An Introduction to Number Theory with Cryptography

Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory.

The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum.

Features of the second edition include

• Over 800 exercises, projects, and computer explorations

• Increased coverage of cryptography, including Vigenere, Stream, Transposition, and Block ciphers, along with RSA and discrete log-based systems

• "Check Your Understanding" questions for instant feedback to students

• New Appendices on "What is a proof?" and on Matrices

• Select basic (pre-RSA) cryptography now placed in an earlier chapter so that the topic can be covered right after the basic material on congruences

• Answers and hints for odd-numbered problems

About the Authors:

Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School.

Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.

《數論與密碼學導論，第二版》在第一版的基礎上進一步擴充了對於密碼學這一熱門且重要的主題的涵蓋，並將其與傳統的數論主題相結合。

作者以引人入勝的風格撰寫了本書，以反映數論日益受到的歡迎。本書旨在供大二、大三和大四的本科生使用，但也適用於高中生進行獨立學習。對於希望超越傳統課程的學生，本書還包含了一些更高級的主題。

第二版的特點包括：

- 超過800個練習、項目和計算機探索
- 增加了對密碼學的涵蓋，包括維吉尼亞、流、置換和分塊密碼，以及RSA和離散對數系統
- 提供“檢查你的理解”問題，以便學生立即獲得反饋
- 新增附錄，介紹“什麼是證明？”和矩陣
- 將基礎（RSA之前的）密碼學放在較早的章節中，以便在對同餘的基礎材料進行學習後立即涵蓋該主題
- 提供奇數問題的答案和提示

關於作者：
Jim Kraft於1987年獲得馬里蘭大學的博士學位，並發表了幾篇代數數論的研究論文。他曾在羅徹斯特大學、加利福尼亞聖瑪麗學院和伊薩卡學院擔任教職，並在通信安全領域工作過。目前，Kraft博士在吉爾曼學校教授數學。

Larry Washington於1974年獲得普林斯頓大學的博士學位，並在數論領域發表了大量論文，包括與Wade Trappe合著的密碼學書籍、循環域和橢圓曲線。Washington博士目前是馬里蘭大學的數學教授和傑出學者教師。

Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School.

Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.

Jim Kraft於1987年從馬里蘭大學獲得博士學位，並在代數數論領域發表了多篇研究論文。他曾在羅徹斯特大學、加州聖瑪麗學院和伊薩卡學院擔任教職，並在通信安全領域工作過。Kraft博士目前在吉爾曼學校教授數學。

Larry Washington於1974年從普林斯頓大學獲得博士學位，並在數論領域廣泛發表論文，包括與Wade Trappe合著的密碼學書籍、循環域和橢圓曲線。Washington博士目前是馬里蘭大學的數學教授和傑出學者教師。