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Published in:
2009 | OriginalPaper | Chapter
Batch Binary Edwards
Author : Daniel J. Bernstein
Published in: Advances in Cryptology - CRYPTO 2009
Publisher: Springer Berlin Heidelberg
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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.