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138 Cha pte r F i v e

5.6 Comments and Conclusions
The experimental results confirm the conclusions obtained in Section
5.2.2 with reference to the comparison between MSE- and LSE-first
multipliers, that is, LSE-first multipliers are more complex (area) than
MSE-first multipliers; however, LSE-first multipliers are faster than
MSE-first ones. It can also be noted that the squaring of polynomials
could be performed with the half of multiplications with respect to
the use of normal multipliers.

5.7 References
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Algorithms.” BS Thesis, Worcester Polytechnic Institute, 1998.
[BP01] D.V. Bailey and C. Paar. “Efficient arithmetic in finite field extensions with
application in elliptic curve cryptography.” Journal of Cryptology, vol. 14, no. 3,
pp. 153–176, 2001.
[GG03] J. von zur Gathen and J. Gerhard. Modern Computer Algebra. 2d ed.,
Cambridge University Press, New York, 2003.
[GGK06] J. Guajardo, T. Güneysu, S. Kumar, C. Paar, and J. Pelzl. “Efficient
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Acta Applicandae Mathematicae, Special Issue, Finite Fields: Applications and
Implementations, vol. 93, pp. 75–118, September 2006.
[GKP04] J. Groβschädl, S. Kumar, and C. Paar. “Architectural Support for Arithmetic
in Optimal Extension Fields.” IEEE Conf. on Application-specific Systems,
Architectures and Processors - ASAP 2004, Galveston, Texas, pp. 111–124, 2004.
[Jun93] D. Jungnickel. Finite Fields. B.I.-Wissenschaftsverlag, Mannheim, Leipzig,
Wien, Zürich, 1993.
[Knu81] D. E. Knuth. The Art of Computer Programming, Vol. 2: Seminumerical
Algorithms, vol. 2, 2d ed., Addison-Wesley, MA, 1981.
[LN83] R. Lidl and H. Niederreiter. Finite Fields, vol. 20 of Encyclopedia of Mathematics
and Its Applications. Addison-Wesley, Reading, Massachusetts, 1983.
[MOV96] A. J. Menezes, P. C. van Oorschot, and S. Vanstone. Handbook of Applied
Cryptography. CRC Press, Boca Raton, Florida, 1996.
[MS99] M. Mignotte and D. Stefanescu. Polynomials. An Algorithmic Approach.
Springer, New York, 1999.