# A multiplicative cipher is defined on Z26 by the rule M5 (m)= 5x26 mA multiplicative cipher is defined on Z26 by the rule M5 (m)= 5x26 m messages in english are coded numerically using the...

A multiplicative cipher is defined on Z26 by the rule

M5 (m)= 5x26 m

A multiplicative cipher is defined on Z26 by the rule

M5 (m)= 5x26 m

messages in english are coded numerically using the correspondence below.

A 1 B 2 C 3 D 4 E 5 F 6 G 7................... Y 25 Z 26

1) encipher the message WHEN using M5 (that is , find the ciphertext for this message.)

2) Write down the deciphering rule for this cipher justifying your answer.

3) A message is enciphered using M5 to give the ciphertext {18,23,23,18} use answer to 2) to find the middle two lwtters of the message. Using answer to part 1) or otherwise find the other two letters and write down the message.

Asked on by winter11

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mlehuzzah | Student, Graduate | (Level 1) Associate Educator

Posted on

the cipher is:
multiply by 5, then subtract a multiple of 26 if your number is "too big"

so:
1 -> 5
2 -> 10
3 -> 15
4 -> 20
5 -> 25
6 -> 30: but 30 is too big (not between 1 and 26), so subtract 26 to obtain:
6 -> 4
7 -> 35: again, too big, subtract 26 and
7 -> 9
8 -> 14
9 -> 19
10 -> 24
11* 5 = 55, 55-26 = 29 is still too big, 55-52=3
11 -> 3

Thus your encryption is:
A -> 1 -> 5 -> E
B -> 2 -> 10 -> J
C -> 3 -> 15 -> O
...
F -> 6 -> 4 -> D
...

K-> 11-> 3 -> C

The deciphering rule is M21
that is, multiply by 21, then subtract a multiple of 26 if your number is "too big"
1 -> 21
2 -> 42: but 42 is too big, so subtract 26
2 -> 16
3 -> 63: 63 is too big, subtract 52
3 -> 11
4 -> 84: 84 is too big, subtract 78
4 -> 6

The reason this works is that 5*21 = 1 + multiple of 26

so, for example, to decipher M3 you use M9, since
3*9 = 1 + multiple of 26

ciphertext 18 23 23 18
18*21 - 26*14 = 14 -> N
23*21 - 26*18 = 15 -> O

your decrypted text is: NOON

PS: if you are interested in learning more about this (why you want 1+ multiple of 26), or why you can't use M2 or M4 to encrypt your text, try reading about "modular arithmetic", say on wikipedia

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