CS 3511  Exam 2 Review Exercises                   Fall Semester, 2006

Here are some exercises similar to ones that might be on the first exam.
The items in parentheses are the corresponding items in the 6th edition 
of the text (since I think everyone is using the 5th edition).

Note that * exercises were in the assignments, but are computationally
too hard as stated (not enough time) to put on an exam - however, a
simpler/easier version may be used.

Ex. 3, 4, 10, 12, 13, 15-31, 36 of Section 2.7 pages 204-206
 (= 3, 4, 10, 12, 13, 15-31, 36 of Section 3.8 of 6th Ed.)

Ex. 35, 36, 41-43 of Chapter 2 Supplement pages 209-211
 (= 42, 43, 47-49 of Chapter 3 Supplement of 6th Ed.)

Ex. 16-17, 21, 22, 23, 25 of Section 3.1 pages 223-225
 (Note: of these, only 17 and 25 remain as questions in 6th Ed.
  16 asks to prove or disprove that 2^n + 1 is prime for positive
  integers n (Hint: what if n = 5?).
  17 is 1.7.32 of 6th Ed.
  21 asks to prove that if p is a prime and a^2 = b^2 mod p, then
  a = b mod p or a = -b mod p (here "=" means "congruent to").
  22 asks to prove or disprove that n^2 - 1 is composite if n is an
  integer > 1 (Easy answer: if n = 2, it is prime; what if n > 2?)
  23 asks to prove that (a mod m)*(b mod m) mod m = a*b mod m, which
  was done in class.
  25 is 3.5.9 of 6th Ed.)

Ex. 15, 19-21, 27-31, 33-35, 36-39, 41-43 of Section 3.2 pages 236-238
 (= 15, 19-21, 27-31, 35-37, 40-43, 45-47 of Section 2.4 of 6th Ed.)


It would be a good idea to know how public key cryptosystems work, and
how RSA works in particular. 

Sample public key questions:
Alice and Bob both have public and secret functions, PA(), SA(), and
PB(), SB().

How does Bob encrypt a message M he wants to send to Alice?
Ans: he computes PA(M) - i.e. uses Alice's public function.

How does Alice decrypt the message?

Sample RSA question:
Given n = pq, how are the public and secret functions defined?

In addition, know about finding the product of two matrices (how many
ordinary multiplications are needed to compute the matrix product of
an n-by-p matrix and a p-by-m matrix?).  If A and B are invertible
matrices, what is the inverse of their product, AB?

Also know about the halting problem, and summation/product notation.