quartonews.it » Math and Science » CHINESE REMAINDER THEOREM: APPLICATIONS IN COMPUTING, CODING, CRYPTOGRAPHY

Author: | D Pei,A Salomaa,C Ding |

Subcategory: | Mathematics |

Language: | English |

Publisher: | World Scientific Publishing Company (October 25, 1996) |

Pages: | 222 pages |

Category: | Math and Science |

Rating: | 4.3 |

Other formats: | azw rtf mobi txt |

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Chinese Remainder Theorem : Applications in Computing, Coding, Cryptography. Chinese Remainder Theorem, CRT, is one of the jewels of mathematics. by C. Ding and Arto Salomaa. It is a perfect combination of beauty and utility or, in the words of Horace, omne tulit punctum qui miscuit utile dulci. Known already for ages, CRT continues to present itself in new contexts and open vistas for new types of applications.

I borrowed this book from the library, hoping to obtain insights in coding and cryptography through a better understanding of the Chinese Remainder Theorem. This theorem is a fascinating one, and I was happy to find (in the library catalog) a whole book on the subject, together with practical applications. Unfortunately, the book is not very well written. It uses some non-standard terminology, without any apparent reason, which just creates confusion for the reader.

Chinese Remainder Theorem: Applications In Computing, Coding, Cryptography Salomaa A Et Al World Scientific Publishing 9789810228279 : Chinese Remainder Theorem, CRT, is one of the jewels of . The individual chapters are largely independent and, consequently, the book can be used as supplementary material for courses in algorithmics, coding theory, cryptography or theory of computing. Of course, the book is also a reference for matters dealing with CRT.

KEYWORDS: Quantum Signature; Group Signature; Chinese Remainder Theorem. All the operations in signing and verifying phase can be executed in quantum circuits. JOURNAL NAME: Journal of Software Engineering and Applications, Vo. N. B, October 12, 2013.

oceedings{Ding1996ChineseRT, title {Chinese Remainder in Computing}, author {Chris H. Q. Ding and D. Y. Pei and Arto Salomaa}, year {1996} }. Chris H. Ding, D. Pei, Arto Salomaa. 2008 International Conference on Intelligent Information Hiding and Multimedia Signal Processing.

World Scientific Publishing Company.

Chinese Remainder Theorem : Applications in Computing, Coding, Cryptography Chinese Remainder Theorem. World Scientific Publishing Company.

Chinese Remainder Theorem, CRT, is one of the jewels of mathematics. Computing was its original field of application, and continues to be important as regards various aspects of algorithmics and modular computations. Theory of codes and cryptography are two more recent fields of application. This book tells about CRT, its background and philosophy, history, generalizations and, most importantly, its applications.

Ding, D. Pei and A. Salomaa, Chinese Remainder Theorem - Applications in Computing, Coding, Cryptography, World Scientific Publishing, 1996. J. Feigenbaum, Locally Random Reductions in Interactive Complexity Theory, in Advances in Computational Complexity Theory, DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 13, American Mathematical Society, Providence, pp. 73–98, 1993.

Video created by Калифорнийский университет в Сан-Диего, Национальный исследовательский университет "Высшая школа экономики" for the course "Number Theory and Cryptography"

Video created by Калифорнийский университет в Сан-Диего, Национальный исследовательский университет "Высшая школа экономики" for the course "Number Theory and Cryptography".

Chinese Remainder Theorem, CRT, is one of the jewels of mathematics. It is a perfect combination of beauty and utility or, in the words of Horace, omne tulit punctum qui miscuit utile dulci. Known already for ages, CRT continues to present itself in new contexts and open vistas for new types of applications. So far, its usefulness has been obvious within the realm of “three C's”. Computing was its original field of application, and continues to be important as regards various aspects of algorithmics and modular computations. Theory of codes and cryptography are two more recent fields of application.

This book tells about CRT, its background and philosophy, history, generalizations and, most importantly, its applications. The book is self-contained. This means that no factual knowledge is assumed on the part of the reader. We even provide brief tutorials on relevant subjects, algebra and information theory. However, some mathematical maturity is surely a prerequisite, as our presentation is at an advanced undergraduate or beginning graduate level. We have tried to make the exposition innovative, many of the individual results being new. We will return to this matter, as well as to the interdependence of the various parts of the book, at the end of the Introduction.

A special course about CRT can be based on the book. The individual chapters are largely independent and, consequently, the book can be used as supplementary material for courses in algorithmics, coding theory, cryptography or theory of computing. Of course, the book is also a reference for matters dealing with CRT.

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