The paper analyzes subcodes of lambda-Gabidulin codes to construct highly efficient McEliece-like and Niederreiter-like cryptosystems, demonstrating that random subcodes of classical Gabidulin codes y…

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…

This paper shows that any boolean matrix with bounded factorization norm can be expressed as a signed sum of blow-up identity matrices, and this result has applications to matrix sequences and complex…

This paper provides a uniform construction for counting the number of flat-foldable assignments in an origami Miura-ori crease pattern with a specific number of single face flips.

This paper introduces a robust OR polynomial framework to derive certificates for positive semidefinite matrices across OR constraints, and applies it to acute-free families and multicolor Ramsey numb…

The paper develops an explicit multi-linear polynomial form for binary polynomial optimization problems after eliminating a subset of variables, allowing for characterization of new special classes wi…

This paper identifies new, algebraically weak classes of instances for the Linear Equivalence Problem (LEP) by generalizing techniques from the Permutation Equivalence Problem (PEP) using power codes…

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.

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 investigates the closeness of singularity for $n imes n$ unimodular matrices, specifically for $(2k+1)$-ary and $(k+1)$-ary cases of $4 imes 4$ nonnegative unimodular matrices.

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 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…

The paper formalizes Razborov's flag algebra method for finite simple graphs and creates a compiler to transform certificate data into algebraic proofs checked by Lean.

This paper introduces and studies the block tensor rank of sum-rank metric codes, showing its additive decomposition and deriving lower bounds.

The paper provides the first machine-checked universal proof, using ring theory, that value-independence implies identical marginal distributions for arithmetic masking, thereby extending the verifica…

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 presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.