This is an upper level MATH course. It is directed at
students in mathematics, electrical engineering, or computer science
who have strong interest in mathematics and want to learn about the
exciting applications of algebra and number theory to cryptography
(encryption/decryption) and cryptanalysis (attacking encrypted messages).
Topics to be covered include:
Cryptography: Simple Ciphers and Cryptograms.
Vigenere Cipher, Hill Cipher, Data Encryption Standard.
Cryptanalysis: Attacks on encrypted messages. Depth, probabilistic methods, trapdoors.
Public-Key ciphers: Rivest-Shamir-Adleman (RSA), Diffie-Hellman. Public Key Protocols.
Number Theory: Congruences. Finite fields. Finding large primes, pseudoprimes and primality testing.
|1||1/22, 1/25||1.1-1.4, 7.4, 7.7||Caesar, Affine and Substitution Ciphers, Integers mod 26|
|2||1/29, 2/1||2.2-2.4, 3.1, 5.2||Probability& Birthday Attacks, Hash Functions,
Sunday Funnies, Frequency Attacks
|3||2/5, 2/8||3.2-3.5||Anagrams, Transposition Ciphers, Permutations|
|4||2/12, 2/15||4.1-4.3||Vigenère Cipher/Kasiski Attack|
|5||2/19, 2/22||4.4-4.5, 7.8||Expected Values/Friedman Attack on Vigenère|
|6||2/26, 2/29||6.1-6.3, 8.1-8.2
|| Hill Cipher/Affine Hill/Attacks on Hill Cipher
Linear Algebra mod n, Shannon's Criteria
|7||3/4, 3/7||7.3, 7.5, 19.4, 26.1-5
Handout on F16
|Finite fields Fq, Affine ciphers over Fq,
Multiplicative inverses, ByteSub, MIME-encoding
|8||3/11, 3/14||6.1-2, handouts on AES||DES (now deprecated), AES and MixColumns, Review|
||3/18, 3/21||R&R||SPRING BREAK|
|9a||3/25 (Tues)||ch. 1-8, 26||Midterm Exam|
|9b||3/28 (Fri)||11.2, 11.5-6||Prime Number Theorem, Euler's logarithmic integral Li(x)|
|10||4/1, 4/4||7.8, 12.1, 12.5, 20.4-5||Primitive roots, Discrete logs; Fast Exponentiation|
|11||4/8, 4/11||10.1-10.4, 13.6-13.7||Public Key Ciphers (RSA, Diffe-Hellman, El Gamal)|
|12||4/15, 4/18||13.1-5, 15.1-5, 22.5||Square root attacks, Legendre symbols|
|13||4/22, 4/25||24, 27.1-2||Factoring attacks and discrete logarithms
|14||4/29, 5/2||28.1-3||Discrete Log ciphers, Elliptic Curves, review.
Term Paper Due Friday 5/2
|15||5/14 (Wed)||Cumulative||Final Exam in ARC 207 (4-7 PM)|
Possible Topics for Term paper:
The paper should be about 10-12 pages in length, and must use at least
three peer-reviewed materials. The grade will be affected by the
accuracy of the citations used.
The Rijndael field F256 is defined as F2[x]/(P), P=x8+x4+x3+x+1. Elements of this field are represented by a pair of haxadecimal digits. For example, the unit 1 is (01) and (53) is short for x6+x4+x+1. Note that (53)*(CA)=1 in this field.
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Last Updated: February 29, 2008