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Highly regular $$m$$-ary powering ladders. (English) Zbl 1267.94071
Jacobson, Michael J. jun. (ed.) et al., Selected areas in cryptography. 16th annual international workshop, SAC 2009, Calgary, Alberta, Canada, August 13–14, 2009. Revised selected papers. Berlin: Springer (ISBN 978-3-642-05443-3/pbk). Lecture Notes in Computer Science 5867, 350-363 (2009).
Summary: This paper describes new exponentiation algorithms with applications to cryptography. The proposed algorithms can be seen as $$m$$-ary generalizations of the so-called Montgomery ladder. Both left-to-right and right-to-left versions are presented.
Similarly to Montgomery ladder, the proposed algorithms always repeat the same instructions in the same order, without inserting dummy operations, and so offer a natural protection against certain implementation attacks. Moreover, as they are available in any radix $$m$$ and in any scan direction, the proposed algorithms offer improved performance and greater flexibility.
For the entire collection see [Zbl 1177.94012].

##### MSC:
 94A60 Cryptography 11Y16 Number-theoretic algorithms; complexity
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