MODD / Mr. Hansen 12/14/2005

Name: _________________________

Multi-Unit Test on Cryptography, Error Correcting Codes, and Information Theory

Time limit: 32 minutes (48 minutes for extended time). A calculator is permitted.
Each question is worth 5 points, except for #18 at the end. Your name is worth 3 points.

Instructions for Part I: For multiple choice questions, write the capital letter of the best choice in the blank provided. For fill-in problems, write the word or phrase that best fits in the space provided.

___ 1.	The father of information theory was . . .
	(A) Shannon (B) Nyquist (C) Bell	(D) Gates (E) none of these
___ 2.	The key term in information theory, defined by the formula –S pi log2 pi , is . . .
	(A) compressibility (B) entropy (C) data capacity (bandwidth)	(D) noise (E) Fano code
___ 3.	Which of the following bitstreams appears to be the most compressible?
	(A) 1111111111111000000000000000 (B) 1001001011101000111001110110 (C) 1001000011101001111001111110	(D) 0001001010001000111011110111 (E) 1001011011101011111001000100
___ 4.	High compressibility is associated with . . .
	(A) low surprisal, i.e., low entropy (B) high surprisal, i.e., low entropy (C) low surprisal, i.e., high entropy	(D) high surprisal, i.e., high entropy (E) none of these
___ 5.	What is the probability-weighted mean surprisal of English text?
	(A) fewer than 3 bits per symbol (B) 8 bits per symbol, since 1 byte = 8 bits (C) somewhere between 8 and 16 bits per symbol (D) 16 bits per symbol, since 1 Unicode character = 16 bits (E) completely unknown, since this value has never been estimated by anyone
___ 6.	What in the world do error correcting codes have to do with metric spaces?
	(A) Nothing. (B) Error correcting codes are sometimes measured in centimeters. (C) Although error correcting codes were once measured in centimeters, they no       longer are. However, the name “metric” has stuck. (D) The received code that is “closest,” in the metric space sense, to a known codeword       is treated as being equal to that code so that the bit errors present (up to some       number that depends on the type of error correcting code used) can be corrected. (E) The received code is compared to a metric space. If the received code precisely       matches one of the known codewords, then the transmission is treated as valid and       is decoded. Otherwise, an error is reported, and the data transmission protocol is       used to command the sending computer to re-send the data block in which the error       occurred.
___ 7.	For this question, assume that there is no compression. A transmission that includes error correcting codes will always be . . .
	(A) longer than the original raw data (plaintext), because of overhead (B) shorter than the plaintext, because the errors have been removed (C) the same length as the plaintext, because the overhead and errors cancel each other out (D) [insufficient information to answer] (E) none of the above

Instructions for Part II: Fill in the blanks for each question. The answers can be quite short.

8.	Write a four-word definition of entropy.
	________________ - ________________ ________________ ________________
9-11.	Let f be an encryption function. Then f (x), where x is a plaintext data block, denotes __________________ . What actions are indicated by the notation f ^–1(f (x)), and in what order have they occurred? __________________________________ __________________________________________________________ . What is the result of f ^–1(f (x)), in notation? ________ What is the result of f ^–1(f (x)), described in your own words? _____________________________________________
12.	If f and g are two encryption functions such that f (g(x)) = g(f (x)), then we say that the keys __________. This is related to the brain teaser about sending a ring through the mail using padlocks, without creating an opportunity for a corrupt postal employee to open the box and steal the ring.
13-14.	Let f and g be two private-key encryption algorithms that commute. A message m encrypted using both keys can be denoted _______________ . Prove that the order in which the recipient applies the decryption keys, namely f ^–1 and g^–1, does not matter.
15.	The letters PKI stand for ________________________________________________ .
16.	The U.S. agency responsible for all codemaking and codebreaking is the __________ .
17.	How many different symbols are involved in bioinformatics, usually? Why?
18. (15 pts.)	(a) Which has more entropy, compressible plaintext or encrypted data of the same source? (b) Explain your answer to part (a) briefly. (c) Which of the following is smarter from a bandwidth or space perspective, not from a security perspective: to compress first and then encrypt a message, or to encrypt first and then compress?
BONUS	Explain (c) briefly.