# LOW AREA SCALABLE MONTGOMERY INVERSION OVER GF(2m)

### Mohamed N. Hassan, Mohammed Benaissa

#### 2008

#### Abstract

In this work, an improved algorithm for Montgomery modular inversion over GF(2m) is proposed. Moreover, A novel scalable hardware architecture for the proposed algorithm is presented which is parameterizable and amenable to interfacing to special purpose processors such as microcontrollers. The architecture supports operations over finite fields GF(2m) up to m 571 without the need to reconfigure the hardware. The results show that, this work can be exploited to construct low resource elliptic curve cryptosystems (ECC).

#### References

- D. Hankerson, A. Menezes, and S. Vanstone.” Guide to Elliptic Curve Cryptography.” Springer-Verlag, 2004.
- N. Koblitz, “Introduction to Elliptic Curves and Modular Forms” Graduate Texts in Mathematics, Vol. 97, Springer, 1984.
- P. L. Montgomery. “Modular Multiplication without Trial Division” Mathematics of Computation, vol.44. April 1985.
- B. Kaliski.”The Montgomery inverse and its applications”. IEEE Transactions on Computers, Vol. 44, No.8, August 1995.
- NIST “Recommended elliptic curves for federal government tuse”, Available at http:// csrc.nist.gov/encryption/.2000.
- M. Shieh. J.Chen, And C.Ming “High-Speed Design of Montgomery Inverse Algorithm over GF(2m)” IEICE Trans. Fundamentals, Vol.E89-A, February 2006.
- C. H. Kim, S. Kwon, J.J. Kim, C.P. Hong, “A Compact and Fast Division Architecture for a Finite Field GF(2m)”. ICCSA 2003, LNCS 2667, pp. 855-864, 2003.

#### Paper Citation

#### in Harvard Style

N. Hassan M. and Benaissa M. (2008). **LOW AREA SCALABLE MONTGOMERY INVERSION OVER GF(2m)** . In *Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)* ISBN 978-989-8111-59-3, pages 363-367. DOI: 10.5220/0001923503630367

#### in Bibtex Style

@conference{secrypt08,

author={Mohamed N. Hassan and Mohammed Benaissa},

title={LOW AREA SCALABLE MONTGOMERY INVERSION OVER GF(2m)},

booktitle={Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)},

year={2008},

pages={363-367},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001923503630367},

isbn={978-989-8111-59-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)

TI - LOW AREA SCALABLE MONTGOMERY INVERSION OVER GF(2m)

SN - 978-989-8111-59-3

AU - N. Hassan M.

AU - Benaissa M.

PY - 2008

SP - 363

EP - 367

DO - 10.5220/0001923503630367