[Impress Group] Learn everything from the basics to the cutting edge of cryptography and coding theory in this one book! “Learn Number Theory, Cryptography, and Coding Theory Through Calculations with PARI/GP” Published Impress Holdings Corporation Press Release: September 26, 2025 To Members of the Media Learn everything from the basics to the cutting edge of cryptography and coding theory in this one book! “Learn Number Theory, Cryptography, and Coding Theory Through Calculations with PARI/GP” Published Kindai Kagakusha Co., Ltd., a member of the Impress Group that publishes specialized books in the fields of science and engineering, began selling the hardcover version of “Number Theory, Cryptography, and Coding Theory” (author: Suzuki Hideo) on August 29, 2025, under the Kindai Kagakusha Digital label (※).
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https://prcdn.freetls.fastly.net/release_image/5875/6877/5875-6877-05f4a4f536a8d137a3946601bbd337b2-1820×2570.jpg ●Bibliographic information [Book title] Learn number theory, cryptography, and coding theory through calculations with PARI/GP [Author] Hideo Suzuki [Specifications] B5, paperback, black and white print version, partial color digital version, 382 pages [Printed version base price] ¥4,200 (excluding tax) [Digital version base price] ¥4,200 (excluding tax) 【ISBN】 (Paperback) 978-4-7649-0757-7 C3041 【ISBN】 (POD) 978-4-7649-6115-9 C3041 【Product
URL】https://www.kindaikagaku.co.jp/book_list/detail/9784764961159/ ●Contents This book is a textbook that provides an integrated explanation of the three subjects of “number theory,” “cryptography,” and “coding theory.” It particularly covers number theory, which is essential for understanding cryptography and coding theory. The chapter on number theory explains the set theory of numbers that underpins modern cryptography, algebraic concepts such as groups, rings, and fields, as well as fundamental theorems such as the principle of division, Euclidean algorithms, congruences, Fermat’s Little Theorem, and the Chinese Remainder Theorem. In particular, elliptic curve operations and Galois fields (finite fields) are explained in great detail. The appendix includes a program that lists all primitive polynomials that can generate Galois fields. The chapter on cryptography focuses on the principles behind modern cryptography and the mathematical challenges that underpin its security. It delves into fundamental cryptographic challenges, such as the security level of public key cryptography, the prime factorization problem, and the discrete logarithm problem, and provides detailed explanations of key technologies such as key exchange protocols, digital signatures, one-way hash functions, message authentication codes (MACs), blockchain, and cryptocurrency. The chapter on coding theory provides an explanation of error correction techniques in information transmission, comprehensively introducing a wide range of coding techniques, from basic concepts of coding theory to the Fundamental Theorems of Source and Channel Coding, LZ77 codes, linear codes, cyclic codes, Hamming codes, Reed-Solomon (RS) codes, BCH codes, convolutional codes, turbo codes, LDPC codes, and the mechanisms of QR codes. This book also presents numerous programming examples using PARI/GP and SageMath. By reliving the actual calculation process, you can gain deep insight into the operating principles and mathematical properties of each algorithm. This is a comprehensive textbook that will also help you acquire practical application skills. ●About the Author Hideo Suzuki Born in Mie Prefecture Completed doctoral course at Tohoku University Graduate School, Ph.D. (Engineering) After working as an assistant at Tohoku University and a visiting researcher at Stanford University, he is currently a professor at Tokyo University of Information Technology. ●Table of Contents Chapter 1: Number Theory 1.1 Modern Cryptography and Number Theory 1.2 Set of Numbers 1.3 Modulus Systems (Sets of Remainders When Divided by Mod) 1.4 Groups, Rings, and Fields 1.5 Polynomial Rings 1.6 Number Theory Calculator 1.7 Number Theory Basics 1.8 Division, Remainders, and Euclidean Algorithms 1.9 Congruence (≡) 1.10 Fermat’s Little Theorem and Its Extension 1.11 Solution of ax≡b(mod m) 1.12 Simultaneous congruence, Chinese 剩艩 theorem 1.13 Polynomial in mod 1.14 Primordial root (generator) 1.15 (mod n) (mod p) Calculating powers and logarithms in x 1.16 Quadratic congruences, quadratic remainders, and quadratic non-remainders 1.17 Modular exponentiation in Z31×x (n = 2, 3, 5, 6, 10, 15, 25) 1.18 Operations on elliptic curves 1.19 Galois field (finite field) Chapter 2 Cryptography Theory 2.1 Modern Cryptography 2.2 Security Levels of Public Key Cryptography 2.3 Decryption Challenge 2.4 Cryptographic Method Selection Competition 2.5 Privacy-Enhancing Technologies (PET) 2.6 OpenSL Encryption Functions Available on Your Computer (PC) 2.7 Arbitrary Precision Arithmetic Package 2.8 Secret Key Cryptography 2.9 Encryption Mode 2.10 Public Key Cryptography 2.11 Number theory problems that form the basis of modern cryptography 2.12 Prime factorization problem 2.13 Discrete logarithm problem 2.14 Key exchange 2.15 Digital Signatures 2.16 One-Way Hash Functions 2.17 Message Authentication Codes (MAC) 2.18 Zero-Knowledge Interactive Proof 2.19 NIST PQC (Post-Quantum Cryptography) 2.20 SIKE (SIDH-based Key Exchange Method) 2.21 McEliece Cipher 2.22 Lattice cryptography Chapter 3 Coding Theory 3.1 Fundamentals of coding theory 3.2 Information source encoding 3.3 Shannon code and Fano code 3.4 Huffman code 3.5 LZ77 (Lempel Ziv 1977) code 3.6 Channel encoding 3.7 Error detection code 3.8 Linear code 3.9 Examples of systematic and non-systematic codes ((7,4,3) Hamming code) 3.10 Cyclic code 3.11 Hamming code 3.12 (8,4,4) Extended Hamming code 3.13 Reed Solomon (RS) code 3.14 BCH code 3.15 Reed Muller (RM) code 3.16 Polar code 3.17 Convolutional code 3.18 Turbo sign 3.19 LDPC code 3.20 QR code Appendix A A.1 PARI/GP installation method A.2 Tips for PARI/GP calculation A.3 PARI/GP Command Problem Practice A.4 PARI/GP Array-Related Command Problem Practice A.5 PARI/GP User-Defined Function Program List A.6 PARI/GP User-Defined Function Program A.7 AES Encryption and Decryption Program Using PARI/GP A.8 How to Install SageMath A.9 Tips for SageMath Calculations A.10 Elliptic Curve Factorization Software GMP-ECM A.11 Prime Factorization Software Msieve A.12 Alpern’s Prime Factorization WebAssembly Program A.13 WebAssembly A.14 Solving Simultaneous Equations A.15 Greek Letters A.16 Prime numbers p less than 6473 (840) and the smallest primitive root g
Kindaikagakusha Digital https://www.kindaikagaku.co.jp/kdd/index.htm Kindaikagakusha Digital is a 21st-century science and technology publishing label promoted by Kindaikagakusha Co., Ltd. By proactively utilizing the power of digital technology, we propose a speedy, on-demand, and sustainable publishing model. 【Kindaikagaku Co., Ltd.】 https://www.kindaikagaku.co.jp/ Kindai Kagakusha Co., Ltd.
(Headquarters: Chiyoda-ku, Tokyo; President and CEO: Hiroaki Otsuka) was founded in 1959. We are engaged in publishing a wide range of specialized science and engineering fields, including academic books based on mathematics, mathematical science, information science, and information engineering, as well as university textbooks for science and engineering. We cover a wide range of topics, from classics to cutting-edge interdisciplinary fields, to meet modern needs that go beyond basic knowledge of the natural sciences and require advanced applications. We also collaborate with major academic societies and associations, as well as renowned research institutions, to pursue academic excellence that meets global standards. 【Impress Group】 https://www.impressholdings.com/ Impress Holdings Corporation (Headquarters: Chiyoda-ku, Tokyo; Representative Director: Yuki Tsukamoto) is a media group with its holding company. We offer highly specialized media, services, and solutions focused on the key themes of “IT,” “music,” “design,” “mountaineering and nature,” “aviation and railways,” “mobile services,” and “academics and science and engineering.” We also develop and operate content business platforms. 【Contact Information】 Kindai Kagakusha Co., Ltd. TEL: 03-6837-4828 Email: kdd-qa@kindaikagaku.co.jp Press release attachments