   Chapter 2.8, Problem 7E

Chapter
Section
Textbook Problem

Suppose the alphabet consists of a through z , in natural order, followed by a colon, a period, and then a forward slash. Associate these "letters" with the numbers 0 ,   1 ,   2 ,   .   .   .   ,   28 , respectively, thus forming a 29 -letter alphabet, C . Use the affine cipher with key a   =   3  and  b   =   22 to decipher the message O   V   V   J   N   T   T   B   B   B   Q   /   F   D   L   W   L   F   Q   /   G   A   T   Y   S   T and state the inverse mapping that deciphers this ciphertext.

To determine

Plain text in 29 letter alphabet C, by using the affine cipher with key a=3 and b=22 to decipher the message, ‘OVVJNTTBBBQ/FDLWLFQ/GATYST’ and state the inverse mapping that will decipher the cipher text.

Explanation

Given information:

(i) a=3 and b=22

(ii) The 29 letter alphabet C -

If alphabet consist of a to z, in natural order followed by a colon, a period, and then a forward slash have 29 “letters” that associates with the integer 0,1,2,3,...,28 as follows:

Alphabet:

abcdef...vwxyz"colon"periodforwardslashC:012345...2122232425262728

Formula used:

Affine cipher:

Define the mapping f:AA by f(x)=ax+bmodn, where a,b are fixed integers and order pair a,b forms a key to affine cipher.

Calculation:

To use affine mapping with, a=3 and b=22 as the key in 29 letter alphabet

The mapping f:CC where C={0,1,2,...,28} is given by,

f(x)=3x+22mod29

In affine mapping f(x)=ax+bmodn to have an inverse, if a and n must be relatively prime

(a,b)=(3,22)=1

Thus, the inverse mapping exists and it is defined as,

f1(x)=10x10(22)mod29 as 1=10(3)mod29

f1(x)=10x+19(22)mod29 as 19=10mod29

f1(x)=10x+418mod29

f1(x)=10x+12mod29 as 418=12mod29

Therefore, the mapping f1:CC such that, f1(x)=10x+12mod29, where C={0,1,2,3,...,28} exist that will decipher the cipher text

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Factor each expression in Problems 7-18 as a product of binomials. 15.

Mathematical Applications for the Management, Life, and Social Sciences

If f(x) = ln(x + ln x), find f(1).

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 2932, find the value(s) of x that satisfy the expression. 29. 2x2 + 3x 2 0

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In Exercises 116, determine whether the argument is valid. pqqrpr

Finite Mathematics for the Managerial, Life, and Social Sciences

True or False: If , then converge absolutely.

Study Guide for Stewart's Multivariable Calculus, 8th

The graph of x = cos t, y = sin2 t is:

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 