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Scalar multiplication in elliptic curve cryptography is the most computational intensive operation. Efficiency of this operation can be significantly improved in hardware implementations by using Frobenius endomorphisms which require integer to τ-adic nonadjacent form conversion. Because conversion is one of the limiting factors in some of Koblitz curve-based cryptosystems, it has become an interesting problem. In this paper, we propose two algorithms and a novel hardware architecture to double the speed of integer to τ-adic nonadjacent form conversion.
Date of Publication: May 2012