応用のための代数学（テキスト） Algebra for Applications : Cryptography, Secret Sharing, Error-correcting, Fingerprinting, Compression (Springer Undergraduate Mathematics)

Slinko, Arkadii

Springer Nature（2015/08発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 269 p.
• 言語 ENG
• 商品コード 9783319219509
• DDC分類 512

Full Description

This book examines the relationship between mathematics and data in the modern world. Indeed, modern societies are awash with data which must be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from an unauthorised access and transmitted over unreliable channels. All of these operations can be understood only by a person with knowledge of basics in algebra and number theory.This book provides the necessary background in arithmetic, polynomials, groups, fields and elliptic curves that is sufficient to understand such real-life applications as cryptography, secret sharing, error-correcting, fingerprinting and compression of information. It is the first to cover many recent developments in these topics. Based on a lecture course given to third-year undergraduates, it is self-contained with numerous worked examples and exercises provided to test understanding. It can additionally be used for self-study.

Contents

Integers.- Cryptology.- Groups.- Fields.- Polynomials.- Secret Sharing.- Error-Correcting Codes.- Compression.- Appendix A: GAP.- Appendix B: Miscellanies.- Solutions to Exercises.