Unifying computational entropies via Kullback-Leibler divergence

@inproceedings{Agrawal2019UnifyingCE,
  title={Unifying computational entropies via Kullback-Leibler divergence},
  author={Rohit Agrawal and Yi-Hsiu Chen and Thibaut Horel and Salil P. Vadhan},
  booktitle={IACR Cryptol. ePrint Arch.},
  year={2019}
}
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… 

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References

SHOWING 1-10 OF 24 REFERENCES

Inaccessible Entropy I: Inaccessible Entropy Generators and Statistically Hiding Commitments from One-Way Functions

TLDR
A new computational notion of entropy is put forth, measuring the (in)feasibility of sampling high-entropy strings that are consistent with a given generator, and a much simpler and more efficient construction of statistically hiding commitment schemes from arbitrary one-way functions is presented.

Inaccessible entropy

TLDR
It is proved that constant-round statistically hiding commitments are necessary for constructing constant- round zero-knowledge proof systems for NP that remain secure under parallel composition (assuming the existence of one-way functions).

Characterizing pseudoentropy and simplifying pseudorandom generator constructions

TLDR
This work provides a characterization of pseudoentropy in terms of hardness of sampling and shows how to improve the seed length of the pseudorandom generator to ~{O}(n3), compared to O(n4) in the construction of Haitner et al.

Efficiency improvements in constructing pseudorandom generators from one-way functions

TLDR
A new construction of pseudorandom generators from any one-way function is given, inspired by the notion of "inaccessible entropy" recently introduced in [Haitner, Reingold, Vadhan, Wee, STOC '09]. An additional advantage over previous constructions is that the pseudoentropy generators are parallelizable and invoke the one- way function in a non-adaptive manner.

Universal One-Way Hash Functions via Inaccessible Entropy

This paper revisits the construction of Universal One-Way Hash Functions (UOWHFs) from any one-way function due to Rompel (STOC 1990). We give a simpler construction of UOWHFs, which also obtains

Efficiency Improvements in Constructing Pseudorandom Generators from One-Way Functions

TLDR
A new construction of pseudorandom generators from any one-way function based on a new notion of next-block pseudoentropy, inspired by the notion of “inaccessible entropy” recently introduced in [I. Haitner, O. Reingold, S. Vadhan, and H. Wee, Proceedings of the $41$st Annual ACM Symposium on Theory of Computing (STOC), 2009, pp. 611--620].

How to generate cryptographically strong sequences of pseudo random bits

  • M. BlumS. Micali
  • Computer Science, Mathematics
    23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)
  • 1982
TLDR
A more operative definition of Randomness should be pursued in the light of modern Complexity Theory.

Perfect Zero-Knowledge Arguments for NP Using Any One-Way Permutation

TLDR
A general construction of zero-knowledge arguments based on specific algebraic assumptions is shown which can be based on any one-way permutation and obtained by a construction of an information-theoretic secure bit-commitment protocol.

Statistically Hiding Commitments and Statistical Zero-Knowledge Arguments from Any One-Way Function

TLDR
One-way functions suffice to give statistical zero-knowledge arguments for any NP statement, whereby even a computationally unbounded adversarial verifier learns nothing other than the fact that the assertion being proven is true, and no polynomial-time adversarial prover can convince the verifier of a false statement.

Constant-Round Oblivious Transfer in the Bounded Storage Model

TLDR
This work achieves the constant round complexity of the oblivious transfer protocol by constructing a novel four-message protocol for Interactive Hashing, in place of the well-known protocol by Naor et al. (known as the NOVY protocol) which involves many rounds of interaction.