Paper 2013/001 Original: eprint.iacr.org/2013/001 ↗

Shielding circuits with groups

Abstract

We show how to efficiently compile any given circuit C into a leakage-resilient circuit C' such that any function on the wires of C' that leaks information during a computation C'(x) yields advantage in computing the product of |C'|^{Omega(1)} elements of the alternating group A_u. Our construction resists NC^1 leakage assuming L \neq NC^1, as was conjectured here and proven later [Miles, ITCS '14]. Also, in combination with new compression bounds for A_u products obtained here, C' withstands leakage from virtually any class of functions against which average-case lower bounds are known. This includes communication protocols, and AC^0 circuits augmented with few arbitrary symmetric gates. In addition, we extend the construction to the multi-query setting by relying on a simple secure hardware component. We build on Barrington's theorem [JCSS '89] and on the previous leakage-resilient constructions by Ishai et al. [Crypto '03] and Faust et al. [Eurocrypt '10]. Our construction exploits properties of A_u beyond what is sufficient for Barrington's theorem.