Description
We initiate the study of a novel class of group-theoretic intractability problems. Inspired by the theory of learning in presence of errors [Regev, STOC'05] we ask if noise in the exponent amplifies intractability. We put forth the notion of Learning with Errors in the Exponent (LWEE) and rather surprisingly show that various attractive properties known to ex- clusively hold for lattices carry over. Most notably are worst-case hardness and post-quantum resistance. In fact, LWEE's "diprosopus" is due to the reducibility to two seemingly orthogonal assumptions: Learning with errors and the representation problem [Brands, Crypto'93]. For suitable parameter choices one obtains double-hard assumptions superposing properties from each individual assumption. The argument holds in the classical and quantum model of computation, and makes LWEE an appealing provisioner of strong security and robustness guarantees. We give the very first construction of a semantically secure public-key encryption system in the standard model. The heart of our construction is an "error recovery" technique to tame the crucial propagation of noise in the exponent which is of independent interest.
Next sessions
-
CryptoVerif: a computationally-sound security protocol verifier
Speaker : Bruno Blanchet - Inria
CryptoVerif is a security protocol verifier sound in the computational model of cryptography. It produces proofs by sequences of games, like those done manually by cryptographers. It has an automatic proof strategy and can also be guided by the user. It provides a generic method for specifying security assumptions on many cryptographic primitives, and can prove secrecy, authentication, and[…]-
Cryptography
-
-
Structured-Seed Local Pseudorandom Generators and their Applications
Speaker : Nikolas Melissaris - IRIF
We introduce structured‑seed local pseudorandom generators (SSL-PRGs), pseudorandom generators whose seed is drawn from an efficiently sampleable, structured distribution rather than uniformly. This seemingly modest relaxation turns out to capture many known applications of local PRGs, yet it can be realized from a broader family of hardness assumptions. Our main technical contribution is a[…]-
Cryptography
-
-
Post-Quantum Public-Key Pseudorandom Correlation Functions for OT
Speaker : Mahshid Riahinia - ENS, CNRS
Public-Key Pseudorandom Correlation Functions (PK-PCF) are an exciting recent primitive introduced to enable fast secure computation. Despite significant advances in the group-based setting, success in the post-quantum regime has been much more limited. In this talk, I will introduce an efficient lattice-based PK-PCF for the string OT correlation. At the heart of our result lie several technical[…] -
Predicting Module-Lattice Reduction
Speaker : Paola de Perthuis - CWI
Is module-lattice reduction better than unstructured lattice reduction? This question was highlighted as `Q8' in the Kyber NIST standardization submission (Avanzi et al., 2021), as potentially affecting the concrete security of Kyber and other module-lattice-based schemes. Foundational works on module-lattice reduction (Lee, Pellet-Mary, Stehlé, and Wallet, ASIACRYPT 2019; Mukherjee and Stephens[…]-
Cryptography
-