Parallel Hashing via List Recoverability

  • Iftach Haitner
  • Yuval Ishai
  • Eran Omri
  • Ronen Shaltiel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9216)

Abstract

Motivated by the goal of constructing efficient hash functions, we investigate the possibility of hashing a long message by only making parallel, non-adaptive calls to a hash function on short messages. Our main result is a simple construction of a collision-resistant hash function \(h:\{0,1\}^n\rightarrow \{0,1\}^k\) that makes a polynomial number of parallel calls to a random function \(f:\{0,1\}^k\rightarrow \{0,1\}^k\), for any polynomial \(n=n(k)\). This should be compared with the traditional use of a Merkle hash tree, that requires at least \(\log (n/k)\) rounds of calls to f, and with a more complex construction of Maurer and Tessaro [26] (Crypto 2007) that requires two rounds of calls to f. We also show that our hash function h satisfies a relaxed form of the notion of indifferentiability of Maurer et al. [27] (TCC 2004) that suffices for implementing the Fiat-Shamir paradigm. As a corollary, we get sublinear-communication non-interactive arguments for NP that only make two rounds of calls to a small random oracle.

An attractive feature of our construction is that h can be implemented by Boolean circuits that only contain parity gates in addition to the parallel calls to f. Thus, we get the first domain-extension scheme which is degree-preserving in the sense that the algebraic degree of h over the binary field is equal to that of f.

Our construction makes use of list-recoverable codes, a generalization of list-decodable codes that is closely related to the notion of randomness condensers. We show that list-recoverable codes are necessary for any construction of this type.

Keywords

Hash Function Random Function LDPC Code Random Oracle Commitment Scheme 
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.

Notes

Acknowledgments

We thank Yevgeniy Dodis, Swastik Kopparty, Phil Rogaway, Atri Rudra and Stefano Tessaro for helpful discussions and pointers.

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Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  • Iftach Haitner
    • 1
  • Yuval Ishai
    • 2
  • Eran Omri
    • 3
  • Ronen Shaltiel
    • 4
  1. 1.Tel Aviv UniversityTel AvivIsrael
  2. 2.TechnionHaifaIsrael
  3. 3.Ariel UniversityArielIsrael
  4. 4.Haifa UniversityHaifaIsrael

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