Abstract. In this note, we report on the first large-scale and practical application of multiparty computation, which took place in January 2008. We also report on the novel cryptographic protocols that were used.
Abstract. We propose an asynchronous protocol for general multiparty computation. The protocol has perfect security and communication complexity O(n 2 |C|k), where n is the number of parties, |C| is the size of the arithmetic circuit being computed, and k is the size of elements in the underlying field. The protocol guarantees termination if the adversary allows a preprocessing phase to terminate, in which no information is released. The communication complexity of this protocol is the same as that of a passively secure solution up to a constant factor. It is secure against an adaptive and active adversary corrupting less than n/3 players. We also present a software framework for implementation of asynchronous protocols called VIFF (Virtual Ideal Functionality Framework), which allows automatic parallelization of primitive operations such as secure multiplications, without having to resort to complicated multithreading. Benchmarking of a VIFF implementation of our protocol confirms that it is applicable to practical non-trivial secure computations.
Abstract. We study the following two related questions:-What are the minimal computational resources required for general secure multiparty computation in the presence of an honest majority? -What are the minimal resources required for two-party primitives such as zero-knowledge proofs and general secure two-party computation? We obtain a nearly tight answer to the first question by presenting a perfectly secure protocol which allows n players to evaluate an arithmetic circuit of size s by performing a total of O(s log s log 2 n) arithmetic operations, plus an additive term which depends (polynomially) on n and the circuit depth, but only logarithmically on s. Thus, for typical largescale computations whose circuit width is much bigger than their depth and the number of players, the amortized overhead is just polylogarithmic in n and s. The protocol provides perfect security with guaranteed output delivery in the presence of an active, adaptive adversary corrupting a (1/3 − ε) fraction of the players, for an arbitrary constant ε > 0 and sufficiently large n. The best previous protocols in this setting could only offer computational security with a computational overhead of poly(k, log n, log s), where k is a computational security parameter, or perfect security with a computational overhead of O(n log n).We then apply the above result towards making progress on the second question. Concretely, under standard cryptographic assumptions, we obtain zero-knowledge proofs for circuit satisfiability with 2 −k soundness error in which the amortized computational overhead per gate is only polylogarithmic in k, improving over the ω(k) overhead of the best previous protocols. Under stronger cryptographic assumptions, we obtain similar results for general secure two-party computation.
We present the first general protocol for secure multiparty computation in which the total amount of work required by n players to compute a function f grows only polylogarithmically with n (ignoring an additive term that depends on n but not on the complexity of f). Moreover, the protocol is also nearly optimal in terms of resilience, providing computational security against an active, adaptive adversary corrupting a (1/2 −) fraction of the players, for an arbitrary > 0.
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