We provide the first two-party protocol allowing Alice and Bob to evaluate privately even against active adversaries any completely positive, trace-preserving map J ∈ L(A_(in) ⊕ B_(in)) —> L(A_(out) ⊕ B_(out)), given as a quantum circuit, upon their joint quantum input state p_(in) € D(A_(in) ⊕ B_(in)). Our protocol leaks no more to any active adversary than an ideal functionality for J provided Alice and Bob have the cryptographic resources for active secure two-party classical computation. Our protocol is constructed from the protocol for the same task secure against specious adversaries presented in [4].
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