Inner Product Masking for Bitslice Ciphers and Security Order Amplification for Linear Leakages

Designers of masking schemes are usually torn between the contradicting goals of maximizing the security gains while minimizing the performance overheads. Boolean masking is one extreme example of this tradeoff: its algebraic structure is as simple as can be (and so are its implementations), but it typically suffers more from implementation weaknesses. For example knowing one bit of each share is enough to know one bit of secret in this case. Inner product masking lies at the other side of this tradeoff: its algebraic structure is more involved, making it more expensive to implement (especially at higher orders), but it ensures stronger security guarantees. For example, knowing one bit of each share is not enough to know one bit of secret in this case. In this paper, we try to combine the best of these two worlds, and propose a new masking scheme mixing a single Boolean matrix product (to improve the algebraic complexity of the scheme) with standard additive Boolean masking (to allow efficient higher-order implementations). We show that such a masking is well suited for application to bitslice ciphers. We also conduct a comprehensive security analysis of the proposed scheme. For this purpose, we give a security proof in the probing model, and carry out an information leakage evaluation of an idealized implementation. For certain leakage functions, the latter exhibits surprising observations, namely information leakages in higher statistical moments than guaranteed by the proof in the probing model, which we can connect to the recent literature on low entropy masking schemes. We conclude the paper with a performance evaluation, which confirms that both for security and performance reasons, our new masking scheme (which can be viewed as a variation of inner product masking) compares favorably to state-of-the-art masking schemes for bitslice ciphers.