How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
How to construct random functions
Journal of the ACM (JACM)
Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
One-way functions and the nonisomorphism of NP-complete sets
Theoretical Computer Science
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
A Dual Version of Reimer's Inequality and a Proof of Rudich's Conjecture
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
The Impossibility of Basing One-Way Permutations on Central Cryptographic Primitives
Journal of Cryptology
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Generic oracles and oracle classes
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Adaptive One-Way Functions and Applications
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Two is a crowd? a black-box separation of one-wayness and security under correlated inputs
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Non-interactive opening for ciphertexts encrypted by shared keys
ICICS'11 Proceedings of the 13th international conference on Information and communications security
On the power of nonuniformity in proofs of security
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Limits of random oracles in secure computation
Proceedings of the 5th conference on Innovations in theoretical computer science
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A one-way permutation (OWP) is one of the most fundamental cryptographic primitives, and can be used as a building block for most of basic symmetric-key cryptographic primitives. However, despite its importance and usefulness, previous black-box separation results have shown that constructing a OWP from another primitive seems hopeless, unless building blocks already achieve "one-way" property and "permutation" property simultaneously. In this paper, in order to clarify more about the constructions of a OWP from other primitives, we study the construction of a OWP from primitives that are very close to a OWP. Concretely, as a negative result, we show that there is no fully black-box construction of a OWP from a length-increasing injective one-way function (OWF), even if the latter is just 1-bit-increasing and achieves strong form of one-wayness which we call adaptive one-wayness. As a corollary, we show that there is no fully black-box construction of a OWP from a regular OWF with regularity greater than 1. Since a permutation is length-preserving and injective, and is a regular OWF with regularity 1, our negative result indicates that to construct a OWP from another primitive is quite difficult, even if we use very close primitives to a OWP as building blocks. Moreover, we extend our separation result of a OWP from a length-increasing injective OWF, and show a certain restrictive form of black-box separations among injective OWFs in terms of how much a function stretches its input. This result shows a hierarchy among injective OWFs (including a OWP).