Secure Arithmetic Computation with Constant Computational Overhead

We study the complexity of securely evaluating an arithmetic circuit over a finite field \(\mathbb {F}\) in the setting of secure two-party computation with semi-honest adversaries. In all existing protocols, the number of arithmetic operations per multiplication gate grows either linearly with \(\log |\mathbb {F}|\) or polylogarithmically with the security parameter. We present the first protocol that only makes a constant (amortized) number of field operations per gate. The protocol uses the underlying field \(\mathbb {F}\) as a black box, and its security is based on arithmetic analogues of well-studied cryptographic assumptions.

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