A quantum XOR oblivious transfer protocol compatible with classical partially homomorphic encryption

XOR oblivious transfer (XOT) is a classical cryptographic primitive which is apparently weaker than 1-out-of-2 oblivious transfer, yet still universal for secure two-party computation. In ideal XOT, Bob initially has two bits, and Alice may choose to obtain either the first bit of Bob's, or the second bit, or their exclusive-or, but does not obtain any more information, while Bob does not learn anything about her choice. In this work we firstly introduce a quantum protocol which implements the functionality of XOT on classical inputs, and we show that such protocol is insecure if Alice cheats. By building on a variant of such protocol, we present a protocol for XOT with partial security for both parties. We then propose a protocol for evaluating linear polynomials, in which Alice's data leakage is limited to a constant number of bits under uniform input distributions, and Bob's input is partially secure. We show a method to combine it with a classical XOR homomorphic encryption scheme, which serves to mitigate the security weakness by computational methods. Finally, we show how to use the quantum protocol for linear polynomials in an interactive two-party computation scheme.Comment: 9 pages. Revised Section V with minor change to Protocol 1, and added Section V