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On the Composition of Zero-Knowledge Proof Systems
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Perfectly one-way probabilistic hash functions (preliminary version)
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The random oracle methodology, revisited (preliminary version)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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Foundations of Cryptography: Basic Tools
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Pseudorandomness and Cryptographic Applications
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CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
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Lower bounds on the efficiency of generic cryptographic constructions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Correcting errors without leaking partial information
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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Extractable Perfectly One-Way Functions
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The Superdiversifier: Peephole Individualization for Software Protection
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A graph game model for software tamper protection
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SIAM Journal on Computing
A note on obfuscation for cryptographic functionalities of secret-operation then public-encryption
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TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
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Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We investigate the possibility of obfuscating point functions in the framework of Barak et al. from Crypto '01. A point function is a Boolean function that assumes the value 1 at exactly one point. Our main results are as follows:We provide a simple construction of efficient obfuscators for point functions for a slightly relaxed notion of obfuscation, for which obfuscating general circuits is nonetheless impossible. Our construction relies on the existence of a very strong one-way permutation, and yields the first non-trivial obfuscator under general assumptions in the standard model. We also obtain obfuscators for point functions with multi-bit output and for prefix matching.Our assumption is that there is a one-way permutation wherein any polynomial-sized circuit inverts the permutation on at most a polynomial number of inputs. We show that a similar assumption is in fact necessary, and that our assumption holds relative to a random permutation oracle.Finally, we establish two impossibility results which indicate that the limitations on our construction, namely simulating only adversaries with single-bit output and using nonuniform advice in our simulator, are in some sense inherent.Previous work gave negative results for the general class of circuits (Barak et al., Crypto '01) and positive results in the random oracle model (Lynn et al., Eurocrypt '04) or under non-standard number-theoretic assumptions (Canetti, Crypto '97). This work represents the first effort to bridge the gap between the two for a natural class of functionalities.