Secure Signed Radix-r Recoding Methods for Constrained-Embedded Devices

摘要

This paper presents two recoding methods for a radix-r representation of a secret scalar which are resistant to SPA. These recoding methods are left-to-right so they can be interleaved with a left-to-right scalar multiplication, removing the need to store both a scalar and its recoding. Next, we show the ideas of left-to-right recoding for a radix-r representation lead to simplified recoding methods for a binary representation. In general our proposed algorithms asymptotically require additional (w + l)-digit and w-bit of RAM in the case of width-w radix-r representation and a special case when r = 2, respectively, which is independent from the digit (bit) size n of the scalar and considerably reduces the required space comparing with previous methods which require n-digit (bit) of RAM additional memory to store the recoded scalar. Consequently, thanks to its left-to-right nature, the scalar multiplication based on it is by far more convenient with respect to memory consumption.