Related papers: Lossy Cryptography from Code-Based Assumptions
Property-preserving hash functions allow for compressing long inputs $x_0$ and $x_1$ into short hashes $h(x_0)$ and $h(x_1)$ in a manner that allows for computing a predicate $P(x_0, x_1)$ given only the two hash values without having…
We introduce a new protocol for a lossy data compression algorithm which is based on constraint satisfaction gates. We show that the theoretical capacity of algorithms built from standard parity-check gates converges exponentially fast to…
We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first…
By analogy with the developed cryptographic theory of discrete logarithm problems, we define several hard problems in Entropoid based cryptography, such as Discrete Entropoid Logarithm Problem (DELP), Computational Entropoid Diffie-Hellman…
In this work, we study the discrete logarithm problem in the context of TFNP - the complexity class of search problems with a syntactically guaranteed existence of a solution for all instances. Our main results establish that suitable…
The use of codes defined by sparse characteristic matrices, like QC-LDPC and QC-MDPC codes, has become an established solution to design secure and efficient code-based public-key encryption schemes, as also witnessed by the ongoing NIST…
Polynomial Pigeonhole Principle (PPP) is an important subclass of TFNP with profound connections to the complexity of the fundamental cryptographic primitives: collision-resistant hash functions and one-way permutations. In contrast to most…
Our main result is a reduction from worst-case lattice problems such as GapSVP and SIVP to a certain learning problem. This learning problem is a natural extension of the `learning from parity with error' problem to higher moduli. It can…
Lattice-based cryptography has emerged as one of the most prominent candidates for post-quantum cryptography, projected to be secure against the imminent threat of large-scale fault-tolerant quantum computers. The Shortest Vector Problem…
Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…
We introduce a cryptographic primitive named threshold trapdoor functions (TTDFs), from which we give generic constructions of threshold and revocation encryptions under adaptive corruption model. Then, we show TTDF can be instantiated…
Identifying governing partial differential equations (PDEs) from noisy spatiotemporal data remains challenging due to differentiation-induced noise amplification and ambiguity from overcomplete libraries. We propose a prior-informed…
We discuss the performance of Low-Density-Parity-Check (LDPC) codes decoded by means of Linear Programming (LP) at moderate and large Signal-to-Noise-Ratios (SNR). Utilizing a combination of the previously introduced pseudo-codeword-search…
Semi-supervised learning (SSL) assumes that neighbor points lie in the same category (neighbor assumption), and points in different clusters belong to various categories (cluster assumption). Existing methods usually rely on similarity…
In this paper, we construct protograph-based spatially coupled low-density parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L, we obtain…
The significant progress in constructing graph spanners that are sparse (small number of edges) or light (low total weight) has skipped spanners that are everywhere-sparse (small maximum degree). This disparity is in line with other network…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the CPA-anonymity and traceability requirements in the random oracle…
Since the classical work of Berlekamp, McEliece and van Tilborg, it is well known that the problem of exact maximum-likelihood (ML) decoding of general linear codes is NP-hard. In this paper, we show that exact ML decoding of a classs of…
The security of the proposed quantum Internet relies on repeater protocols designed under the assumption of stochastic, characterizable noise. We demonstrate that in adversarial environments this assumption induces performance…