Secure Conversion between Boolean and Arithmetic Masking of Any Order

Abstract

An effective countermeasure against side-channel attacks is to mask all sensitive intermediate variables with one (or more) random value(s). When a cryptographic algorithm involves both arithmetic and Boolean operations, it is necessary to convert from arithmetic masking to Boolean masking and vice versa. At CHES 2001, Goubin introduced two algorithms for secure conversion between arithmetic and Boolean masks, but his approach can only be applied to first-order masking. In this paper, we present and evaluate new conversion algorithms that are secure against attacks of any order. To convert masks of a size of k bits securely against attacks of order n, the proposed algorithms have a time complexity of O(n 2 k) in both directions and are proven to be secure in the Ishai, Sahai, and Wagner (ISW) framework for private circuits. We evaluate our algorithms using HMAC-SHA-1 as example and report the execution times we achieved on a 32-bit AVR microcontroller.

Faster Mask Conversion with Lookup Tables

“…We used three different word sizes (namely = 1, 2, 4) for the second-order conversion algorithm and a word size of = 4 for first-order masked addition 7 . In order to compare our results with that of existing techniques, we also implemented the Coron-Großschädl-Vadnala (CGV) method [3] for second-order conversion and the Karroumi-Richard-Joye (KRJ) method [7] for first-order secure addition. As expected, the improvement in case of the second-order conversion algorithms is significant due to the reduction of the number of shares from five to three.…”

“…However, almost all secure conversion techniques reported in the literature are only applicable to first-order masking [4][5][6][7]10]. Among the few exceptions is the second-order conversion scheme due to Vadnala and Großschädl [13] and the recent higher-order conversion scheme by Coron, Großschädl and Vadnala [3]. We outline both schemes below.…”

“…Coron-Großschädl-Vadnala Scheme [3]. Recently, Coron, Großschädl and Vadnala proposed conversion algorithms that are secure against attacks of any order [3].…”

“…Recently, Coron, Großschädl and Vadnala proposed conversion algorithms that are secure against attacks of any order [3]. They first proposed a secure solution to add Boolean shares directly by generalizing Goubin's recursion formula [6].…”

“…The generic solution of Coron, Großschädl and Vadnala [3] requires five shares to protect against second-order attacks, which entails a significant overhead in terms of the required amount of random numbers and execution time. Although the algorithms proposed by Vadnala and Großschädl [13] require only three shares to achieve second-order resistance, they become infeasible for implementation on low-resource devices (e.g.…”