This is for Discrete Mathematics. 1. Decrypt these messages encrypted using the

Question

This is for Discrete Mathematics.

1. Decrypt these messages encrypted using the caesar cipher

a) EOXH MHDQV

b) WHVW WRGDB

c) HDW GLP VXP

2. use the euclidean algorithm to find

a) gcd (1, 5)

b) gcd (100, 101)

c) gcd (123, 277)

d) gcd (1529, 14039)

e) gcd (1529, 14038)

f) gcd (11111, 111111)

3a. Compute the multiplicative inverses x^ 1 (mod 31), in each of the following cases: x = 30, x = 5, x = 16, and x = 17.

3b. Compute the multiplicative inverses x^ 1 (mod 31879), in each of the following cases: x = 30, and x = 17.

3c. Compute Euler’s (n) for n = 31879.

3d. Compute m = 30^31365 (mod 31879).

Explanation / Answer

Answer of question (1) : Here as per the rule of caesar cipher i.e. f(p)= f(p-3)mod26, we just have to subtract 3 letters from each given letter to get the required code.

So (i ) E O X H M H D Q V

5 15 24 8 13 8 4 17 22

2 12 21 5 10 5 1 14 19

B L U E J E A N S

(II) W H V W W R G D B

23 8 22 23 23 18 7 4 2

21 5 19 20 21 15 4 1 26

U E S T U O D A Z ---------> That is converted code

(iii) H W D G L P V X P

8 23 4 7 12 16 22 24 16

5 20 1 4 9 13 19 21 13

E T A D I M S U M ..........> that is required converted code.

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