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This paper presents a provably secure, higher-order, and leakage-resilient (LR) rekeying scheme named LR Rekeying with Random oracle Repetition (LR4), along with a quantitative security evaluation methodology. Many existing LR primitives are based on a concept of leveled implementation, which still essentially require a leak-free sanctuary (i.e., differential power analysis (DPA)-resistant component(s)) for some parts. In addition, although several LR pseudorandom functions (PRFs) based on only bounded DPA-resistant components have been developed, their validity and effectiveness for rekeying usage still need to be determined. In contrast, LR4 is formally proven under a leakage model that captures the practical goal of side-channel attack (SCA) protection (e.g., masking with a practical order) and assumes no unbounded DPA-resistant sanctuary. This proof suggests that LR4 resists exponential invocations (up to the birthday bound of key size) without using any unbounded leak-free component, which is the first of its kind. Moreover, we present a quantitative SCA success rate evaluation methodology for LR4 that combines the bounded leakage models for LR cryptography and a state-of-the-art information-theoretical SCA evaluation method. We validate its soundness and effectiveness as a DPA countermeasure through a numerical evaluation; that is, the number of secure calls of a symmetric primitive increases exponentially by increasing a security parameter under practical conditions. |
