Rate-1, linear time and additively homomorphic UC commitments

Abstract

We construct the first UC commitment scheme for binary strings with the optimal properties of rate approaching 1 and linear time complexity (in the amortised sense, using a small number of seed OTs). On top of this, the scheme is additively homomorphic, which allows for applications to maliciously secure 2-party computation. As tools for obtaining this, we make three contributions of independent interest: we construct the first (binary) linear time encodable codes with non-trivial distance and rate approaching 1, we construct the first almost universal hash function with small seed that can be computed in linear time, and we introduce a new primitive called interactive proximity testing that can be used to verify whether a string is close to a given linear code.