Dr. A. Betten
Fall 2009
MATH 360 Mathematics of Information Security
Assignment # 4
Problem # 16
In a public-key system using RSA, you intercept the ciphertext c = 10 sent to a user whose
public key is e = 5, n = 35. What is the plaintext m?
Problem # 17
In an RSA system, the public key of a given user is e = 31, n = 3599. What is the private
key of the user?
Problem # 18
You intercept the RSA ciphertext
1227, 1729, 822, 500, 2067, 2126, 1009, 798
sent to a user whose public key is e = 11, n = 2257. Decipher the message. For the encoding
of the letters, the scheme a = 01, b = 02, c = 03, . . . , z = 26 is used, and digits are grouped
in groups of three each and encrypted together. You may use the web site
http://www.math.umn.edu/~stanton/mytest2.html
for the arithmetic.
Problem # 19
In this problem, you are asked to factor the number n = 2572807 in different ways. Use the
web site above for your computations. Show all your work and don’t cheat!
a) Factor using the p − 1 method with bound B = 15.
b) Factor using Fermat’s method.
Problem # 20
Use Miller-Rabin with base 2 to test 13, 747 for primality.
Problem # 21
If 22 = 5x mod 37, what is x? Use the Pohlig Hellman algorithm.