Adaptive Zero-Knowledge Proofs and Adaptively Secure Oblivious Transfer

Yehuda Lindell and Hila Zarosim


In the setting of secure computation, a set of parties wish to securely compute some function of their inputs, in the presence of an adversary. The adversary in question may be static (meaning that it controls a predetermined subset of the parties) or adaptive (meaning that it can choose to corrupt parties during the protocol execution and based on what it sees). In this paper, we study two fundamental questions relating to the basic zero-knowledge and oblivious transfer protocol problems:

We provide surprising answers to the above questions, showing that achieving adaptive security is sometimes harder than achieving static security, and sometimes not. First, we show that assuming the existence of one-way functions only, there exist adaptive zero-knowledge proofs for all languages in NP. In order to prove this, we overcome the problem that all adaptive zero-knowledge protocols known until now used equivocal commitments (which would enable an all-powerful prover to cheat). Second, we prove a black-box separation between adaptively secure oblivious transfer and enhanced trapdoor permutations. As a corollary, we derive a black-box separation between adaptively and statically securely oblivious transfer. This is the first black-box separation to relate to adaptive security and thus the first evidence that it is indeed harder to achieve security in the presence of adaptive adversaries than in the presence of static adversaries.


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