Black-Box, Round-Efficient Secure Computation via Non-malleability Amplification

We present round-efficient protocols for secure multi-party computation with a dishonest majority that rely on black-box access to the underlying primitives. Our main contributions are as follows: * a O(log^∗ n)-round protocol that relies on black-box access to dense cryptosystems, homomorphic encryption schemes, or lossy encryption schemes. This improves upon the recent O(1)^{log∗ n} -round protocol of Lin, Pass and Venkitasubramaniam (STOC 2009) that relies on non-black-box access to a smaller class of primitives. * a O(1)-round protocol requiring in addition, black-box access to a one-way function with sub-exponential hardness, improving upon the recent work of Pass and Wee (Euro crypt 2010). These are the first black-box constructions for secure computation with sub linear round complexity. Our constructions build on and improve upon the work of Lin and Pass (STOC 2009) on non-malleability amplification, as well as that of Ishai et al. (STOC 2006) on black-box secure computation. In addition to the results on secure computation, we also obtain a simple construction of a O(log^∗ n)-round non-malleable commitment scheme based on one-way functions, improving upon the recent O(1)^{log∗ n}-round protocol of Lin and Pass (STOC 2009). Our construction uses a novel transformation for handling arbitrary man-in-the-middle scheduling strategies which improves upon a previous construction of Barak (FOCS 2002).