Efficient software implementation of binary field arithmetic using vector instruction sets
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This paper sets new software speed records for high-security Diffie-Hellman computations, specifically 251-bit elliptic-curve variable-base-point scalar multiplication. In one second of computation on a $200 Core 2 Quad Q6600 CPU, this paper's software performs 30000 251-bit scalar multiplications on the binary Edwards curve d(x + x 2 + y + y 2) = (x + x 2)(y + y 2) over the field ${\bf F}_2[t]/(t^{251}+t^7+t^4+t^2+1)$ where d = t 57 + t 54 + t 44 + 1. The paper's field-arithmetic techniques can be applied in much more generality but have a particularly efficient interaction with the completeness of addition formulas for binary Edwards curves.