TCC 2016: Theory of Cryptography pp 139-158

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

Conference paper

DOI: 10.1007/978-3-662-53641-4_6

Volume 9985 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Komargodski I. (2016) Leakage Resilient One-Way Functions: The Auxiliary-Input Setting. In: Hirt M., Smith A. (eds) Theory of Cryptography. TCC 2016. Lecture Notes in Computer Science, vol 9985. Springer, Berlin, Heidelberg

## 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.

## Copyright information

© International Association for Cryptologic Research 2016

## Authors and Affiliations

1. 1.Weizmann Institute of ScienceRehovotIsrael