Most cryptographic schemes are designed in a model where perfect secrecy of the secret key is assumed. In most physical implementations, however, some form of information leakage is inherent and unavoidable. To deal with this, a flurry of works showed how to construct basic cryptographic primitives that are resilient to various forms of leakage. Dodis et al. (FOCS ’10) formalized and constructed leakage resilient one-way functions. These are one-way functions f such that given a random image f(x) and leakage g(x) it is still hard to invert f(x). Based on any one-way function, Dodis et al. constructed such a one-way function that is leakage resilient assuming that an attacker can leak any lossy function g of the input. In this work we consider the problem of constructing leakage resilient one-way functions that are secure with respect to arbitrary computationally hiding leakage (a.k.a auxiliary-input). We consider both types of leakage — selective and adaptive — and prove various possibility and impossibility results. On the negative side, we show that if the leakage is an adaptivelychosen arbitrary one-way function, then it is impossible to construct leakage resilient one-way functions. The latter is proved both in the random oracle model (without any further assumptions) and in the standard model based on a strong vector-variant of DDH. On the positive side, we observe that when the leakage is chosen ahead of time, there are leakage resilient one-way functions based on a variety of assumption.
CITATION STYLE
Komargodski, I. (2016). Leakage resilient one-way functions: The auxiliary-input setting. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9985 LNCS, pp. 139–158). Springer Verlag. https://doi.org/10.1007/978-3-662-53641-4_6
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