# ENG 204 Data Security Homework

*label*Science

*timer*Asked: Feb 21st, 2019

*account_balance_wallet*$20

### Question Description

please no plagiarism !!! 0% similarity

I will attach the word file please solve all question.

## Tutor Answer

Attached.

Homework 2

Rule: Finish all of the following on your own.

1. Compute the following with detailed steps. (Hints: Use Fermat Theorem, Euler Theorem,

properties of totient functions, etc, or write program code as assistance)

(1) 123416 mod 17

Based on the Fermat theorem

17 is a prime, gcd (1234,17) = 1,

Therefore, 123416 mod 17 = 1

(2) 5451 mod 17

17 is a prime, gcd (54,17) = 1 , ø(17) = 16

Then,

(54)51 mod 17 = (54 mod 17)(51 mod 16) mod 17

= (3)3 mod 17 = (27) mod 17 = 10

(3) ø(51)

Thus, ø(51) = 32

(4) gcd(33, 121)

gcd (33, 121) = gcd (121, 33)= gcd (33, 22)

= gcd (22, 11) = gcd (11, 0) = 11

(5) 2-1 mod 17 (i.e., multiplicative inverse of 2 mod 17)

2−1 mod 17 = −8 mod 17 = 9

Through Extended Euclid algorithm,

y3 = 1 = gcd (2, 17)

y2 = −8 = 2−1 mod 17

(6) ind2,5(4)

2x mod 5 = 4 then, x=2

(7) ø(8000)

Therefore, ø(8000) = 64

(8) ø(98803519)

Hence, ø(98803519) = 98783640

2. Write a computer program to implement the extended Euclid’s algorithm, use

your code to compute the following. Submit your code and results.

a. GCD(10012012,2314213)

b. GCD(28176412,29108188)

c. GCD(38172,23812188)

d. The multiplicative inverse of 12091 mod 24123123.

Mat Lab Code:

e. The multiplicative inverse of 28173928 mod 129182771.

Mat Lab Code:

3. Prove that ...

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