Handouts

• Reserve List

• English Alphabet Frequencies

• Two tables on letters and di/tri-grams frequencies.
  From: "ICSA Guide to Cryptography", R.K. Nichols, McGraw Hill, 1999.
• A better table on trigram frequencies.
  From: "ICSA Guide to Cryptography", R.K. Nichols, McGraw Hill, 1999.

• Linear Feedback Shift Register lfsr.ps lfsr.pdf

• The Effects of Averaging a Distribution

• Binomial Distribution for Large n

• The Index of Coincidence

• ICand Kasiski typescripts.

• Analyzing Vigenere Ciphers

• Analysis of Vigenere Cipher

• List 1 List2 Primitive Polynomials over GF(2) for Shift-Register Sequences: The old list has been withdrawn; these lists use octal notation.
  For example, for degree 4, "23" signifies 010 011 = 10011 which is x^4 + x^1 + x^0 = x^4 + x + 1, which I used in class.
  Upper case E,F,G,H designate primitive polynomials.

• Shannon's Theorem and the One-Time Pad

• The (Weak) Law of Large Numbers

• Coding Examples from 10 September 2004

• The Shannon Theory of Cryptology

• Hellman's Time/Space Tradeoff

• Meet-in-the-Middle Attacks plus some Probability

• Birthday Paradox and Computations

• Expected Sampling Times

• Lecture of 8 October 2004

• Euclid's Algorithm and Inverses

• The Fermat/Euler Theorems

• Exponentiation via Fermat and Euler

• The Chinese Remainder Theorem

• Square Roots

• Generators of Finite Fields

• Lecture of 19 October

• The Miller-Rabin Test for Primality

• Breaking RSA

• Floyd/Pollard Rho Factoring

• A sqrt{n} Bound on the Rho Algorithm

• Factor-Base Factoring

• Survey of Attacks on RSA Cryptosystem

• Using Index Calculus to Find Discrete Logarithms

• The Pohlig-Hellman Algorithm for Discrete Logarithms

  Shamir's Secret-Sharing Scheme(.ps); (.pdf} .

• Pratt's Proof that PRIME(q) is in NP & coNP

• Lecture of 10 December

Quantum Cryptology Links

• Bibliography of Quantum Cryptography
• Oxford Quantum Information articles
• Quantum Information at Los Alamos National Laboratory
• Laboratory for Theoretical and Quantum Computing
• Web pages of interest to cryptography researchers (not only QC)

Zero Knowledge proofs

• Oded Goldreich's web page
• Foundation of cryptography (Fragment of a book)
• Probabilistic Proof Systems
• Electronic Colloquium on Computational Complexity (large collection of books and papers)