Paper 2011/028

The Parazoa Family: Generalizing the Sponge Hash Functions

Elena Andreeva, Bart Mennink, and Bart Preneel


Sponge functions were introduced by Bertoni et al. as an alternative to the classical Merkle-Damgaard design. Many hash function submissions to the SHA-3 competition launched by NIST in 2007, such as CubeHash, Fugue, Hamsi, JH, Keccak and Luffa, derive from the original sponge design, and security guarantees from some of these constructions are typically based on indifferentiability results. Although indifferentiability proofs for these designs often bear significant similarities, these have so far been obtained independently for each construction. In this work, we introduce the parazoa family of hash functions as a generalization of ``sponge-like'' functions. Similarly to the sponge design, the parazoa family consists of compression and extraction phases. The parazoa hash functions, however, extend the sponge construction by enabling the use of a wider class of compression and extraction functions that need to satisfy certain properties. More importantly, we prove that the parazoa functions satisfy the indifferentiability notion of Maurer et al. under the assumption that the underlying permutation is ideal. Not surprisingly, our indifferentiability result confirms the bound on the original sponge function, but it also carries over to a wider spectrum of hash functions and eliminates the need for a separate indifferentiability analysis.

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. appears in the International Journal of Information Security
Parazoa functionssponge functionshash function designindifferentiability
Contact author(s)
bart mennink @ esat kuleuven be
2012-02-10: last of 4 revisions
2011-01-16: received
See all versions
Short URL
Creative Commons Attribution


      author = {Elena Andreeva and Bart Mennink and Bart Preneel},
      title = {The Parazoa Family: Generalizing the Sponge Hash Functions},
      howpublished = {Cryptology ePrint Archive, Paper 2011/028},
      year = {2011},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.