Math 395 (An Introduction to Cryptology)

Prof. Weibel

Spring 2003

  • Lectures TF2 ARC 207 (Busch Campus); Office hours and Homework assignments
  • Text: Making, Breaking Codes; an introduction to Cryptology by Paul Garrett, Prentice Hall, 2001.
  • go to lecture table or go to list of paper topics

    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.

    Tentative Course Syllabus

     Homework Assignments are on a separate web page.

    WeekLecture datesSections topics
    1 1/21, 1/24 (TF) 1.1-1.4, 7.7 Caesar, Affine and Substitution Ciphers, Integers mod 26
    2 1/28,1/31 (TF) 2.2-2.4, 3.1 Probability& Birthday Attacks,
    Sunday Funnies, Frequency Attacks
    3 2/4, 2/7 (TF) 3.2-3.5 Anagrams, Transposition Ciphers, Permutations
    4 2/11, 2/14 (TF) 4.1-3 Vigenère Cipher/Kasiski Attack
    5 2/18, 2/21 (TF) 4.4-5 Expected Values/Friedman Attack on Vigenère
    6 2/25, 2/28 (TF) 8.1-8.2, 7.4-7.5, 6.1 Hill Cipher/Affine Hill/Attacks on Hill Cipher
    Linear Algebra mod n, Shannon's Criteria
    7 3/4, 3/7 (TF) 26.1-5 Finite fields, Affine ciphers over Fq
    8 3/11, 3/14 (TF) 6.2, handout DES, IDEA, Review
    8.5 3/18, 3/21 R&R SPRING BREAK
    9a 3/25 (T) ch. 1-8, 26 Midterm Exam
    9b 3/28 (F) 6.3, 7.8, 20.4-5 Rijndael AES Cipher, Primitive roots, Discrete logs
    10 4/1, 4/4 (TF) 10.1-10.4,
    12.1, 12.5, 13.6-13.7     		Public Key Ciphers (RSA, Diffe-Hellman, El Gamal)    Fast Exponentiation
    11 4/8, 4/11 (TF) 12.6-7, 13.8, 15.1-5 Square Roots mod n, Legendre and Jacobi symbols
    12 4/15, 4/18 (TF) 13.1-5, 16.1-5, 22.5 Square Roots mod p (p=1 mod 4), Hash Functions, Square root oracles
    13 4/22, 4/25 (TF) 18.3-18.7 Secret Sharing, Pseudoprime numbers, Factorization Attacks, Prime testing
    14 4/29, 5/1 (TF) 24.1-2, 23.3-4 PGP, Digital Signatures
    15 5/1/03 (F) Last Class Term Paper Due (Thursday)
    16 5/8 (Thursday)Cumulative Final Exam in ARC 207 (12-3 PM)

    Possible Topics for Term paper :

    The paper should be about 10 pages in length, and must use at least three peer-reviewed materials. The grade will be affected by the accuracy of the citations used. (These topics were taken from several sources, including Garrett's page.)

    Miscellaneous Links:
     Handbook of Applied Cryptography
    Britain's GCHQ challenge potentially leading to employment
    MIT Lecture Notes on Cryptography (by Goldwasser & Bellare)

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    Charles Weibel / weibel@math.rutgers.edu /Oct. 28, 2002