http://ieeexplore.ieee.org TOC Alert for Publication# 4149673 2009 June 19 k), where P = 2^m 2 - 1 and GF(2^k) is generated by an irreducible all one polynomial. The proposed unified dual-field multiplier uses the LSB-first bit-serial architecture for multiplication in GF(P) and GF(2^k) other than the Montgomery multiplication algorithm, which has been employed by most existing dual-field multipliers. The proposed unified dual-field multiplier costs little space and time complexities. The new multiplier is scalable for operands of any size while other existing dual-field multipliers are only scalable for operands with multiples of m. Furthermore, the proposed multiplier has simplicity, regularity, modularity and concurrency and is very suitable to be implement in VLSI.]]> 3 2 45 52 176 3 2 53 59 177 n) multipliers has been proposed recently. The corresponding algorithm for software implementations is developed. While its recursive implementation is as simple as that of the Karatsuba algorithm, it requires much less memory to store the look-up table. Therefore it is quite suitable for memory-constrained applications, for example smart cards.]]> 3 2 60 65 154 2224), is much less than the complexity of exhaustive search attack on the internal state, O(²³⁸⁴), but larger than the claimed security level, that is O(2128).]]> 3 2 66 73 228