan, Ganesh Garga, Rajdeep Mondal, Ranjani Narayan, S. K. Nandy

Abstract

Flexibility in implementation of the underlying field algebra kernels often dictates the life-span of an Elliptic Curve Cryptography solution. The systems/methods designed to realize binary field arithmetic operations can be tuned either for performance or for flexibility. Usually flexibility of these solutions adversely affects their performance. For solutions to reduction operation this adverse effect is particularly prominent. Therefore it is a non-trivial task to design a flexible reduction method/system without compromising performance. In this paper we present a method for flexible reduction. The proposed reduction technique is based on the well-known repeated multiplication technique and Barrett reduction. This technique is particularly appealing in the context of coarse-grain programmable architectures where performance of any kernel is heavily influenced by granularity of operations. In this context we propose a design of a polynomial multiplier based on the well-known Interleaved Galois Field multiplier to accelerate the underlying multi-word polynomial multiplications. We show that this modified IGF multiplier offers a significant improvement in throughput over a purely software realization or a hybrid software-hardware implementation using a conventional polynomial multiplier.

References

  1. Barrett, P. (1987). Implementing the rivest shamir and adleman public key encryption algorithm on a standard digital signal processor. In Odlyzko, A., editor, Advances in Cryptology CRYPTO 86, volume 263 of Lecture Notes in Computer Science, pages 311-323. Springer Berlin / Heidelberg. 10.1007/3-540-47721- 7 24.
  2. Eberle, H., Gura, N., Shantz, S. C., and Gupta, V. (2003). A cryptographic processor for arbitrary elliptic curves over GF(2m). Technical report, Mountain View, CA, USA.
  3. Hinkelmann, H., Zipf, P., Li, J., Liu, G., and Glesner, M. (2009). On the design of reconfigurable multipliers for integer and galois field multiplication. Microprocessors and Microsystems - Embedded Hardware Design, 33(1):2-12.
  4. Karatsuba, A. and Ofman, Y. (1963). multidigit numbers on automata. Doklady, 7(7):595-596.
  5. Knezevic, M., Sakiyama, K., Fan, J., and Verbauwhede, I. (2008). Modular reduction in GF(2n) without precomputational phase. In von zur Gathen, J., Iman˜a, J. L., and C¸ etin Kaya Koc¸, editors, WAIFI, volume 5130 of Lecture Notes in Computer Science, pages 77-87. Springer.
  6. Peter, S., Langendörfer, P., and Piotrowski, K. (2007). Flexible hardware reduction for elliptic curve cryptography in GF(2m ). In Lauwereins, R. and Madsen, J., editors, DATE, pages 1259-1264. ACM.
  7. Saqib, N. A., Rodriguez-Henriquez, F., and Diaz-Pirez, A. (2004). A parallel architecture for fast computation of elliptic curve scalar multiplication over GF(2m). Parallel and Distributed Processing Symposium, International, 4:144a.
  8. Satoh, A. and Takano, K. (2003). A scalable dual-field elliptic curve cryptographic processor. IEEE Transactions on Computers, 52:449-460.
Download


Paper Citation


in Harvard Style

Das S., Varadarajan K., Garga G., Mondal R., Narayan R. and Nandy S. (2011). A METHOD FOR FLEXIBLE REDUCTION OVER BINARY FIELDS USING A FIELD MULTIPLIER . In Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2011) ISBN 978-989-8425-71-3, pages 50-58. DOI: 10.5220/0003447500500058


in Bibtex Style

@conference{secrypt11,
author={Saptarsi Das and Keshavan Varadarajan and Ganesh Garga and Rajdeep Mondal and Ranjani Narayan and S. K. Nandy},
title={A METHOD FOR FLEXIBLE REDUCTION OVER BINARY FIELDS USING A FIELD MULTIPLIER},
booktitle={Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2011)},
year={2011},
pages={50-58},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003447500500058},
isbn={978-989-8425-71-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2011)
TI - A METHOD FOR FLEXIBLE REDUCTION OVER BINARY FIELDS USING A FIELD MULTIPLIER
SN - 978-989-8425-71-3
AU - Das S.
AU - Varadarajan K.
AU - Garga G.
AU - Mondal R.
AU - Narayan R.
AU - Nandy S.
PY - 2011
SP - 50
EP - 58
DO - 10.5220/0003447500500058