The polynomial-time hierarchy and sparse oracles
Journal of the ACM (JACM)
Relativizing complexity classes with sparse oracles
Journal of the ACM (JACM)
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Algorithmic information theory
Algorithmic information theory
On one-way functions and polynomial-time isomorphisms
Theoretical Computer Science
Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Relativized Questions Involving Probabilistic Algorithms
Journal of the ACM (JACM)
A relativized failure of the Berman-Hartmanis conjecture
A relativized failure of the Berman-Hartmanis conjecture
Polynomial reducibilities and complete sets.
Polynomial reducibilities and complete sets.
The cpa's responsibility for the prevention and detection of computer fraud.
The cpa's responsibility for the prevention and detection of computer fraud.
On the power of 1-way functions
CRYPTO '88 Proceedings on Advances in cryptology
The random oracle hypothesis is false
Journal of Computer and System Sciences
The quasilinear isomorphism challenge
ACM SIGACT News
The Use of Interaction in Public Cryptosystems (Extended Abstract)
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
The First-Order Isomorphism Theorem
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
Information and Computation
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Berman and Hartmanis [BH77] conjectured that there is a polynomial-time computable isomorphism between any two languages m-complete (“Karp” complete) for NP. Joseph and Young [JY85] discovered a structurally defined class of NP-complete sets and conjectured that certain of these sets (the Kkƒ's) are not isomorphic to the standard NP-complete sets for some one-way functions ƒ. These two conjectures cannot both be correct.We introduce a new family of strong one-way functions, the scrambling functions. If ƒ is a scrambling function, then Kkfnof; is not isomorphic to the standard NP-complete sets, as Joseph and Young conjectured, and the Berman-Hartmanis conjecture fails. As evidence for the existence of scrambling functions, we show that much more powerful one-way functions--the annihilating functions--exist relative to a random oracle.