   Chapter 8.2, Problem 62ES Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584

Solutions

Chapter
Section Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584
Textbook Problem

Decoding Decode the message GBBZ OJQBWJ TBR GJHI that was encrypted using the congruence c ≡ ( 7 p + 1 ) mod 26 .

To determine

Decode the below message that was encrypted using the congruence c(7p+1)mod26

GBBZ OJQBWJ TBR GJHI

Explanation

Given: The encrypted message is GBBZ OJQBWJ TBR GJHI and the congruence is c(7p+1)mod26

Calculation:

Congruence is given as

c(7p+1)mod26

Let us solve the above congruence for p , we have

c=7p+1

c1=7p

Since 15 is multiplicative inverse of 7 In

mod26

Thus, we have

15(c1)=15.7p

15(c1)=105p

p=15(c1)

Hence, we have

p=15(c1)mod26

Now, the word in cipher text is given as

GBBZ OJQBWJ TBR GJHI

Decryption is carried as follows

G   p=15(71)mod26=90mod26=12   Decode as L

B   p=15(21)mod26=15mod26=15   Decode as O

Z   p=15(01)mod26=

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