Shielding circuits with groups

We show how to efficiently compile any given circuit C into a leakage-resistant 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'|Ω(1) elements of the alternating group Au. In combination with new compression bounds for Au products, also obtained here, C' withstands leakage from virtually any class of functions against which average-case lower bounds are known. This includes communication protocols, and AC0 circuits augmented with few arbitrary symmetric gates. If NC1 ' TC0 then then the construction resists TC0 leakage as well. We also conjecture that our construction resists NC1 leakage. 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-resistant constructions by Ishai et al. [Crypto '03] and Faust et al. [Eurocrypt '10]. Our construction exploits properties of Au beyond what is sufficient for Barrington's theorem.

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