Unifying Leakage Models: From Probing Attacks to Noisy Leakage

A recent trend in cryptography is to formally show the leakage resilience of cryptographic implementations in a given leakage model. One of the most prominent leakage models -- the so-called bounded leakage model -- assumes that the amount of leakage is a-priori bounded. Unfortunately, it has been pointed out that the assumption of bounded leakages is hard to verify in practice. A more realistic assumption is to assume that leakages are sufficiently noisy, following the engineering observation that real-world physical leakages are inherently noisy. While the noisy leakage assumption has first been studied in the seminal work of Chari et al. (CRYPTO 99), the recent work of Prouff and Rivain (Eurocrypt 2013) provides the first analysis of a full masking scheme under a physically motivated noise model. In particular, the authors show that a block-cipher implementation that uses an additive masking scheme is secure against noisy leakages. Unfortunately, the security analysis of Prouff and Rivain has three important shortcomings: (1) it requires leak-free gates, (2) it considers a restricted adversarial model (random message attacks), and (3) the security proof has limited application for cryptographic settings. In this work, we provide an alternative security proof in the same noisy model that overcomes these three challenges. We achieve this goal by a new reduction from noisy leakage to the important theoretical model of probing adversaries (Ishai et al~ -- CRYPTO 2003). Our work can be viewed as a next step of closing the gap between theory and practice in leakage resilient cryptography: while our security proofs heavily rely on concepts of theoretical cryptography, we solve problems in practically motivated leakage models.