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This paper considers the problem of finding a minimumweighted representation of an integer under any modified radix-r number system. Contrary to existing methods, the proposed transformation is carried out from the left to the right (i.e., from the most significant position). This feature finds numerous applications and especially in fast arithmetic techniques because it reduces both time and space complexities, which is particularly attractive for small devices like smart cards.

New Minimal Modified Radix-r Representation with Applications to Smart Cards