Chapter 2.8, Problem 12E

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8th Edition

Gilbert + 2 others

ISBN: 9781285463230

Textbook Problem

Suppose the alphabet consists of a through

To determine

Plain text in the

Explanation

**Given information:**

(i) The 29-letter alphabet

If alphabet consist of

Alphabet:

ii) Euclidean Algorithm:

Let

is known as Euclidean Algorithm.

Since the integers

If

**Formula used:**

Affine cipher:

Define the mapping

**Calculation:**

As plaintext begins with “

The ciphertext B and O corresponds to the plain text “b” and ”.”.

Translating these into the set

Now, to determine the key from the following system of equations for

Use

Subtract (1) from (2), gives

Now, to find the multiplicative inverse of

Thus,

Thus,

The inverse

Consider,

Now, from (1),

Therefore,

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