Research Objectives:
Research on Next-Generation Cryptography
Relying on Quantum Interactions and L-Functions

The safety of the RSA encryption, which is based on the computational intractability of the prime factorization, is no longer assured if quantum computers are realized. Quantum interaction models like the quantum Rabi model are used in a basic element of quantum computers.
We study the mathematical structure of such models. Among them, the non-commutative harmonic oscillators (NcHOs) are thought to be a sort of universal one. We aim to extend the existing theory and methodology about the NcHOs and to clarify the structure of models treated in quantum optics from various viewpoints — representation theory, number theory, functional analysis and dynamical system. We also develop the efficient method to perform extensive numerical experiments by using systems of orthogonal functions towards verification of the deep Riemann hypothesis (DRH) for various kinds of zeta and L-functions. Furthermore, we study the DRH and its relation to the post-quantum cryptography along with new construction of Ramanujan graphs through L-functions by employing the probability theory and combinatorial theory.