Special Problem
Use the exponentiation algorithm to compute 4126 mod 127
x = 4 , e = 126, m = 127
prod = 1
prod = 1
x = x2 = 42 = 16 mod 127 = 16; e = 126/2 = 63
while (e > 1) cfw_
prod = prodx = 116
Problem 1
(a) Define: the prime subfield of finite field F
The smallest subfield containing the multiplicative identity of
F
(b) Define: primitive element of finite field K
An element whose first n-1
Problem 1
(a) Define: the prime subfield of finite field F
The smallest subfield containing the multiplicative identity of
F
(b) Define: primitive element of finite field K
An element whose first n-1
Advanced Discrete Exam 4 Name (Print) _
Do all work on this exam.
For questions 1 to 5, let f(x) = x3 + x2 + 1 and GF8 = GF2[x]/f(x). The table of powers of in
GF8 is given on the last page of this ex
Public Key Homework Problems
1 The ciphertext 5859 was obtained from the RSA algorithm using
m = 11413 and e = 7457. Using the factorization 11413 = 101113,
find the plaintext.
= 100112 = 11200
d = e
Advanced Discrete Exam 3
Name _
1. Let f(x),g(x),h(x) GF7[x] be as follows: f(x) = 3x2 + 2x + 5, g(x) = 4x2 + 5x + 6 and
h(x) = 6x5 + 3x4 + x3 + 2x2 + x + 5.
Express the following as polynomials over
Problem 1
(a) State Fermats Little Theorem
(b) Define (n) (Eulers Phi Function)
(c) State Eulers Theorem
See slides or text
(e) Define: primitive root of a prime p
(d) Compute (72533224)
(72533224) =
Advanced Discrete Exam 1
Solution
1.
abcdsux
0123456
ABCDSUX
3 4
Hill cipher with m = 2 and key = 4 2
3 4
Note: 4 2
1
4 6 4 1
=
6 6 = 1 1
Your job is to produce the plaintext corresponding the c
Advanced Discrete Exam 1
Solution
1.
(a) The Optimists Society of Tampa restricts their plaintext messages to use only the
seven letters b, c, d, g, o, s and u. They represent the letters by the numbe
Problem 1
(a) State Fermats Little Theorem
(b) Define (n) (Eulers Phi Function)
(c) State Eulers Theorem
See slides or text
(e) Define: primitive root of a prime p
(d) Compute (72533224)
(72533224) =
Advanced Discrete Exam 1
Solution
1.
The Critics Society of Tampa restricts their plaintext messages to use only the seven
letters a, b, c, d, s, u and t. They represent the letters by the numbers fro