**Leakage Resilient One-Way Functions: The Auxiliary-Input Setting**

*Ilan Komargodski*

**Abstract: **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 adaptively-chosen 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.

**Category / Keywords: **foundations / leakage resilience, one-way function, auxiliary input

**Date: **received 18 Aug 2016

**Contact author: **ilan komargodski at weizmann ac il

**Available format(s): **PDF | BibTeX Citation

**Version: **20160820:165510 (All versions of this report)

**Short URL: **ia.cr/2016/791

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