Simultaneous scalar multiplication method

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...

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Bibliographic Details
Main Authors ANTIPA, ADRIAN, POELUEV, YURI
Format Patent
LanguageEnglish
French
German
Published 18.06.2014
Subjects
CALCULATING
COMPUTING
COUNTING
ELECTRIC COMMUNICATION TECHNIQUE
ELECTRIC DIGITAL DATA PROCESSING
ELECTRICITY
PHYSICS
TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHICCOMMUNICATION
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Summary: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.
Bibliography:Application Number: EP20120172540