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The Many Entropies in One-Way Functions

Part of the Information Security and Cryptography book series (ISC)

Abstract

Computational analogues of information-theoretic notions have given rise to some of the most interesting phenomena in the theory of computation. For example, computational indistinguishability, Goldwasser and Micali [9], which is the computational analogue of statistical distance, enabled the bypassing of Shannon’s impossibility results on perfectly secure encryption, and provided the basis for the computational theory of pseudorandomness. Pseudoentropy, Håstad, Impagliazzo, Levin, and Luby [17], a computational analogue of entropy, was the key to the fundamental result establishing the equivalence of pseudorandom generators and oneway functions, and has become a basic concept in complexity theory and cryptography.

This tutorial discusses two rather recent computational notions of entropy, both of which can be easily found in any one-way function, the most basic cryptographic primitive. The first notion is next-block pseudoentropy, Haitner, Reingold, and Vadhan [14], a refinement of pseudoentropy that enables simpler and more efficient construction of pseudorandom generators. The second is inaccessible entropy, Haitner, Reingold, Vadhan, andWee [11], which relates to unforgeability and is used to construct simpler and more efficient universal one-way hash functions and statistically hiding commitments.

Keywords

  • Hash Function
  • Shannon Entropy
  • Security Parameter
  • Commitment Scheme
  • Pseudorandom Generator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Iftach Haitner .

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Haitner, I., Vadhan, S. (2017). The Many Entropies in One-Way Functions. In: Lindell, Y. (eds) Tutorials on the Foundations of Cryptography. Information Security and Cryptography. Springer, Cham. https://doi.org/10.1007/978-3-319-57048-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-57048-8_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57047-1

  • Online ISBN: 978-3-319-57048-8

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