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- W2034170947 abstract "At Crypto 2009, Bernstein (LNCS, vol 5677. Springer, Berlin, pp 317–336, 2009) proposed two optimized Karatsuba formulas for binary polynomial multiplication. Bernstein obtained these optimizations by re-expressing the reconstruction of one or two recursions of the Karatsuba formula. In this paper we present a generalization of these optimizations. Specifically, we optimize the reconstruction of $$s$$ recursions of the Karatsuba formula for $$s ge 1$$ . To reach this goal, we express the recursive reconstruction through a tree and reorganize this tree to derive an optimized recursive reconstruction of depth $$s$$ . When we apply this approach to a recursion of depth $$s=log _2(n)-2$$ we obtain a parallel multiplier with a space complexity of $$3.75 n^{log _2(3)}+O(n)$$ XOR gates and $$1.78 n^{log _2(3)}$$ AND gates and with a delay of $$(2log _2(n)-1) D_oplus +D_otimes $$ where $$D_oplus $$ represents the delay of an XOR gate and $$D_otimes $$ the delay of an AND gate." @default.
- W2034170947 created "2016-06-24" @default.
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- W2034170947 date "2014-01-07" @default.
- W2034170947 modified "2023-10-18" @default.
- W2034170947 title "Efficient binary polynomial multiplication based on optimized Karatsuba reconstruction" @default.
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- W2034170947 doi "https://doi.org/10.1007/s13389-013-0066-2" @default.
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