Adaptive zero-knowledge proofs and adaptively secure oblivious transfer

Yehuda Lindell, Hila Zarosim

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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: Adaptive zero-knowledge proofs: We ask whether it is possible to construct adaptive zero-knowledge proofs (with unconditional soundness) for all of $\mathcal{NP}$ . Beaver (STOC [1996]) showed that known zero-knowledge proofs are not adaptively secure, and in addition showed how to construct zero-knowledge arguments (with computational soundness). Adaptively secure oblivious transfer: All known protocols for adaptively secure oblivious transfer rely on seemingly stronger hardness assumptions than for the case of static adversaries. We ask whether this is inherent, and in particular, whether it is possible to construct adaptively secure oblivious transfer from enhanced trapdoor permutations alone. 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 $\mathcal{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 secure 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.

Original languageEnglish
Pages (from-to)761-799
Number of pages39
JournalJournal of Cryptology
Issue number4
Early online date28 Jul 2010
StatePublished - Oct 2011

Bibliographical note

Funding Information:
This research was supported by the israel science foundation (grant No. 781/07).


This research was supported by the israel science foundation (grant No. 781/07).

FundersFunder number
Israel Science Foundation781/07


    • Adaptive security
    • Black-box separations
    • Minimal assumptions
    • Oblivious transfer
    • Zero-knowledge proofs


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