SPA Counter-measure Based on Unsigned Left-to-Right Recodings

摘要

Vuillaume-Okeya presented unsigned recoding methods for protecting modular exponentiations against side channel attacks, which are suitable for tamper-resistant implementations of RSA or DSA which does not benefit from cheap inversions. This paper describes new recoding methods for producing SPA-resistant unsigned representations which are scanned from left to right (i.e., from the most significant digit to the least significant digit) contrary to the previous ones. Our contributions are as follows; (1) SPA-resistant unsigned left-to-right recoding with general width-w, (2) special case when w = 1, i.e., unsigned binary representation using the digit set {1,2}. These methods reduce the memory required to perform the modular exponentiation g~k.