## Lecture Notes

Lecture notes are available as either webpages or as .pdf files of the slides used in class. Most lectures cover two class periods, but some are shorter and those which are only for one class period are indicated with an a or b in the week designation.

Week Lecture NotesTopics
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)
(.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
6bKnapsack 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
8Factoring
(.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
10Digital 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
12aMcEliece Cryptosystem
(.pdf - file of slides)
The cryptosystem, example, drawbacks, security, Goppa Codes
12bIntro 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
14Elliptic 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
15Current Events
(.pdf - file of slides)
Topics vary
16aIdentification Schemes
(.pdf - file of slides)
16bAuthentication Codes
(.pdf - file of slides)

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