[Resource Topic] 2022/921: Low-Delay 4, 5 and 6-Term Karatsuba Formulae in $\mathbb{F}_2[x]$ Using Overlap-free Splitting

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Title:
Low-Delay 4, 5 and 6-Term Karatsuba Formulae in \mathbb{F}_2[x] Using Overlap-free Splitting

Authors: Haining Fan

Abstract:

The overlap-free splitting method, i.e., even-odd splitting and its generalization, can reduce the XOR delay of a Karatsuba multiplier. We use this method to derive Karatsuba formulae with one less XOR delay in each recursive iteration. These formulae need more multiplication operations, and are trade-offs between space and time. We also show that finding common subexpressions'' performs better than the refined identity’’ in 4-term formula: we reduce the number of XOR gates given by Cenk, Hasan and Negre in IEEE T. Computers in 2014.

ePrint: https://eprint.iacr.org/2022/921

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