A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On Constructing Parallel Pseudorandom Generators from One-Way Functions
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Bounds on the Efficiency of Generic Cryptographic Constructions
SIAM Journal on Computing
COMPUTATIONALLY PRIVATE RANDOMIZING POLYNOMIALS AND THEIR APPLICATIONS
Computational Complexity
SIAM Journal on Computing
On Pseudorandom Generators with Linear Stretch in NC0
Computational Complexity
Cryptography with constant input locality
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Efficiency improvements in constructing pseudorandom generators from one-way functions
Proceedings of the forty-second ACM symposium on Theory of computing
On the complexity of non-adaptively increasing the stretch of pseudorandom generators
TCC'11 Proceedings of the 8th conference on Theory of cryptography
On the complexity of parallel hardness amplification for one-way functions
TCC'06 Proceedings of the Third conference on Theory of Cryptography
On the complexity of non-adaptively increasing the stretch of pseudorandom generators
TCC'11 Proceedings of the 8th conference on Theory of cryptography
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The standard approach for constructing a large-stretch pseudo-randomgenerator given a one-way permutation or given a smallerstretch pseudo-randomgenerator involves repeatedly composing the given primitive with itself. In this paper, we consider whether this approach is necessary, that is, whether there are constructions that do not involve composition. More formally, we consider black-box constructions of pseudorandom generators from pseudo-random generators of smaller stretch or from one-way permutations, where the constructions make only nonadaptive queries to the given object.We consider three classes of such constructions, and for each class, we give a black-box impossibility result that demonstrates a contrast between the stretch that can be achieved by adaptive and non-adaptive black-box constructions. We first consider constructions that make constantly-many nonadaptive queries to a given pseudo-random generator, where the seed length of the construction is at most O(log n) bits longer than the length n of each oracle query. We show that such constructions cannot achieve stretch that is even a single bit greater than the stretch of the given pseudo-random generator. We then consider constructions with arbitrarily long seeds, but where oracle queries are collectively chosen in a manner that depends only on a portion of the seed whose length is atmost O(log n) bits longer than the length n of each query. We show that such constructionsmaking constantly-many non-adaptive queries cannot achieve stretch that is ω(log n) bits greater than the stretch of the given pseudo-random generator. Finally, we consider a class of constructions motivated by streaming computation. Specifically, we consider constructions where the computation of each individual output bit depends only on the seed and on the response to a single query to a one-way permutation. We allow the seed to have a public portion that is arbitrarily long but must always be included in the output, and a non-public portion that is at most O(log n) bits longer than the length n of each oracle query. We show that such constructions whose queries are chosen non-adaptively based only on the non-public portion of the seed cannot achieve linear stretch.