Cryptography – Particular algorithmic function encoding
Reexamination Certificate
2006-11-03
2011-10-25
Reza, Mohammad W (Department: 2436)
Cryptography
Particular algorithmic function encoding
C380S043000, C380S045000, C380S259000, C380S268000, C380S280000, C713S170000
Reexamination Certificate
active
08045705
ABSTRACT:
In computing point multiples in elliptic curve schemes (e.g. kP and sQ) separately using, for example, Montgomery's method for the purpose of combining kP+sQ several operations are repeated in computing kP and sQ individually, that could be executed at the same time. A simultaneous scalar multiplication method is provided that reduces the overall number of doubling and addition operations thereby providing an efficient method for multiple scalar multiplication. The elements in the pairs for P and Q method are combined into a single pair, and the bits in k and s are evaluated at each step as bit pairs. When the bits in k and s are equal, only one doubling operation and one addition operation are needed to compute the current pair, and when the bits in k and s are not equal, only one doubling operation is needed and two addition operations.
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Antipa Adrian
Poeluev Yuri
Bhole Anil
Blake Cassels & Graydon LLP
Certicom Corp.
Orange John R. S.
Reza Mohammad W
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