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Batch binary Edwards
 In Crypto 2009, volume 5677 of LNCS
, 2009
"... Abstract. This paper sets new software speed records for highsecurity DiffieHellman computations, specifically 251bit ellipticcurve variablebasepoint scalar multiplication. In one second of computation on a $200 Core 2 Quad Q6600 CPU, this paper’s software performs 30000 251bit scalar multipli ..."
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Cited by 17 (7 self)
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Abstract. This paper sets new software speed records for highsecurity DiffieHellman computations, specifically 251bit ellipticcurve variablebasepoint scalar multiplication. In one second of computation on a $200 Core 2 Quad Q6600 CPU, this paper’s software performs 30000 251bit scalar multiplications on the binary Edwards curve d(x + x 2 + y + y 2) = (x + x 2)(y + y 2) over the field F2[t]/(t 251 + t 7 + t 4 + t 2 + 1) where d = t 57 + t 54 + t 44 + 1. The paper’s fieldarithmetic techniques can be applied in much more generality but have a particularly efficient interaction with the completeness of addition formulas for binary Edwards curves. Keywords. Scalar multiplication, Diffie–Hellman, batch throughput, vectorization, Karatsuba, Toom, elliptic curves, binary Edwards curves, differential addition, complete addition formulas 1
Edwards curves and CM curves
, 2009
"... Edwards curves are a particular form of elliptic curves that admit a fast, unified and complete addition law. Relations between Edwards curves and Montgomery curves have already been described. Our work takes the view of parameterizing elliptic curves given by their jinvariant, a problematic that a ..."
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Cited by 3 (1 self)
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Edwards curves are a particular form of elliptic curves that admit a fast, unified and complete addition law. Relations between Edwards curves and Montgomery curves have already been described. Our work takes the view of parameterizing elliptic curves given by their jinvariant, a problematic that arises from using curves with complex multiplication, for instance. We add to the catalogue the links with Kubert parameterizations of X0(2) and X0(4). We classify CM curves that admit an Edwards or Montgomery form over a finite field, and justify the use of isogenous curves when needed. 1