# Cryptography - Spring 2000

### Dr. Amos Beimel

Webster dictionary defines cryptography as: ``The enciphering and deciphering of messages in secret code or cipher.'' However, cryptography today is a much broader field; it aims to protect honest parties from malicious parties. For example, malicious parties can eavesdrop to the communication on the Internet and try to read messages sent by other parties; they can try to impersonate other parties, or login to computers without permission. Basic topics in cryptography are secure encryption, digital signatures, and fault-tolerant protocols. The course will cover these topics, their realizations, and applications.

This is a 4-credit course, consisting of two weekly 2-hour meetings. It is intended for graduate students and third year undergrad students. Pre-required course is the algorithms course.

## Announcements:

Ex 4 is checked. You can come to my office and take it.

## Course Book:

1. D. R. Stinson. CRYPTOGRAPHY: Theory and Practice. CRC Press. 1995.

## Lectures:

 Num. Topic Date Handouts, exercises textbook 1 Introduction.  Overview of course 21.2.00 Announcement 2 Classical encryptions and their cryptanalysis. 22.2.00 Chapter 1 3 Perfect encryption: definition, examples, and limitations. 28.2.00 Chapter 2.1 4 Data Encryption Standard (DES). 29.2.00 DES, Ex1 Chapters 3.1-3.3 5 Attacks on DES. 6.3.00 [Matsui] 6 DES modes of operations. Modular Arithmetic. 7.3.00 Chapter 3.4 Chapter 1.1.1 7 More Number Theory. 13.3.00 Chapters 4.2, 4.4 8 Even more Number Theory. 14.3.00 Ex2 Chapter 4.2 9 Arithmetic modulo composites. 27.3.00 10 The RSA public key encryption. 28.3.00 Chapters 4.3, 4.4 11 Attacks on RSA. 3.4.00 [Boneh] 12 Diffie-Hellman Key Exchange, ElGamal Encryption. 4.4.00 Chapters 5.1 (until p. 166), 8.2.2 13 Digital Signatures: Definitions,   Rabin's Signature scheme. 10.4.00 Ex3 Chapter 6.1,   Chapter 4.7 (modified) 14 ElGamal Signature scheme . 11.4.00 Chapter 6.2 15 DSS Signature scheme . 1.5.00 Chapter 6.3 16 Cryptographic Hash functions. 2.5.00 Chapters 7.1-7.3,7.6 17 Message Authentication Codes (MAC), CBC-MAC. 15.5.00 HMAC [BCK1] (ps)  (pdf) Chapter 3.4.1 18 HMAC and MAC based on universal hashing. 16.5.00 ex4 [BCK2] 19 Secure Socket Layer (SSL). 22.5.00 Slides: (1)  (2) (3)  (4) [Stallings,Chapters 14.1, 14.2] 20 SSL (cont.), Brief description of Secure Electronic Transmission (SET). 23.5.00 Slides: (5)  (6) [Stallings,Chapters 14.3 (pages 461-467)] 21 Thershold Secret Sharing Schemes. 29.5.00 [Chapter 11.1] 22 General Secret Sharing Schemes. 5.6.00 [Chapter 11.2] 23 Summary of Course. 6.6.00

[Matsui] M. Matsui. Linear Cryptanalysis Method for DES Cipher. In EUROCRYPT 93, vol. 765 of Lecture Notes in Computer Science, pages 386--397, Springer-Verlag, 1994.
[Boneh] D. Boneh. Twenty years of attacks on the RSA Cryptosystem. In Notices of the American Mathematical Society (AMS), Vol. 46, No. 2, pp. 203--213, 1999.
[BCK1] M. Bellare, R. Canetti, and H. Krawczyk. The HMAC Construction. CryptoBytes, Vol. 2, No 1, pages 12-15, 1996.
[BCK2] M. Bellare, R. Canetti, and H. Krawczyk. Keying Hash Functions for Message Authentication. Abridged version appears in CRYPTO '96, vol. 1109 of Lecture Notes in Computer Science, pages 1-15, Springer-Verlag, 1996.
[Stallings] W. Stallings. Cryptography and Network Security. Second Edition. Prentice Hall. 1998.

## Syllabus:

1. Introduction
• Overview of course
• Classical cryptography [Chapter 1].
2. Secret Key Encryption
• Perfect Secrecy - One time pads [Chapter 2.1].
• Merkle puzzles.
• Stream ciphers and the Data Encryption Standard (DES) [Chapter 3 (excluding 3.6.2 -3.6.3)].
3. Public Key Encryption
• Factoring and the RSA encryption [Chapter 4 (excluding 4.5 -4.8)].
• Discrete log. Diffie-Hellman Key Exchange [Chapter 8.4 (only pages 270-273)] . El Gamal encryption [Chapter 5 (only pages 162-164)] .
4. Digital Signatures [Chapter 6 (excluding 6.5 - 6.6)]
• One-time signatures.
• Rabin and ElGamal signatures schemes.
• Digital Signature Standard (DSS).
5. Hashing [parts of Chapter 7]
• Motivation and applications.
• Cryptographically Secure Hashing.
• Message Authentication Codes (MAC).
6. Network Security
• Secure Socket Layer (SSL)
• IPsec
7. Secret Sharing [Chapter 11.1,11.2,11.3]
• Definition. Shamir's threshold scheme.
• General secret sharing schemes.
• Visual secret sharing schemes.

## Other Books:

1. A. J. Menezes, P. C. van Oorschot and S. A. Vanstone. The Handbook of Applied Cryptography. CRC Press. 1996. Available online.
2. W. Stallings. Cryptography and Network Security. Second Edition. Prentice Hall. 1998.