Hash Proof Systems over Lattices Revisited

  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.},
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. 
A Framework for UC-Secure Commitments from Publicly Computable Smooth Projective Hashing
This paper introduces a new feature (a third mode of hashing) that allows to compute the hash value of an SPHF without having access to neither the witness nor the hashing key, but some additional auxiliary information.
A Gapless Code-Based Hash Proof System based on RQC and its Applications
This work shows how to build a hash proof system from code-based cryptography and presents a way, based on a proof of knowledge, to fully negate the gap, and proposes two applications of the construction, a witness encryption scheme and a password authenticated key exchange (PAKE).
Two-Round Adaptively Secure Multiparty Computation from Standard Assumptions
We present the first two-round multiparty computation (MPC) protocols secure against malicious adaptive corruption in the common reference string (CRS) model, based on DDH, LWE, or QR. Prior
Smooth Hash Proof System Based on the Learning With Errors Problem With Multi-Bit Key Output
A novel reconciliation mechanism based on the learning with errors (LWE) problem is inspired and an efficient LWE-based HPS scheme is proposed which can generate multiple encapsulated key bits and perform better in both computation and storage costs than other related results.
ANewRing-Based SPHF andPAKEProtocol on Ideal Lattices
This work presents a new efficient ring-based smooth projective hash function “(Ring-SPHF)” using Lyubashevsky, Peikert, and Regev’s dual-style cryptosystem based on the Learning With Errors over Rings (Ring-LWE) problem and proposes an efficient password-based authenticated key exchange protocol over rings whose security relies on ideal lattice assumptions.
Multi-theorem Preprocessing NIZKs from Lattices
This work takes an initial step toward constructing multi-theorem NIZKs for general NP languages from standard lattice assumptions by considering a relaxation to the preprocessing model and a new model the authors call the designated-prover model.
Post-Quantum UC-Secure Oblivious Transfer in the Standard Model with Adaptive Corruptions
This paper shows how to construct an OT scheme based on lattices, from a collision-resistant chameleon hash scheme (CH) and a CCA encryption scheme accepting a smooth projective hash function (SPHF).
Two-Round PAKE Protocol over Lattices Without NIZK
This paper proposes the first two-round PAKE protocol over lattices without NIZK, which is in accordance with the framework of Abdalla et al. (PKC’15) while attaining post-quantum security.
Covert Authentication from Lattices
A new generic construction of covert Mutual Authentication (MA) protocol is provided, that departs from given blueprint and that requires somewhat weaker properties regarding the employed cryptographic ingredients, and is proven secure in the random oracle model and potentially quantum-safe.
PAKEs: New Framework, New Techniques and More Efficient Lattice-Based Constructions in the Standard Model
A new PAKE framework is introduced, and two realizations in the standard model are provided under the Learning With Errors (LWE) and Ring-LWE assumptions, respectively, which are much more efficient than previous proposals.


Disjunctions for Hash Proof Systems: New Constructions and Applications
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
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
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
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
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
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
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
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.