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XOR oblivious transfer is a universal cryptographic primitive that can berelated to linear polynomial evaluation. We firstly introduce some bipartitequantum protocols for XOR oblivious transfer, which are not secure if one partycheats, and some of them can be combined with a classical XOR homomorphicencryption scheme for evaluation of linear polynomials modulo 2 with hybridsecurity. We then introduce a general protocol using modified versions of theXOR oblivious transfer protocols to evaluate linear polynomials modulo 2 withpartial information-theoretic security. When combined with the ability toperform arbitrary quantum computation, this would lead to deterministicinteractive two-party computation which is quite secure in theinformation-theoretic sense when the allowed set of inputs is large. For thetask of classical function evaluation, although the quantum computationapproach is still usable, we also discuss purely classical post-processingmethods based on the proposed linear polynomial evaluation protocols.

Quantum linear polynomial evaluation based on XOR oblivious transfer compatible with classical partially homomorphic encryption