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

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…

This paper systematically analyzes binomial functions over $\mathbb{F}_{p^n}$ in characteristic 3, providing a classification and rigorous proof of specific classes of exponents that yield extremely l…

The paper introduces a stringology-based fingerprinting (SBF) framework to structurally analyze cryptographic sequences, demonstrating that pattern analysis can reveal measurable structural signatures…

The paper proposes a novel method using random walks and equitable partitions to derive an inequality for the total variation distance of codes, generalizing existing bounds for finite abelian groups.

This paper analyzes the computational complexity of evaluating recurrent functions, showing that the complexity depends heavily on how the input offsets are encoded and the structure of the recurrence…

The paper proposes a novel set of combined cellular automaton (CA)-based pseudo-random number generators (PRNGs) that overcome the weak equidistribution issues of existing CA-based PRNGs, achieving ma…

This paper completely characterizes cyclic equalizability for two words over any finite alphabet by proving that the words must share the same Parikh vector.

This paper proposes Stringology-Based Cryptology (SBC), a novel approach that analyzes the structural properties of cryptographic outputs by treating them as symbolic sequences, offering complementary…

This paper presents methods for ranking and unranking permutations avoiding a pattern of length three in lexicographic or colexicographic order.

This paper measures the lower bound for the shortest program generating a sequence, proving a conservation law and providing a deterministic engine to recover generating programs for certain sequences…

The paper systematically investigates the conditions under which linear layers in AES-like ciphers avoid related-differential structures, proving that the MDS property is necessary and identifying spe…

This paper introduces a novel algorithm for generating k Hamming weight binary words in linear time while minimizing random bit consumption.

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 derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

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…

The paper analyzes language generation and identification in the limit under bounded memory, showing that memory constraints significantly alter learnability, particularly affecting achievable density…

The paper investigates the relationship between optimal proof systems and recursive jump operators, showing that while the existence of a jump operator rules out optimality, the converse is provably h…