Lecture Notes

Week	Lecture Notes	Topics
1	Redundancy and Information Theory (.pdf - file of slides)	Hamming Error Correction, Entropy, Markov Processes, Redundancy
2a	Classical Cryptology (.pdf - file of slides)	Concealment, Russian Nihilist, Bacon's Bi-Literal Cipher, Transposition Substitution (Monoalphabetic, Polyalphabetic)
2b	Classical Cryptology cont. (.pdf - file of slides)	Hill Cipher, Cryptanalysis of a Monoalphabetic Substitution, Friedman (Kappa) Test Cryptomachines, Enigma, One-Time Pad, Kerckhoff's Principle
3	Linear Feedback Shift Registers (.pdf - file of slides)	Pseudo-Random Sequences, Feedback Shift Registers, LFSR's, PN-sequences, Linear Equivalence Minimal Characteristic Polynomials, Non-linear functions, Jennings Multiplexing Algorithm
4	Data Encryption Standard (DES) Advanced Encryption Standard (AES) (.pdf - file of slides)	The DES Algorithm, Weaknesses of DES, Modes of Operation, Message Authentication Rijndael, GF(256), AES algorithm, Decrypting Rijndael
5-7	Public Key Cryptosystems (.pdf - file of slides)	Difficulties with Private Keys, Public Keys, Trapdoor Functions, Signature Schemes
5a	RSA (.pdf - file of slides)	RSA Algorithm, Euler's function, Practical Considerations, Breaking RSA, PGP
5a	The extended Euclidean Algorithm (.pdf - file of slides)	Division, Euclidean Algorithm, Extended Euclidean Algorithm, Inverses mod n, Example
5b	The Solovay-Strassen Primality Test (.pdf - file of slides)	Quadratic residues, Legendre symbol, Jacobi symbol, Pseudo-Primes Solovay-Strassen Algorithm
6a	Protocol Failure (.pdf - file of slides)	Square and Multiply, Dictionary Attacks, Common Modulus Problem, Other Failures
6b	Knapsack Problems (.pdf - file of slides)	Subset Sum Problem, Super Increasing Sets, Merkle-Hellman Cryptosystem, Security
7	Finite Fields (.pdf - file of slides)	Characteristic, Splitting fields, Constructing fields, Finding Irreducible Polynomials GF(8), GF(9), Subfields, Automorphisms of fields
8	Factoring (.pdf - file of slides)	Trial Division, Fermat Factoring, p-1 factoring, factor base algorithms, Quadratic Sieve RSA Challenge Numbers
9a	Discrete Logarithm Problem (.pdf - file of slides)	Diffie-Hellman Key Exchange, Man in the Middle Attack, El-Gamal's Cryptosystem Shank's Algorithm, Pohlig-Hellman Algorithm
9b	The Chinese Remainder Theorem (.pdf - file of slides)	The algorithm, example
9b	Example of the Pohlig-Hellman Algorithm (.pdf - file of slides)	Example
10	Digital Signatures (.pdf - file of slides)	RSA Signatures, El-Gamal Signature Scheme, Hash Functions, Birthday Attacks Digital Signature Standard
11	Coding Theory I Coding Theory II Coding Theory III (.pdf - file of slides)	Linear Codes, Hamming Codes, Syndrome Decoding
12a	McEliece Cryptosystem (.pdf - file of slides)	The cryptosystem, example, drawbacks, security, Goppa Codes
12b	Intro to Projective Geometry (.pdf - file of slides)	Vector spaces, Projective Geometries, Coordinates, Hyperplanes, Ovals, Conics, Knots
13	Secret Sharing Schemes (.pdf - file of slides)	Shamir's Threshold Scheme, Geometric Schemes, Multilevel Schemes, Bank example
14	Elliptic Curve Schemes (.pdf - file of slides)	Forms, Addition Law, Even Characteristic, Hasse's Theorem, Elliptic Curve Cryptosystem Discrete Logs, Representing Plaintext, El-Gamal Digital Signature Scheme, Factoring
15	Current Events (.pdf - file of slides)	Topics vary
16a	Identification Schemes (.pdf - file of slides)
16b	Authentication Codes (.pdf - file of slides)