International Symposium on Mathematics, Quantum Theory, and Cryptography: Proceedings of MQC 2019Tsuyoshi Takagi, Masato Wakayama, Keisuke Tanaka, Noboru Kunihiro, Kazufumi Kimoto, Yasuhiko Ikematsu This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography. |
Contents
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xii | |
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Number Theoretic Study in Quantum Interactions | 95 |
A Data Concealing Technique with Random Noise Disturbance and a Restoring Technique for the Concealed Data by Stochastic Process Estimation | 102 |
Quantum Optics with Giant Atomsthe First Five Years | 125 |
Topics in Mathematics | 147 |
Extended Divisibility Relations for Constraint Polynomials of the Asymmetric Quantum Rabi Model | 149 |
Generalized GroupSubgroup Pair Graphs | 169 |
PostQuantum Cryptography | 186 |
A Survey of Solving SVP Algorithms and Recent Strategies for Solving the SVP Challenge | 189 |
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Resource Estimation and Survey of Experiments | 39 |
Towards Constructing Fully Homomorphic Encryption without Ciphertext Noise from Group Theory | 56 |
From the Bloch Sphere to PhaseSpace Representations with the GottesmanKitaevPreskill Encoding | 79 |
Quantum Interactions | 93 |
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Common terms and phrases
algorithm assumption attack Author(s Cayley graphs chapter’s Creative Commons ciphertext concealed data constraint polynomials construction coupling points Creative Commons license cryptography cryptosystems CSIDH decryption defined denote eigenvalue element elliptic curves encoded encryption scheme equation expander graphs finite giant atoms given group G hash functions homomorphic encryption integer isogenies j-invariants key exchange Kimoto Kockum Lamb shifts lattice vector Lemma linear LNCS Math Mathematics for Industry matrix min-entropy multivariate output p-value pair graphs parameter Phys pictorial image plaintext polynomials post-quantum problem proof public key quadratic quantum circuits quantum computer quantum factoring quantum optics quantum Rabi model quaternion algebra qubit Ramanujan graphs random number realization relaxation rates samples secret key Sect sequence Shor’s small atoms Springer superconducting supersingular Takagi Theorem theory Toffoli gate users variables Wakayama waveguide Wigner function