Rate-1, Linear Time and Additively Homomorphic UC Commitments.

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.