Hash Proof Systems over Lattices Revisited

@inproceedings{Benhamouda2017HashPS,
  title={Hash Proof Systems over Lattices Revisited},
  author={Fabrice Benhamouda and Olivier Blazy and L{\'e}o Ducas and Willy Quach},
  booktitle={IACR Cryptol. ePrint Arch.},
  year={2017}
}
Hash Proof Systems or Smooth Projective Hash Functions (SPHFs) are a form of implicit arguments introduced by Cramer and Shoup at Eurocrypt’02. They have found many applications since then, in particular for authenticated key exchange or honest-verifier zero-knowledge proofs. While they are relatively well understood in group settings, they seem painful to construct directly in the lattice setting. 
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References

SHOWING 1-10 OF 34 REFERENCES
Disjunctions for Hash Proof Systems: New Constructions and Applications
TLDR
This paper shows how to construct hash proof systems for the disjunction of languages defined generically over cyclic, bilinear, and multilinear groups, which enables them to construct the most efficient one-time simulation-sound (quasi-adaptive) non-interactive zero-knowledge arguments for linear languages overcyclic groups.
Smooth Projective Hashing for Conditionally Extractable Commitments
TLDR
This paper addresses the problem of building smooth projective hash functions for more complex languages and shows how to build such functions for languages that can be described in terms of disjunctions and conjunctions of simpler languages for which smooth projectives hash functions are known to exist.
Smooth Projective Hashing and Password-Based Authenticated Key Exchange from Lattices
TLDR
This work describes a public-key encryption scheme based on lattices that is secure against chosen-ciphertext attacks while admitting (a variant of) smooth projective hashing and obtains the first PAKE protocol whose security relies on a lattice-based assumption.
Round-Optimal Password-Based Authenticated Key Exchange
We show a general framework for constructing password-based authenticated key-exchange protocols with optimal round complexity—one message per party, sent simultaneously—in the standard model,
Bonsai Trees, or How to Delegate a Lattice Basis
TLDR
A new lattice-based cryptographic structure called a bonsai tree is introduced, and it is used to resolve some important open problems in the area of number-theoretic cryptography.
Trapdoors for hard lattices and new cryptographic constructions
TLDR
A new notion of trapdoor function with preimage sampling, simple and efficient "hash-and-sign" digital signature schemes, and identity-based encryption are included.
Public-key cryptosystems provably secure against chosen ciphertext attacks
We show how to construct a public-key cryptosystem (as originally defined by DiNe and Hellman) secure against chosen ciphertezt attacks, given a public-key cryptosystern secure against passive
Two-Round PAKE from Approximate SPH and Instantiations from Lattices
TLDR
A framework for constructing PAKE from CCA-secure PKE with associated ASPH is given, which uses only two-round messages by carefully exploiting a splittable property of the underlying PKE and its associated non-adaptive ASPH.
Smooth Projective Hashing and Two-Message Oblivious Transfer
TLDR
A general framework for constructing two-message oblivious transfer protocols using a modification of Cramer and Shoup’s notion of smooth projective hashing is presented and it is observed that the safe-prime requirement is unnecessary for many prior constructions of factoring-based smooth universal hashing.
New Techniques for SPHFs and Efficient One-Round PAKE Protocols
TLDR
This paper presents the first concrete one-round PAKE protocols, where the two players just have to send simultaneous flows to each other, at the cost of simulation-sound non-interactive zero-knowledge proofs.
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