Chris Christensen


Professor of Mathematics
Department of Mathematics
Northern Kentucky University
Highland Heights
, KY 41099

859-572-6672
FAX: 859-572-6097
 

MAT 483 - 001

Fall 2007

 

Here is a copy of the syllabus for MAT 483 - 001.

Here is a copy of the Department of Mathematics syllabus that applies to all MAT and STA classes.

Form for encryption and cryptanalysis

Some software and projects from previous classes can be found at http://www.nku.edu/~mcsc/mat494/.

Monday, August 20

            Simple substitution ciphers

            Solving a cryptogram

For Wednesday, August 22:  Solve the cryptogram that you received and create two cryptograms (around 120 characters).  One cryptogram should show word length and punctuation; the other should not – it should be blocked in 5-letter blocks.

Wednesday, August 22

For Friday, August 24:  Solve the cryptogram that you received that included word length and punctuation.  Be prepared to discuss your solution and how you constructed the key for the ciphertext that you created.

            Next week we will discuss how you did with the ciphertext that did not have word length and punctuation.

Friday, August 24

           Create a Caesar cipher to exchange on Monday.  Do not give word length or punctuation; block in five-letter blocks.

            Caesar ciphers

Monday, August 27

            Multiplicative ciphers

            For Wednesday, August 29, cryptanalyze the Caesar cipher that you received.

Wednesday, August 29

            Multiplicative ciphers.

Friday, August 31

            Euclidean Algorithm

            Euclid's Elements

Monday, September 3

            Holiday

Wednesday, September 5

            Affine ciphers

            Examples

            For Friday, create an affine cipher to exchange form.  Use a = 1, …, z = 26.

Friday, September 7

            Keyword ciphers

            Examples

            For Monday, create three ciphers to exchange – one affine (not Caesar or multiplicative), one Caesar, and one keyword.

            On Monday we will discuss the affine ciphers that you exchanged today.

Monday, September 10

           

Wednesday, September 12

            Homophonic ciphers

            Playfair cipher

            For Friday, create a Playfair cipher to exchange.  Give at least one line of plaintext as a crib.

Friday, September 14

            Digraph frequencies

            Monday, discuss the three unknown ciphers that you received on Wednesday and the three keyword cipher exercises that were distributed in class.

 

Monday, September 17

            Hill cipher

            A Playfair cipher in literature

            For Monday, find the Playfair square for the plaintext/ciphertext that you received.

Wednesday, September 19

            For Friday, encrypt a 2 X 2 Hill cipher to exchange.  Give a crib.

Test one

            Here is a pdf of test one.

            Here is a Word file of test one.

Wednesday, September 26

            Transposition ciphers

Friday, September 28

            Example

            ADFGVX cipher

            For Monday, encrypt a transposition cipher to exchange.

Monday, October 1

            Cryptography of the Vigenere cipher

            Gronsfeld cipher

            For Wednesday, create a Vigenère cipher to exchange

Wednesday, October 3

            Cryptanalysis of the Vigenere cipher

Friday, October 5

            Friedman test

            Determing length of keyword

            For Friday, October 12, break the transposition cipher and the Vigenère cipher that you received.

Monday, October 8

            Enigma

            Setting up Enigma

            Enigma monthly setting sheet from Codebreakers by Hinsley and Stripp.

            Link to Tony Sale’s Enigma emulator http://www.codesandciphers.org.uk/enigma/emachines/enigmad.htm

Wednesday, October 10

            Viewed Ultra Enigma.

            For Friday, break the transposition cipher and the Vigenère cipher that you received.

Friday, October 12

            For next Wednesday, encrypt an Enigma message.  Instructions.

 

Monday, October 15

Fall break.

 

Friday, October 19

Read chapter 6.

SIGSALY

Picture of the US-soviet Union hotline

 

Monday, October 22

No class.

 

Wednesday, October 24

Stream ciphers

ASCII

Examples

http://www.cs.uky.edu/~klapper/

 

Wednesday, October 31

 

Introduction to DES from Trapp & Washington Introduction to Cryptography with Coding Theory

Simplified DES algorithm from Trapp & Washington

Example of simplified DES algorithm

DES algorithm  from Schneier’s Applied Cryptography

http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation  wikipedia discussion of block cipher modes

 

http://www.cacr.math.uwaterloo.ca/hac/ link to Handbook of Applied Cryptography by Menezes, van Oorschot, and Vanstone

 

 

 

Here is a copy of test two.

 

Here is Word file of test two.

 

Monday, November 5

Craig Bauer “Cryptanalysis of the Running Key Cipher”

 

Wednesday, November 7

Introduction to finite fields I

 

Friday, November 9

Introduction to finite fields II

 

Monday, November 12

Simplified IDEA algorithm by Nick Hoffman.

 

Wednesday, November 14

Simplified AES

 

Friday, November 16

Introduction to public key cryptography

 

Monday, November 19

Knapsack cipher

 

Monday, November 26

A superincreasing set of weights.

{3, 4, 8, 16, 32, 64, 128, 260, 520, 1040, 2080, 4160, 8320, 16640, 33300, 66580, 133200, 266400, 532800, 1066000, 2132000, 4264000, 8530000, 17060000}.

A modulus

68236000

A multiplier

321

Scientific American article introducing RSA.

 

Wednesday, November 28

RSA

 

Friday, November 30

Modular exponentiation

Mathematical attack on RSA

 

Here is a copy of the final exam.

Here is a Word file of the final exam.

 

Monday, December 3

Primality testing

The mathematics of the RSA cryptosystem

Twenty years of attack on the RSA cryptosystem