Je# Kahn, Michael Saks, and Cli# Smyth. A dual version of Reimer's inequality and a proof of Rudich's conjecture. In 15th Annual IEEE Conference on Computational Complexity (Florence, 2000), pages 98--103. IEEE Computer Soc., Los Alamitos, CA, 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....all those basic cryptographic primitives, but it is not the case for trapdoor functions as they do not imply OT [7] and thus PIR [4] So there seems to be something special for being a permutation which deserves further study. We also know that one way functions do not imply one way permutations [20, 16], so permutation does not seem to be a property that one can have for free. We know that one way permutations imply none of the primitives in public cryptography [12] so on top of one wayness, one can not trade permutations for any of the additional properties required in public cryptography. ....

.... et al. 7] It is known that a random function is one way with high probability, even relative to a PSPACE complete function [12] Then, OWF exists relative to an oracle containing a random function and a PSPACE complete function, but on the other hand, OWP does not relative to such an oracle [20, 16]. We want to separate OWP from TDF and PIR. Each time we look for a special function which realizes the additional property required by that primitive but does not yield permutations. By adding such a function to the oracle, we can build the corresponding primitive, TDF or PIR, but relative to the ....

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Je Kahn, Michael E. Saks, and Cli Smyth. A dual version of Reimer's inequality and a proof of Rudich's conjecture. In Proceedings of the 15th Annual IEEE Conference on Computational Complexity, pages 98-103, 2000.

....Blackbox reductions work relative to any oracle. Therefore, one way to prove that a blackbox reduction of B to A is impossible is to prove the existence of an oracle relative to which A exist whereas B does not. Since the initial work of Impagliazzo and Rudich [15] many other separation results [23, 7, 8, 22, 21, 13] in this model have appeared. We use a related technique (used previously [16, 6] here. To show a lower bound on the e#ciency of constructions of B from A, we show an oracle for A relative to which a construction of B beating the bound would yield the unconditional existence of something beyond ....

J. Kahn, M. Saks, and C. Smyth. A Dual Version of Reimer's Inequality and a Proof of Rudich's Conjecture. In Proceedings of the 15th IEEE Conference on Computational Complexity, 2000.

....give strong evidence that black box access to one way permutations cannot yield secure key exchange. In [Sim98] Simon proves that one way permutations are not sufficient to construct collision resistant hash functions (which is a stronger primitive than UOWHF s) Finally a very recent result [KSS00] shows that there is no construction of one way permutations based on one way functions. 1 One could derive our result from Impagliazzo s proof and from the fact that a random function is indistinguishable from a random permutation. Anyway, our proof is quite different from Impagliazzo s, and a ....

....result in the Impagliazzo Rudich 4 setting implies a relativized impossiblity result, so that the Impagliazzo Rudich setting is more general. Among previous impossibility results, a very recent result showing that there is no construction of one way permutations based on one way functions [Rud88, KSS00] is in the Impagliazzo Rudich model, while other results are based on relativizations [Rud91, Sim98, KST99] 2.2 Model for Pseudorandom Generator Constructions We say that a permutation : f0; 1g n f0; 1g n is (S; ffl) one way if for every circuit A of size S we have Pr x [A( x) x] ....

J. Kahn, M. Saks, and C. Smyth. A dual version of Reimer's inequality and a proof of rudich's conjecture. In Proceedings of the 15th IEEE Conference on Computational Complexity, 2000. 11

....[IR89] give strong evidence that black box access to one way permutations cannot yield secure key exchange. In [Sim98] Simon proves that one way permutations are not sucient to construct collision resistant hash functions (which is a stronger primitive than UOWHF s) Finally a very recent result [KSS00] shows that there is no construction of one way permutations based on one way functions. 1 One could derive our result from Impagliazzo s proof and from the fact that a random function is indistinguishable from a random permutation. Anyway, our proof is quite di erent from Impagliazzo s, and a ....

....result in the Impagliazzo Rudich 4 setting implies a relativized impossiblity result, so that the Impagliazzo Rudich setting is more general. Among previous impossibility results, a very recent result showing that there is no construction of one way permutations based on one way functions [Rud88, KSS00] is in the Impagliazzo Rudich model, while other results are based on relativizations [Rud91, Sim98, KST99] 2.2 Model for Pseudorandom Generator Constructions We say that a permutation : f0; 1g n f0; 1g n is (S; one way if for every circuit A of size S we have Pr x [A( x) x] ....

J. Kahn, M. Saks, and C. Smyth. A dual version of Reimer's inequality and a proof of rudich's conjecture. In Proceedings of the 15th IEEE Conference on Computational Complexity, 2000.

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Je# Kahn, Michael Saks, and Cli# Smyth. A dual version of Reimer's inequality and a proof of Rudich's conjecture. In 15th Annual IEEE Conference on Computational Complexity (Florence, 2000), pages 98--103. IEEE Computer Soc., Los Alamitos, CA, 2000.

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J. Kahn, M. Saks, and C. Smyth. A dual version of Reimer's inequality and a proof of rudich's conjecture. In Proceedings of the 15th IEEE Conference on Computational Complexity, 2000. 11

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J. Kahn, M.E. Saks, and C.D. Smyth. A Dual Version of Reimer's Inequality and a Proof of Rudich's Conjecture. 15th IEEE Conference on Computational Complexity, IEEE, pp. 98--103, 2000.

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J. Kahn, M. Saks, and C. Smyth. A dual version of Reimer's inequality and a proof of Rudich's conjecture. Computational Complexity 2000.

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J. Kahn, M.E. Saks, and C.D. Smyth. A Dual Version of Reimer's Inequality and a Proof of Rudich's Conjecture. 15th IEEE Conference on Computational Complexity, IEEE, pp. 98--103, 2000.

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Je# Kahn, Michael Saks, and Cli# Smyth. A dual version of reimer's inequality and a proof of rudich's conjecture. In Proceedings of the 15th Annual IEEE Conference on Computational Complexity, 2000.

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