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Applied Algebra: Codes, Ciphers and Discrete Algorithms

Darel W. Hardy, Fred Richman, Carol L. Walker

Chapter 4

Ciphers - all with Video Answers

Educators


Section 1

Cryptography

Problem 1

Use the Caesar cipher to encrypt the plaintext
Hello.

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02:27

Problem 2

Use the Caesar cipher to decrypt the ciphertext
ZOVMQ LDOXM EVFPQ EBPZF BKZBL CPBZO
BQTOF QFKD

Prathan Jarupoonphol
Prathan Jarupoonphol
Numerade Educator

Problem 3

Use the shift cipher $y=x+6$ to encrypt the plaintext
Encryption products with less than sixty four bits are freely exportable.

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Problem 4

Use the affine cipher $y=5 x+7 \bmod 26$ to encrypt the plaintext
The width of a complete filled rectangle must be a divisor of the length of the message.

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02:27

Problem 5

Use the Caesar cipher to decrypt the ciphertext
JRRGE BH

Prathan Jarupoonphol
Prathan Jarupoonphol
Numerade Educator
10:00

Problem 6

Use the Caesar cipher to unscramble the ciphertext
LDPJR LQJWR VSDLQ WRILJ KWDQD UPBZL
WKRXW DJHQH UDODQ GWKHQ FHWRW KHHDV
WWRIL JKWDJ HQHUD OZLWK RXWDQ DUPB
This statement is ascribed to Julius Caesar himself.

Bryan Lynn
Bryan Lynn
Numerade Educator

Problem 7

Unscramble the following ciphertext, which was encrypted using the affine cipher $y=x+5 \bmod 26$.
HFJXF WNXHT SXNIJ WJIYT GJTSJ TKYMJ
KNWXY UJWXT SXYTM FAJJA JWJRU QTDJI
JSHWD UYNTS KTWYM JXFPJ TKXJH ZWNSL
RJXXF LJX

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Problem 8

Use the Vigenère cipher with keyword SING to encrypt the plaintext
There are two kinds of music: country and western.

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10:35

Problem 9

Use the Vigenere cipher with keyword GOLF to decrypt the ciphertext JFTAKTZWYVZBVIEYLCCIUIRM

Victoria Dollar
Victoria Dollar
Numerade Educator
10:35

Problem 10

Decrypt the ciphertext
HEJGI JTTPU WHBDH UHPBH AMREH SBIUF
IZOFT IZUJS IHVHU B
which was encrypted using an affine cipher $y=m x+b \bmod 26$, knowing that the plaintext begins with el.

Victoria Dollar
Victoria Dollar
Numerade Educator

Problem 11

Encrypt the message
You should be aware that encrypted communications are illegal in some parts of the world.
using a polyalphabetic cipher that alternates the use of the three affine ciphers
$$
\begin{aligned}
& f(x)=11 x+2 \bmod 26 \\
& g(x)=15 x+5 \bmod 26 \\
& h(x)=19 x+7 \bmod 26
\end{aligned}
$$

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07:13

Problem 12

Decrypt the ciphertext
DGFEH LDJNE DNPOF DEFHV LU
encrypted using a polyalphabetic cipher that alternated the use of the three affine ciphers
$$
\begin{array}{r}
f(x)=11 x+2 \bmod 26 \\
g(x)=15 x+5 \bmod 26 \\
h(x)=19 x+7 \bmod 26
\end{array}
$$

Bryan Lynn
Bryan Lynn
Numerade Educator
02:05

Problem 13

Plaintext is encrypted using the affine cipher $y=3 x+5 \bmod 26$; then the ciphertext in encrypted again using the affine cipher $y=15 x+4 \bmod 26$. Give a simple equivalent to the compound cipher.

Bryan Lynn
Bryan Lynn
Numerade Educator

Problem 14

The affine cipher $y=m x+b \bmod 26$ has an inverse cipher for only 12 different choices of $m$. What is the effect of increasing the alphabet size from 26 to 27 ? How about 29? 30?

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