• Journal of the Korea Institute of Information Security & Cryptology
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• v.18 no.2
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• pp.3-10
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• 2008

The choice of basis for representation of element in $GF(2^m)$ affects the efficiency of a multiplier. Among them, a multiplier using redundant representation efficiently supports trade-off between the area complexity and the time complexity since it can quickly carry out modular reduction. So time of a previous multiplier using redundant representation is faster than time of multiplier using others basis. But, the weakness of one has a upper space complexity compared to multiplier using others basis. In this paper, we propose a new efficient multiplier with consideration that polynomial exponentiation operations are frequently used in cryptographic hardwares. The proposed multiplier is suitable fer left-to-right exponentiation environment and provides efficiency between time and area complexity. And so, it has both time delay of $T_A+({\lceil}{\log}_2m{\rceil})T_x$ and area complexity of (2m-1)(m+s). As a result, the proposed multiplier reduces $2(ms+s^2)$ compared to the previous multiplier using equally-spaced polynomials in area complexity. In addition, it reduces $T_A+({\lceil}{\log}_2m+s{\rceil})T_x$ to $T_A+({\lceil}{\log}_2m{\rceil})T_x$ in the time complexity.($T_A$:Time delay of one AND gate, $T_x$:Time delay of one XOR gate, m:Degree of equally spaced irreducible polynomial, s:spacing factor)