BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

Solutions

Chapter
Section
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
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
Sect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6ESect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.1 P-10ESect-2.1 P-11ESect-2.1 P-12ESect-2.1 P-13ESect-2.1 P-14ESect-2.1 P-15ESect-2.1 P-16ESect-2.1 P-17ESect-2.1 P-18ESect-2.1 P-19ESect-2.1 P-20ESect-2.1 P-21ESect-2.1 P-22ESect-2.1 P-23ESect-2.1 P-24ESect-2.1 P-25ESect-2.1 P-26ESect-2.1 P-27ESect-2.1 P-28ESect-2.1 P-29ESect-2.1 P-30ESect-2.1 P-31ESect-2.1 P-32ESect-2.1 P-33ESect-2.1 P-34ESect-2.1 P-35ESect-2.2 P-1ESect-2.2 P-2ESect-2.2 P-3ESect-2.2 P-4ESect-2.2 P-5ESect-2.2 P-6ESect-2.2 P-7ESect-2.2 P-8ESect-2.2 P-9ESect-2.2 P-10ESect-2.2 P-11ESect-2.2 P-12ESect-2.2 P-13ESect-2.2 P-14ESect-2.2 P-15ESect-2.2 P-16ESect-2.2 P-17ESect-2.2 P-18ESect-2.2 P-19ESect-2.2 P-20ESect-2.2 P-21ESect-2.2 P-22ESect-2.2 P-23ESect-2.2 P-24ESect-2.2 P-25ESect-2.2 P-26ESect-2.2 P-27ESect-2.2 P-28ESect-2.2 P-29ESect-2.2 P-30ESect-2.2 P-31ESect-2.2 P-32ESect-2.2 P-33ESect-2.2 P-34ESect-2.2 P-35ESect-2.2 P-36ESect-2.2 P-37ESect-2.2 P-38ESect-2.2 P-39ESect-2.2 P-40ESect-2.2 P-41ESect-2.2 P-42ESect-2.2 P-43ESect-2.2 P-44ESect-2.2 P-45ESect-2.2 P-46ESect-2.2 P-47ESect-2.2 P-48ESect-2.2 P-49ESect-2.2 P-50ESect-2.2 P-51ESect-2.2 P-52ESect-2.2 P-53ESect-2.2 P-54ESect-2.2 P-55ESect-2.2 P-56ESect-2.2 P-57ESect-2.3 P-1TFESect-2.3 P-2TFESect-2.3 P-3TFESect-2.3 P-4TFESect-2.3 P-5TFESect-2.3 P-6TFESect-2.3 P-7TFESect-2.3 P-8TFESect-2.3 P-9TFESect-2.3 P-10TFESect-2.3 P-1ESect-2.3 P-2ESect-2.3 P-3ESect-2.3 P-4ESect-2.3 P-5ESect-2.3 P-6ESect-2.3 P-7ESect-2.3 P-8ESect-2.3 P-9ESect-2.3 P-10ESect-2.3 P-11ESect-2.3 P-12ESect-2.3 P-13ESect-2.3 P-14ESect-2.3 P-15ESect-2.3 P-16ESect-2.3 P-17ESect-2.3 P-18ESect-2.3 P-19ESect-2.3 P-20ESect-2.3 P-21ESect-2.3 P-22ESect-2.3 P-23ESect-2.3 P-24ESect-2.3 P-25ESect-2.3 P-26ESect-2.3 P-27ESect-2.3 P-28ESect-2.3 P-29ESect-2.3 P-30ESect-2.3 P-31ESect-2.3 P-32ESect-2.3 P-33ESect-2.3 P-34ESect-2.3 P-35ESect-2.3 P-36ESect-2.3 P-37ESect-2.3 P-38ESect-2.3 P-39ESect-2.3 P-40ESect-2.3 P-41ESect-2.3 P-42ESect-2.3 P-43ESect-2.3 P-44ESect-2.3 P-45ESect-2.3 P-46ESect-2.3 P-47ESect-2.3 P-48ESect-2.3 P-49ESect-2.4 P-1TFESect-2.4 P-2TFESect-2.4 P-3TFESect-2.4 P-4TFESect-2.4 P-5TFESect-2.4 P-6TFESect-2.4 P-7TFESect-2.4 P-8TFESect-2.4 P-9TFESect-2.4 P-10TFESect-2.4 P-11TFESect-2.4 P-12TFESect-2.4 P-13TFESect-2.4 P-1ESect-2.4 P-2ESect-2.4 P-3ESect-2.4 P-4ESect-2.4 P-5ESect-2.4 P-6ESect-2.4 P-7ESect-2.4 P-8ESect-2.4 P-9ESect-2.4 P-10ESect-2.4 P-11ESect-2.4 P-12ESect-2.4 P-13ESect-2.4 P-14ESect-2.4 P-15ESect-2.4 P-16ESect-2.4 P-17ESect-2.4 P-18ESect-2.4 P-19ESect-2.4 P-20ESect-2.4 P-21ESect-2.4 P-22ESect-2.4 P-23ESect-2.4 P-24ESect-2.4 P-25ESect-2.4 P-26ESect-2.4 P-27ESect-2.4 P-28ESect-2.4 P-29ESect-2.4 P-30ESect-2.4 P-31ESect-2.4 P-32ESect-2.4 P-33ESect-2.4 P-34ESect-2.4 P-35ESect-2.5 P-1TFESect-2.5 P-2TFESect-2.5 P-3TFESect-2.5 P-4TFESect-2.5 P-5TFESect-2.5 P-6TFESect-2.5 P-7TFESect-2.5 P-1ESect-2.5 P-2ESect-2.5 P-3ESect-2.5 P-4ESect-2.5 P-5ESect-2.5 P-6ESect-2.5 P-7ESect-2.5 P-8ESect-2.5 P-9ESect-2.5 P-10ESect-2.5 P-11ESect-2.5 P-12ESect-2.5 P-13ESect-2.5 P-14ESect-2.5 P-15ESect-2.5 P-16ESect-2.5 P-17ESect-2.5 P-18ESect-2.5 P-19ESect-2.5 P-20ESect-2.5 P-21ESect-2.5 P-22ESect-2.5 P-23ESect-2.5 P-24ESect-2.5 P-25ESect-2.5 P-26ESect-2.5 P-27ESect-2.5 P-28ESect-2.5 P-29ESect-2.5 P-30ESect-2.5 P-31ESect-2.5 P-32ESect-2.5 P-33ESect-2.5 P-34ESect-2.5 P-35ESect-2.5 P-36ESect-2.5 P-37ESect-2.5 P-38ESect-2.5 P-39ESect-2.5 P-40ESect-2.5 P-41ESect-2.5 P-42ESect-2.5 P-43ESect-2.5 P-44ESect-2.5 P-45ESect-2.5 P-46ESect-2.5 P-47ESect-2.5 P-48ESect-2.5 P-49ESect-2.5 P-50ESect-2.5 P-51ESect-2.5 P-52ESect-2.5 P-53ESect-2.5 P-54ESect-2.5 P-55ESect-2.5 P-56ESect-2.5 P-57ESect-2.5 P-58ESect-2.6 P-1TFESect-2.6 P-2TFESect-2.6 P-3TFESect-2.6 P-4TFESect-2.6 P-5TFESect-2.6 P-6TFESect-2.6 P-7TFESect-2.6 P-8TFESect-2.6 P-1ESect-2.6 P-2ESect-2.6 P-3ESect-2.6 P-4ESect-2.6 P-5ESect-2.6 P-6ESect-2.6 P-7ESect-2.6 P-8ESect-2.6 P-9ESect-2.6 P-10ESect-2.6 P-11ESect-2.6 P-12ESect-2.6 P-13ESect-2.6 P-14ESect-2.6 P-15ESect-2.6 P-16ESect-2.6 P-17ESect-2.6 P-18ESect-2.6 P-19ESect-2.6 P-20ESect-2.6 P-21ESect-2.6 P-22ESect-2.6 P-23ESect-2.6 P-24ESect-2.6 P-25ESect-2.6 P-26ESect-2.7 P-1TFESect-2.7 P-2TFESect-2.7 P-3TFESect-2.7 P-4TFESect-2.7 P-1ESect-2.7 P-2ESect-2.7 P-3ESect-2.7 P-4ESect-2.7 P-5ESect-2.7 P-6ESect-2.7 P-7ESect-2.7 P-8ESect-2.7 P-9ESect-2.7 P-10ESect-2.7 P-11ESect-2.7 P-12ESect-2.7 P-13ESect-2.7 P-14ESect-2.7 P-15ESect-2.7 P-16ESect-2.7 P-17ESect-2.7 P-18ESect-2.7 P-19ESect-2.7 P-20ESect-2.7 P-21ESect-2.7 P-22ESect-2.7 P-23ESect-2.7 P-24ESect-2.7 P-25ESect-2.7 P-26ESect-2.8 P-1TFESect-2.8 P-2TFESect-2.8 P-3TFESect-2.8 P-1ESect-2.8 P-2ESect-2.8 P-3ESect-2.8 P-4ESect-2.8 P-5ESect-2.8 P-6ESect-2.8 P-7ESect-2.8 P-8ESect-2.8 P-9ESect-2.8 P-10ESect-2.8 P-11ESect-2.8 P-12ESect-2.8 P-13ESect-2.8 P-14ESect-2.8 P-15ESect-2.8 P-16ESect-2.8 P-17ESect-2.8 P-18ESect-2.8 P-19ESect-2.8 P-20ESect-2.8 P-21ESect-2.8 P-22ESect-2.8 P-23ESect-2.8 P-24ESect-2.8 P-25ESect-2.8 P-26E

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

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

Mathematical Applications for the Management, Life, and Social Sciences

Finding Derivatives In Exercises 51-62, find f(x). f(x)=6x25x2+7x3

Calculus: An Applied Approach (MindTap Course List)

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