   Chapter 8.2, Problem 61ES 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 SNUUHQ FM VFALHDZ that was encrypted using the congruence c ≡ ( 5 p + 9 ) mod 26 .

To determine

Decode the below message that was encrypted using the congruence c(5p+9)mod26

SNUUHQ FM VFALHDZ

Explanation

Given: The encrypted message is SNUUHQ FM VFALHDZ and the congruence is c(5p+9)mod26

Calculation:

Congruence is given as

c(5p+9)mod26

Let us solve the above congruence for p , we have

c=5p+9

c9=5p

Since 21 is multiplicative inverse of 5 in mod26

Thus, we have

21(c9)=21.5p

21(c9)=105p

p=21(c9)

Hence, we have

p=21(c9)mod26

Now, the word in cipher text is given as

SNUUHQ FM VFALHDZ

Decryption is carried as follows

S

p=21(199)mod26=210mod26=2   Decode as B

N   p=21(149)mod26=105mod26=1   Decode as A

U   p=21(219)mod26=252mod26=18   Decode as R

H   p=21

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