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International Association for Cryptologic Research (IACR)
Abstract
In this paper, we propose a new type of non-recursive Mastrovito multiplier for GF(2m) using a n-term Karatsuba algorithm (KA), where GF(2m) is defined by an irreducible trinomial, xm+xk+1,m=nk. We show that such a type of trinomial combined with the n-term KA can fully exploit the spatial correlation of entries in related Mastrovito product matrices and lead to a low complexity architecture. The optimal parameter n is further studied.
As the main contribution of this study, the lower bound of the space complexity of our proposal is about O(2m2​+m3/2). Meanwhile, the time complexity matches the best Karatsuba multiplier known to date. To the best of our knowledge, it is the first time that Karatsuba-based multiplier has reached such a space complexity bound while maintaining relatively low time delay
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