Finite field arithmetic for cryptography
IEEE Circuits and Systems Magazine
Atomicity improvement for elliptic curve scalar multiplication
CARDIS'10 Proceedings of the 9th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Application
Memory-efficient fault countermeasures
CARDIS'11 Proceedings of the 10th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Applications
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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.