Masking is an effective and widely-used countermeasure to thwart Differential Power Analysis (DPA) attacks on symmetric cryptosystems. When a symmetric cipher involves a combination of Boolean and arithmetic operations, it is necessary to convert the masks from one form to the other. There exist algorithms for mask conversion that are secure against first-order attacks, but they can not be generalized to higher orders. At CHES 2014, Coron, Großschädl and Vadnala (CGV) introduced a secure conversion scheme between Boolean and arithmetic masking of any order, but their approach requires d=2t+1 shares to protect against attacks of order t. In the present paper, we improve the algorithms for second-order conversion with the help of lookup tables so that only three shares instead of five are needed, which is the minimal number for second-order resistance. Furthermore, we also improve the first-order secure addition method proposed by Karroumi, Richard and Joye, again with lookup tables. We prove the security of all presented algorithms using well established assumptions and models. Finally, we provide experimental evidence of our improved mask conversion applied to HMAC-SHA-1. Simulation results show that our algorithms improve the execution time by 85% at the expense of little memory overhead.
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