Vigenère Cipher encryption/decryption

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Question statement

Suppose we wish to encrypt the (nonsense) plaintext {message} using the Vigenère Cipher.

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			Name	Type	Generated Value

alphabet	string	ABCDEFGHIJKLMNOPQRSTUVWXYZ
numbermessage	list	[ 8, 12, 0, 23, 8, 3, 18, 21 ]
message	string	IMAXIDSV
numberkey	list	[ 22, 20, 8, 6 ]
key	string	WUIG
ciphertext	string	REPVBDSE
numberciphertext	list	[ 17, 4, 15, 21, 1, 3, 18, 4 ]

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Name

Data type

Value

xxxxxxxxxx
 
"ABCDEFGHIJKLMNOPQRSTUVWXYZ"

JME function reference

Description

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Generated value: `string`

ABCDEFGHIJKLMNOPQRSTUVWXYZ

→ Used by:

ciphertext
key
message

Matrix entry

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Encrypt the plaintext using the key {key}. (Express your answer as a sequence of elements of $\mathbb{Z}_{26}$ .)

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Correct answer

xxxxxxxxxx
 
matrix(map(mod(numbermessage[i]+numberkey[mod(i,4)],26),i,0..7))

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a) We convert each letter into an element of $\mathbb{Z}_{26}$ , so {message} becomes {numbermessage}. Similarly we convert the key {key} to {numberkey}. To encrypt the first four message numbers we add the corresponding key numbers, working modulo 26 so we obtain $[\var{numbermessage[0]}+\var{numberkey[0]},\var{numbermessage[1]}+\var{numberkey[1]},\var{numbermessage[2]}+\var{numberkey[2]},\var{numbermessage[3]}+\var{numberkey[3]}]$ $\equiv\var{map(mod(numbermessage[i]+numberkey[i],26),i,0..3)}$ .

To encrypt the next four message numbers we then repeat that sequence of key numbers, which gives $[\var{numbermessage[4]}+\var{numberkey[0]},\var{numbermessage[5]}+\var{numberkey[1]},\var{numbermessage[6]}+\var{numberkey[2]}, \var{numbermessage[7]}+\var{numberkey[3]}]\equiv\var{map(mod(numbermessage[i]+numberkey[i-4],26),i,4..7)}$ .

b) Similarly we convert the ciphertext {ciphertext} into numerical form {numberciphertext}. To decrypt we now subtract the elements of {numberkey} from each element of the ciphertext in turn, again working modulo 26. We obtain $[\var{numberciphertext[0]}-\var{numberkey[0]},\var{numberciphertext[1]}-\var{numberkey[1]},\var{numberciphertext[2]}-\var{numberkey[2]},\var{numberciphertext[3]}-\var{numberkey[3]},\var{numberciphertext[4]}-\var{numberkey[0]},$ $\var{numberciphertext[5]}-\var{numberkey[1]},\var{numberciphertext[6]}-\var{numberkey[2]},\var{numberciphertext[7]}-\var{numberkey[3]}]\equiv\var{map(mod(numberciphertext[i]-numberkey[mod(i,4)],26),i,0..7)}$ .

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This question is used in the following exam:

NTC Assignment 1 Quiz by Maura Paterson in Maura's workspace.

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Taxonomy: mathcentre

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Maura Paterson 1 year, 7 months ago

Maura Paterson 1 year, 7 months ago

Maura Paterson 1 year, 7 months ago

Error in variable testing condition

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Generated value: `string`

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Vigenère Cipher encryption/decryption

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Maura Paterson 1 year, 7 months ago

Maura Paterson 1 year, 7 months ago

Maura Paterson 1 year, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Matrix entry

Advanced settings

Generated value: `string`