Daniel Panario

Computing Gröbner bases associated with lattices

2016 · Advances in Mathematics of Communications

We specialize Möller's algorithm to the computation ofGröbner bases related to lattices. We give the complexityanalysis of our algorithm. Then we provide experiments showingthat our algorithm is more efficient than Buchberger's algorithmfor computing the associated …

Evaluating the generalized Buchshtab function and revisiting the variance of the distribution of the smallest components of combinatorial objects

2022 · arXiv (Cornell University)

Let $n\geq 1$ and $X_{n}$ be the random variable representing the size of the smallest component of a random combinatorial object made of $n$ elements. A combinatorial object could be a permutation, a monic polynomial …

A Concrete LIP-Based KEM With Simple Lattices

2024 · IEEE Access

Recent developments have been made in the construction of cryptosystems with security based on the hardness of the lattice isomorphism problem (LIP). Due to lattice conjectures, one may expect in the future that breaking such …