1,087 research outputs found
Efficiency Improvements in Constructing Pseudorandom Generators from One-way Functions
ABSTRACT We give a new construction of pseudorandom generators from any one-way function. The construction achieves better parameters and is simpler than that given in the seminal work of HĂ„stad, Impagliazzo, Levin, and Luby [SICOMP '99]. The key to our construction is a new notion of nextblock pseudoentropy, which is inspired by the notion of "inaccessible entropy" recently introduced in [Haitner, Reingold, Vadhan, and Wee, STOC '09]. An additional advantage over previous constructions is that our pseudorandom generators are parallelizable and invoke the one-way function in a non-adaptive manner. Using [Applebaum, Ishai, and Kushilevitz, SICOMP '06], this implies the existence of pseudorandom generators in NC 0 based on the existence of one-way functions in NC 1
Some Applications of Coding Theory in Computational Complexity
Error-correcting codes and related combinatorial constructs play an important
role in several recent (and old) results in computational complexity theory. In
this paper we survey results on locally-testable and locally-decodable
error-correcting codes, and their applications to complexity theory and to
cryptography.
Locally decodable codes are error-correcting codes with sub-linear time
error-correcting algorithms. They are related to private information retrieval
(a type of cryptographic protocol), and they are used in average-case
complexity and to construct ``hard-core predicates'' for one-way permutations.
Locally testable codes are error-correcting codes with sub-linear time
error-detection algorithms, and they are the combinatorial core of
probabilistically checkable proofs
Cryptanalysis of LFSR-based Pseudorandom Generators - a Survey
Pseudorandom generators based on linear feedback shift registers (LFSR) are a traditional building block for cryptographic stream ciphers. In this report, we review the general idea for such generators, as well as the most important techniques of cryptanalysis
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Complexity Theory
Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developements are related to diverse mathematical ïŹelds such as algebraic geometry, combinatorial number theory, probability theory, quantum mechanics, representation theory, and the theory of error-correcting codes
Unifying computational entropies via Kullback-Leibler divergence
We introduce hardness in relative entropy, a new notion of hardness for
search problems which on the one hand is satisfied by all one-way functions and
on the other hand implies both next-block pseudoentropy and inaccessible
entropy, two forms of computational entropy used in recent constructions of
pseudorandom generators and statistically hiding commitment schemes,
respectively. Thus, hardness in relative entropy unifies the latter two notions
of computational entropy and sheds light on the apparent "duality" between
them. Additionally, it yields a more modular and illuminating proof that
one-way functions imply next-block inaccessible entropy, similar in structure
to the proof that one-way functions imply next-block pseudoentropy (Vadhan and
Zheng, STOC '12)
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