Lossy Cryptography from Code-Based Assumptions

• URL: http://arxiv.org/abs/2402.03633v1
• Date: Tue, 6 Feb 2024 02:17:08 GMT
• Title: Lossy Cryptography from Code-Based Assumptions
• Authors: Quang Dao, Aayush Jain,
• Abstract summary: A proliferation of advanced cryptographic primitives imply hard problems in the complexity class $SZK$. This poses a barrier for building advanced primitives from code-based assumptions. We propose a new code-based assumption: Dense-Sparse, that falls in the complexity class $BPPSZK$ and is conjectured to be secure against subexponential time adversaries.
• Score: 7.880958076366762
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Over the past few decades, we have seen a proliferation of advanced cryptographic primitives with lossy or homomorphic properties built from various assumptions such as Quadratic Residuosity, Decisional Diffie-Hellman, and Learning with Errors. These primitives imply hard problems in the complexity class $SZK$ (statistical zero-knowledge); as a consequence, they can only be based on assumptions that are broken in $BPP^{SZK}$. This poses a barrier for building advanced primitives from code-based assumptions, as the only known such assumption is Learning Parity with Noise (LPN) with an extremely low noise rate $\frac{\log^2 n}{n}$, which is broken in quasi-polynomial time. In this work, we propose a new code-based assumption: Dense-Sparse LPN, that falls in the complexity class $BPP^{SZK}$ and is conjectured to be secure against subexponential time adversaries. Our assumption is a variant of LPN that is inspired by McEliece's cryptosystem and random $k\mbox{-}$XOR in average-case complexity. We leverage our assumption to build lossy trapdoor functions (Peikert-Waters STOC 08). This gives the first post-quantum alternative to the lattice-based construction in the original paper. Lossy trapdoor functions, being a fundamental cryptographic tool, are known to enable a broad spectrum of both lossy and non-lossy cryptographic primitives; our construction thus implies these primitives in a generic manner. In particular, we achieve collision-resistant hash functions with plausible subexponential security, improving over a prior construction from LPN with noise rate $\frac{\log^2 n}{n}$ that is only quasi-polynomially secure.

Related papers

• New constructions of pseudorandom codes [23.22566380210149]
  Pseudorandom error-correcting codes (PRCs) are a new cryptographic primitive with applications in watermarking generative AI models. We show that if both the planted hyperloop assumption introduced in [BKR23] and security of a version of Goldreich's PRG hold, then there exist public-key PRCs for which no efficient adversary can distinguish a number of codewords from random. We show how to construct secret-key PRCs of length $O(n)$ which are $textitunconditionally$ indistinguishable random by $textpoly(
  arXiv  Detail & Related papers  (2024-09-11T19:14:39Z)
• Fast Rates for Bandit PAC Multiclass Classification [73.17969992976501]
  We study multiclass PAC learning with bandit feedback, where inputs are classified into one of $K$ possible labels and feedback is limited to whether or not the predicted labels are correct. Our main contribution is in designing a novel learning algorithm for the agnostic $(varepsilon,delta)$PAC version of the problem.
  arXiv  Detail & Related papers  (2024-06-18T08:54:04Z)
• Perturb-and-Project: Differentially Private Similarities and Marginals [73.98880839337873]
  We revisit the input perturbations framework for differential privacy where noise is added to the input $Ain mathcalS$. We first design novel efficient algorithms to privately release pair-wise cosine similarities. We derive a novel algorithm to compute $k$-way marginal queries over $n$ features.
  arXiv  Detail & Related papers  (2024-06-07T12:07:16Z)
• Crooked indifferentiability of the Feistel Construction [53.572703605492904]
  The Feistel construction is a fundamental technique for building pseudorandom permutations and block ciphers. This paper shows that a simple adaptation of the construction is resistant, even to algorithm substitution attacks.
  arXiv  Detail & Related papers  (2024-04-15T04:29:24Z)
• Quantum One-Wayness of the Single-Round Sponge with Invertible Permutations [49.1574468325115]
  Sponge hashing is a widely used class of cryptographic hash algorithms. Intrepid permutations have so far remained a fundamental open problem. We show that finding zero-pairs in a random $2n$-bit permutation requires at least $Omega (2n/2)$ many queries.
  arXiv  Detail & Related papers  (2024-03-07T18:46:58Z)
• Efficient quantum algorithms for some instances of the semidirect discrete logarithm problem [2.90985742774369]
  We show that the SDLP is even easier in some important special cases. We show that SPDH-Sign and similar cryptosystems whose security assumption is based on the presumed hardness of the SDLP are insecure against quantum attacks.
  arXiv  Detail & Related papers  (2023-12-21T16:58:59Z)
• Signatures From Pseudorandom States via $\bot$-PRFs [0.11650821883155184]
  We introduce new definitions for $bot$-PRG and $bot$-PRF. Our main application is a (quantum) digital signature scheme with classical public keys and signatures.
  arXiv  Detail & Related papers  (2023-11-01T20:54:50Z)
• A Quantum Approach for Reducing Communications in Classical Cryptographic Primitives [2.3465488122819123]
  We show that, perhaps surprisingly, it's possible to solve this problem with quantum techniques under much weaker assumptions. Our work conveys an interesting message that quantum cryptography could outperform classical cryptography in a new type of problems.
  arXiv  Detail & Related papers  (2023-10-08T16:07:46Z)
• Publicly-Verifiable Deletion via Target-Collapsing Functions [81.13800728941818]
  We show that targetcollapsing enables publiclyverifiable deletion (PVD) We build on this framework to obtain a variety of primitives supporting publiclyverifiable deletion from weak cryptographic assumptions.
  arXiv  Detail & Related papers  (2023-03-15T15:00:20Z)
• Quantum copy-protection of compute-and-compare programs in the quantum random oracle model [48.94443749859216]
  We introduce a quantum copy-protection scheme for a class of evasive functions known as " compute-and-compare programs" We prove that our scheme achieves non-trivial security against fully malicious adversaries in the quantum random oracle model (QROM) As a complementary result, we show that the same scheme fulfils a weaker notion of software protection, called "secure software leasing"
  arXiv  Detail & Related papers  (2020-09-29T08:41:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.