Research on Next-Generation Cryptography

Relying on Quantum Interactions and L-Functions

Member Lists | ||
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Masato Wakayama | Professor, Institute of Mathematics for Industry, Kyushu University | HP |

Fumio Hiroshima | Professor, Faculty of Mathematics, Kyushu University | HP |

Masao Ishikawa | Professor, Graduate School of Natural Science and Technology, Okayama University | HP |

Jun Muramatsu | Senior Researcher, NTT Communication Science Laboratories | |

Kazufumi Kimoto | Professor, Faculty of Science, University of the Ryukyus | HP |

Yoshinori Yamasaki | Associate Professor, Graduate School of Science and Engineering, Ehime University | HP |

Shingo Sugiyama | Research Associate, College of Science and Technology, Nihon University | HP |

Nguyen Thi Hoai Linh | Research Fellow, Institute of Mathematics for Industry, Kyushu University | HP |

Cid Reyes | Research Fellow, Institute of Mathematics for Industry, Kyushu University |

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.