MODD / Mr. Hansen
12/16/2005

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 those 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.

What does Nyquist’s Theorem have to do with information theory?

 

(A) Nothing.
(B) Nyquist’s Theorem states that if two private keys commute, then order does not matter.
(C) Nyquist’s Theorem gives a lower bound for the amount of information that a given
       channel can accommodate when a given bandwidth is employed.
(D) Nyquist’s Theorem provides an explanation for why error correcting codes cannot be
       guaranteed to recover 100% of corrupted bits.
(E) Nyquist’s Theorem was first formally proved by Claude Shannon, the father of
       information theory.

 

 

___ 2.

Entropy, defined by the formula –S pi log2 pi , is measured in what units?

 

(A) bits
(B) bytes
(C) inches

(D) bits per symbol
(E) bytes per lightyear

 

 

___ 3.

Which of the following hex data blocks appears to have the greatest surprisal?

 

(A) 0x0000000000000000
(B) 0x0123456789ABCDEF
(C) 0x0202020202020202

(D) 0x00000000FFFFFFFF
(E) 0x1357135713571357

 

 

___ 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.

Let A and B be defined as follows:

A = probability-weighted mean surprisal of a certain novel written in English and represented as an uncompressed text file

B = probability-weighted mean surprisal of the same text file after it has been run through a data compression routine that reduces its size to about ¼ that of the original

Which of the following describes the relationship between A and B?

 

 

 

(A) A = B
(B) A < B
(C) A = 2B

(D) A = 4B
(E)


 

___ 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.

Assume that there is no data 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.

Symmetric-key cryptography is sometimes used as a term to refer to which of these?

 

(A) private-key cryptosystems
(B) public-key cryptosystems and PKI
(C) functions that commute

(D) cryptanalysis
(E) error correcting codes

 

 

10.

A one-way function is a function that ______________________________________

_______________ but __________________________________________________ .

 

 

11.

Explain briefly why multiplying two large prime integers is an example of a one-way function.

 

 

12-14.

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? _____________________________________________

 

15.

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.

 

 

16-17.

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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

18.

The letters RSA are most closely associated with which of the following?

 

(A) triple-DES
(B) AES
(C) PKI

(D) NSA
(E) Hamming

 

 

19.

The simplest type of error detection protocol (with no correction) is . . .

 

(A) cyclic redundancy check
(B) parity check
(C) Hamming code
(D) a perfect code
(E) bit suppression

 

 

20.

In #19, if an error is detected, what should the protocol cause to happen?

 

(A) drop connection
(B) retransmit entire message once
(C) retransmit entire message multiple times
(D) retransmit data block once
(E) retransmit data block multiple times