This paper studies the expressivity of shallow polynomial neural networks with monomial activation functions over finite fields, quantifying it by the cardinality of the neuromanifold and deriving low…

The paper explains a method for finding the number of solutions to a system of multivariate polynomial inequalities over a finite field and applies it to find formulas for the number of contiguous sup…

This paper introduces new algorithms for finding prime numbers up to a given bound, achieving a speedup of log N over the sieve of Eratosthenes.

The paper proves that the reversible elementary second order cellular automaton rule 115 is periodic when started on finite initial configurations.

The paper establishes bijections between tree records, girth of connected endofunctions, and genesis sequences, deriving generating functions for tree and forest record numbers using Cayley's tree fun…

This paper provides the first comprehensive cryptanalysis of the Legendre Pseudorandom Function over extension fields, demonstrating key recovery attacks under both passive and active threat models.

This paper identifies a technical oversight in Mossel and Peres (2005) theorem on designing Bernoulli factories for multivariable functions and provides a counterexample.

This paper introduces the concept of 'large' zeros in linear recurrence sequences and establishes that they either do not exist or are very sparse, which could lead to decidability of the Skolem Probl…

This paper presents a new nondeterministic finite automaton (NFA) for recognizing repetition-free words over a given alphabet, improving on the previous construction.

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…

This paper provides a focused, preparatory introduction to sheaves and topoi, establishing the necessary structural background to understand the advanced sheaf-theoretic framework used in cryptographi…

This paper provides the first unconditional proof for Weber's Conjecture for the case $k ext{ up to } 12$, which is crucial for lattice-based cryptography.

The paper introduces the base-m length codec, a canonical and robust encoding scheme that maps byte strings to lists of residues modulo m, essential for finite-ring cryptosystems.

The paper shows that syntactic separation implies computational indistinguishability in local syntactic systems, proving new derivation-length and cryptographic bounds.

This paper presents a quantum attack on Module-LWE based lattice schemes like ML-KEM, demonstrating a polynomial-time quantum algorithm with a high success probability.

This paper characterizes the graph structure, including cycle and path lengths, of Chebyshev permutation polynomials over the ring $\mathbb{Z}_{2^{k_1}3^{k_2}}$, demonstrating strong regularities desp…