   Chapter 8.4, Problem 20ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# In 19-24, use the RSA cipher from Examples 8.4.9 and 8.4.10. In 19-21, teranslate the message into its numeric equivalent and encrypt it. In 22-24, decrypt the ciphertext and translate the result in to letters of the alphabet to discover the message. WELCOME

To determine

Write the message into its numeric and encrypt it.

Explanation

Given information:

The given message is “WELCOME”.

Formula used:

Division algorithm:

Let a be an integer and d be a positive integer. Then, there are unique integers qandr with 0r<d such that a=dq+r, here, q is the quotient and r is the remainder.

RSA Cipher Work:

The formula of the RSA cryptography is C=Memodpq.

The numeric values of the letters WELCOME are:

W=23,E=05,L=12,C=03,O=15,M=13,E=05

To encrypt the letters, use the formula C=Memodpq …… (1)

Where, e=3 and pq=55.

To encrypt W, substitute 23 for W in the equation (1).

C=233mod55=12167mod55=12    [12167=221×55+12]

To encrypt E, substitute 5 for E in the equation (1)

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