Suppose the alphabet consists of a through , in natural order, followed by a blank, a comma, and a period, in that order. Associate these "letters" with the numbers , respectively, thus forming a -letter alphabet, . Use the affine cipher to decipher the message
if you know that the plaintext message begins with " " and ends with ".". Write out the affine mapping and its inverse.
Plain text in the letter alphabet , by using the affine cipher to decipher the message “ BZZK, AUZNZG, RSKZ, AUWAO” and the plain text message begins with “b” followed by “.” Write down the affine mapping and .
(i) The 29-letter alphabet -
If alphabet consist of to , in natural order followed by blank, a comma and a period, then have “letters” that associates with the integer as follows:
ii) Euclidean Algorithm:
Let and are integers with , then the procedure
is known as Euclidean Algorithm.
Since the integers are decreasing and are all non-negative, there is a smallest integer , such that :
If , then the last non-zero remainder is always greatest common divisor of and .
Define the mapping by . Where are fixed integers and order pair forms a key to affine cipher.
As plaintext begins with “” and ends with “.”
The ciphertext B and O corresponds to the plain text “b” and ”.”.
Translating these into the set ,
Now, to determine the key from the following system of equations for and .
Subtract (1) from (2), gives
Now, to find the multiplicative inverse of using Euclidean algorithm.
The inverse .
Now, from (1),
Therefore, and is the solution of the system
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