Manifest: Thursday 25 January 2005
Assignments Due

• Now: CS588 Pledge
• Thursday, 3 February: Problem Set 1

Optional readings:

• Claude Shannon, Theory of Secrecy Systems: Part 1, Part 2. Bell System Technical Journal, October 1949.

Notes
Entropy: H(M) = Σ Prob [M_i] log₂ ([1 / Prob [M_i])
(Sum over all messages M_i.)

Entropy is a measure of information. The amount of new information a message conveys, depends on how surprising it is.

If M is a source that produces n messages that are all equally probable, what is H(M)?

Absolute Rate: R = how much information can be encoded

Rate: r = H(M) / N
    M is the source of N-letter messages

How many meaningful 20-letter messages are there in English?

Redundancy: D = R - r

Unicity Distance: U = H(K) / D

Unicity distance is the expected minimum amount of ciphertext needed for a brute-force attack to succeed. If you have less than this, cannot determine if a particular guess is correct.

Questions

• Is there any source M' that produces n messages that has higher entropy than M (the source for which all n messages are equally likely described above)?
• Is Shakespearean English more or less redundant that your email?
• How could you determine the rate of English?
• What is the unicity distance of a one-time pad?
• Why is there no cipher that is both information-theoretically perfect and practical?
  

Information theory has perhaps ballooned to an importance beyond its actual accomplishments. — Claude Shannon

University of Virginia Department of Computer Science CS 588: Cryptology - Principles and Applications

cs588–staff@cs.virginia.edu