We study the problem of secure function evaluation in the so called commodity based cryptography model as proposed by Beaver in his STOC 97 paper. We propose very efficient protocols for implementing addition and multiplication over GF(q). Differently than in previous works, in our protocol each step of the computation is verifiable. Moreover, no copying of commitments is necessary, because commitments are not destroyed during the computation. Also, no error correcting techniques are necessary here yielding simpler protocols. The protocol is based on novel verifiable primitives (one time multiplication proofs, multiplication gates and pre-distributed commitments) in the commodity based model which allow two players to perform secure multiplication of shares over GF(q) with round-complexity equal to one.
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