Homework 02
ECE 443/518
1. (4 points) Solve Problem 1.4 (p25 in Understanding Cryptography).
2. (3 points)
A. Calculate 2x mod 13 for x = 1, 2, . . . , 12.
B. Calculate 3x mod 13 for x = 1, 2, . . . , 12.
C. Argue that if p is a prime number and 1 ≤ x < y ≤ p − 1 are two integers,
then for any integer 1 ≤ a ≤ p − 1, ax mod p and ay mod p cannot be the
same.
3. (3 points)
A. Calculate 2x mod 13 for x = 1, 2, . . . , 12.
B. Calculate 3x mod 13 for x = 1, 2, . . . , 12.
C. What do the infinite sequences 2x mod 13 and 3x mod 13 look like for x =
1, 2, . . . ,?
4. (2 points) Solve Problem 2.4 (p52 in Understanding Cryptography).
5. (2 points) Solve Problem 4.16 (p121 in Understanding Cryptography).
For Moore’s Law, simply assume that computer power doubles every 18 months.
6. (1 points) Solve Problem 5.9 (p146 in Understanding Cryptography).
1
