The paper presents a new worst-case to average-case reduction for the Learning Parity with Noise (LPN) problem, achieving hardness for inverse-polynomial noise rates previously unattainable.

The paper analyzes low-degree estimation thresholds for recovering hidden signals in planted hypergraphs and tensor PCA, establishing sharp phase transitions and providing polynomial-time recovery alg…

The paper introduces a novel public key encryption scheme with high security by leveraging the conjectured intractability of two types of highly corrupted constraint satisfaction problems (CSPs).

The paper refutes Steurer's conjecture regarding the existence of large constant-separated sets within families of unit-norm vectors with low average correlation, using high-dimensional expanders to s…

This paper unconditionally proves the Orthogonal Vectors and Monotone Orthogonal Vectors conjectures in concrete computational models, and provides stronger lower bounds for Boolean formulas and branc…

The paper studies the resources required to batch verify Boolean functions and provides lower bounds on the witness-query tradeoff based on approximate degree.

The paper establishes new hardness amplification results for Learning Parity with Noise (LPN) and its sparse variants, showing that solving the problem on a small fraction of instances implies solving…

The paper proves a stochastic comparison for Gaussian maxima, resolving the Weak Simplex Conjecture and proving the Simplex Mean Width Conjecture.

This paper introduces witness complexity, a measure for the minimum running time of a string's near-shortest description on a universal Turing machine.

This paper studies the existence of polynomial measures of dependence between two random variables that satisfy the data processing inequality and vanish on independence. It proves that no such polyno…

This paper proves that random linear codes have nearly optimal discrepancy properties in various regimes, extending classical results and enabling new applications.

This paper connects a generalized notion of tensor rank with multiplicative complexity, enabling control of arithmetic complexity in any constant degree of multilinearity and applications to fine-grai…

This paper extends quantum lattice reduction techniques (CDPR) from ideal to module lattices over cyclotomic rings, achieving a constant module reduction factor and providing a rigorous, bounded-preci…

The paper addresses secure distributed hypothesis testing, proving impossibility in the standard setting and achieving secure testing for simple and general classes by incorporating a shared secret ke…

The paper introduces a modular version of rank and linear-complexity tests for pseudorandom number generators and provides a Rust program, modlin, to detect statistical bias in generators that are lin…