Security of weak secrets based cryptographic primitives via the Rényi entropy

Abstract

In ideality, cryptographic primitives take for granted that the secret sources are derived from uniform distribution. However, in reality, we may only obtain some ‘weak’ random sources guaranteed with high unpredictability (e.g. biometric data, physical sources, and secrets with partial leakage). Formally, the security of cryptographic primitives is measured by the expectation of some function, called ‘perfect’ expectation in the ideal model and ‘weak’ expectation in the real model. The authors propose some elementary inequalities which show that the ‘weak’ expectation is not much worse than the ‘perfect’ expectation. The authors present how to overcome weak expectations dependent on the Renyi entropy other than the min and collision entropies by Dodis and Yu [TCC 2013]. The authors achieve these results by capturing on two approaches: one is by observing a new relationship between the collision entropy and other Renyi entropy, the other is by developing the connection between different moments of a variable. Furthermore, pseudorandom generator, and pairwise independent hash function family, the authors extend key derivation functions based on the Renyi entropy. The results are applied to all unpredictability applications and ‘square-friendly’ indistinguishability applications including CPA-secure symmetric-key encryption schemes.