Webster dictionary defines cryptography as: ``The enciphering and deciphering of messages in secret code or cipher.'' However, modern cryptography is a much broader field; it provides algorithms and protocols which protect honest parties from malicious parties. Malicious parties can, for example, 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 include secure encryption, digital signatures, and authentication.
In this course I will discuss these topics, their realizations, and applications. The material covers cryptosystems that are both practical and theoretically interesting. To achieve this goal, I'll also teach some background in number theory that is necessary to understand modern cryptosystems such as RSA. This is a 4credit course, consisting of two weekly 2hour meetings. It is intended for graduate students as well as third year undergraduate students. Prerequired course is the algorithms course.
Num.  Topic  Date  Handouts, exercises 
textbook 
1  Introduction.
Classic Encryption Systems 
5.3.01 
Announcement, syllabus 

2 (3 hours)  Classic encryptions; their cryptanalysis. Perfect encryption: examples, limitations.  6.3.01  Chapter 1
Chapter 2.1 

3 (3 hours)  Data Encryption Standard (DES).  26.3.01  DES, Ex1  Chapters 3.13.4 
4 (3 hours)  Attacks on DES.
Advanced Encryption Standard (AES). 
27.3.01 
[Matsui]
Rijndael 

5 (3 hours)  Introduction to Number Theory: modular arithmetic, Euclid's algorithm.  2.4.01  EX2  Chapters 1.1.1, 4.2, 4.4 
6 (3 hours)  Number Theory: Chinese remainder theorem, structure of Zp, Quadratic Residues.  3.4.01  Chapter 4.2  
7  The RSA public key encryption.  16.4.01  Ex3  Chapters 4.3, 4.4 
8  RSA: Implementations and Attacks.  17.4.01  [Boneh]  
9  DiffieHellman Key Exchange, ElGamal Encryption.  23.4.01  Chapters 5.1 (until p. 166), 8.2.2  
10  Digital Signatures: Definitions, Rabin's Signature scheme.  30.4.01  Ex4  Chapter 6.1, Chapter 4.7 (modified) 
11  ElGamal Signature scheme.
Onetime signature schemes. 
1.5.01  Chapter 6.2


12  Digital Signature Standard (DSS).  7.5.01  Chapter 6.3, [DSS]  
13  Cryptographic Hash functions.  8.5.01  Chapters 7.17.3,7.6  
14  Message Authentication Codes (MAC), CBCMAC.  14.5.01  Ex5  Chapter 3.4.1 
15  HMAC and MAC based on universal hashing.  15.5.01  [BCK1] (ps) (pdf)  [BCK1] [BCK2] 
16  Secure Socket Layer (SSL).  21.5.01  Slides: (1) (2) (3) (4) (5)  [Stallings,Chapters 14.1, 14.2] 
17  SSL (cont.), Brief description of IPsec.  22.5.01  [Stallings, Chapters 13]  
18  Threshold Secret Sharing Schemes.  5.6.01  Chapter 11.1  
19  Private Information Retrieval  11.6.01  
20  Summary of Course.  12.6.01  
21  Example questions  2.7.01 
Lectures hours:  Monday 1820, Room 224 Building 90 
Tuesday 1820, Room 224 Building 90  
Reception hours:  Monday 1315, Room 205 Building 58 (Math and CS) 
Email:  beimel at cs.bgu.ac.il 
Phone:  647 7858 