H. デルフス

H. クネーブル

Hans Delfs

Helmut Knebl

林 芳樹

Due to the rapid growth of digital communication and electronic data exchange, information security has become a crucial issue in industry, business, and administration. Modern cryptography provides essential techniques for securing information and protecting data. In the first part, this book covers the key concepts of cryptography on an undergraduate level, from encryption and digital signatures to cryptographic protocols. Essential techniques are demonstrated in protocols for key exchange, user identification, electronic elections and digital cash. In the second part, more advanced topics are addressed, such as the bit security of one-way functions and computationally perfect pseudorandom bit generators. The security of cryptographic schemes is a central topic. Typical examples of provably secure encryption and signature schemes and their security proofs are given. Though particular attention is given to the mathematical foundations, no special background in mathematics is presumed. The necessary algebra, number theory and probability theory are included in the appendix. Each chapter closes with a collection of exercises. The second edition contains corrections, revisions and new material, including a complete description of the AES, an extended section on cryptographic hash functions, a new section on random oracle proofs, and a new section on public-key encryption schemes that are provably secure against adaptively-chosen-ciphertext attacks.

内容紹介

This book covers key concepts of cryptography, from encryption and digital signatures to cryptographic protocols, presenting techniques and protocols for key exchange, user ID, electronic elections and digital cash. Advanced topics include bit security of one-way functions and computationally perfect pseudorandom bit generators. Assuming no special background in mathematics, it includes chapter-ending exercises and the necessary algebra, number theory and probability theory in the appendix. This edition offers new material including a complete description of the AES, a section on cryptographic hash functions, new material on random oracle proofs, and a new section on public-key encryption schemes that are provably secure against adaptively-chosen-ciphertext attacks.

内容詳細

Due to the rapid growth of digital communication and electronic data exchange, information security has become a crucial issue in industry, business, and administration. Modern cryptography provides essential techniques for securing information and protecting data. In the first part, this book covers the key concepts of cryptography on an undergraduate level, from encryption and digital signatures to cryptographic protocols. Essential techniques are demonstrated in protocols for key exchange, user identification, electronic elections and digital cash. In the second part, more advanced topics are addressed, such as the bit security of one-way functions and computationally perfect pseudorandom bit generators. The security of cryptographic schemes is a central topic. Typical examples of provably secure encryption and signature schemes and their security proofs are given. Though particular attention is given to the mathematical foundations, no special background in mathematics is presumed. The necessary algebra, number theory and probability theory are included in the appendix. Each chapter closes with a collection of exercises. The second edition contains corrections, revisions and new material, including a complete description of the AES, an extended section on cryptographic hash functions, a new section on random oracle proofs, and a new section on public-key encryption schemes that are provably secure against adaptively-chosen-ciphertext attacks.

From the reviews: "Introduction to Cryptography discusses basic and also some more advanced aspects of public-key cryptography. Two appendices provide necessary mathematical prerequisites. Appendix A covers necessary background in algebra and number theory, Appendix B in probability and information theory. The book provides a useful introduction to public-key cryptography with the exception of elliptic curve cryptography. It gives not only a standard informal description of the key structures, but presents also strict mathematical definitions and proofs of some cryptographic properties." (Lenka Fibikova, Zentralblatt MATH, Vol. 995 (20), 2002)

レビュー

本書では、前半で、対称および非対称鍵概念、デジタル署名、暗号プロトコル(相手認証方式、電子選挙、電子現金等)を扱っている。後半では、暗号方式の安全性や関数の一方向性の性質のような基礎概念がどのように厳密化されうるか、またRSA方式のような公開鍵暗号方式の安全性をどんな仮定が保障するかを、確率論を使用して示した。一方向性関数のビット安全性、計算量的完全擬似ランダム生成器、ランダム性と暗号方式の安全性の間の緊密な関係のような、より進んだ話題が解説し、証明可能安全暗号方式や署名方式の典型的な例、そしてそれらの安全性証明を与えている。

暗号と確率的アルゴリズム入門―数学理論と応用

F. シャトラン

Francoise Chaitin‐Chatelin

伊理 正夫

伊理 由美

本書は線形代数の入門書よりも一歩進んだ知識を体系的に整理し、中核的主題『固有値問題』に的を絞った応用志向のテキストである。理論的事項から最新の数値計算技法までが、広角度の応用をねらいとして平易に具体的に解説がなされている。練習問題:良問だけを120題に精選(解答付き)。独習にも最適。

出版社：シュプリンガーフェアラーク東京の検索結果

暗号と確率的アルゴリズム入門―数学理論と応用

行列の固有値―最新の解法と応用