Multiplication cipher

ID: 209429 score:

This cipher uses multiplication cipher theory. In this case we take each letter (P) and multiply it by a value (a). For example "c" becomes 2, and multiplied by 2 gives 4, which gives "e". As the value may be greater than 25, we take a modulo 26 operation to make sure we end up with a letter, such as:

\(C = (a \times P) \mod 26\)

Where P is the character in the plain text, and a is the multiplier. The mod operator is the remainder from an integer divide (for example 11 mod 4 gives 3). In order to create unique cipher characters, we must use a multiplier which is co-prime (the values do not share any factors when dividing) in relation to the size of the alphabet (26), so you should use either 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 or 25. In the following plain text values, find the ciphers. We have used multipliers (P) of 3, 5, 7 or 9:

Plain text	Answer	Cipher
geometry (with multiplier of 3)
beach (with multiplier of 5)

Outline

In order to create unique cipher characters, we must use a multiplier which is co-prime (the values do not share any factors when dividing) in relation to the size of the alphabet (26), so you should use either 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 or 25.

For example if we use "abcdefghijklmnopqrstuvwxyz" and a multiplier of 3, gives "adgjmpsvybehknqtwzcfilorux"

To help you, here are the letters with numeric values:

a - 0
b - 1
c - 2
d - 3
e - 4
f - 5
g - 6
h - 7
i - 8
j - 9
k - 10
l - 11
m - 12
n - 13
o - 14
p - 15
q - 16
r - 17
s - 18
t - 19
u - 20
v - 21
w - 22
x - 23
y - 24
z - 25

Multiplication cipher

Outline

Example