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On the Impossibilities of Basing One-Way Permutations on Central Cryptographic Primitives
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Lower bounds on the efficiency of encryption and digital signature schemes
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On obfuscating point functions
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Black-box constructions for secure computation
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Exposure-Resilient Extractors and the Derandomization of Probabilistic Sublinear Time
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CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Cell probe lower bounds for succinct data structures
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On the (Im)Possibility of Key Dependent Encryption
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
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TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
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ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
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SCN'02 Proceedings of the 3rd international conference on Security in communication networks
A linear lower bound on the communication complexity of single-server private information retrieval
TCC'08 Proceedings of the 5th conference on Theory of cryptography
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CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Chosen-Ciphertext Security via Correlated Products
SIAM Journal on Computing
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PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
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SIAM Journal on Computing
Simple extractors via constructions of cryptographic pseudo-random generators
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On round-efficient argument systems
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On hardness amplification of one-way functions
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
On the generic insecurity of the full domain hash
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On the (im)possibility of obfuscating programs
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TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
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TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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We present lower bounds on the efficiency of constructions for Pseudo-Random Generators (PRGs) and Universal One-Way Hash Functions (UOWHFs) based on black-box access to one-way permutations. Our lower bounds are tight as they match the efficiency of known constructions. A PRG (resp. UOWHF) construction based on black-box access is a machine that is given oracle access to a permutation. Whenever the permutation is hard to invert, the construction is hard to break. In this paper we give lower bounds on the number of invocations to the oracle by the construction. If S is the assumed security of the oracle permutation /spl pi/ (i.e. no adversary of size S can invert /spl pi/ on a fraction larger than 1/S of its inputs) then a PRG (resp. UOWHF) construction that stretches (resp. compresses) its input by k bits must query /spl pi/ in q=/spl Omega/(k/log S) points. This matches known constructions. Our results are given in an extension of the Impagliazzo-Rudich model. That is, we prove that a proof of the existence of PRG (resp. UOWHF) black-box constructions that beat our lower bound would imply a proof of the unconditional existence of such construction (which would also imply P/spl ne/NP).