How many one-to-one affine caesar ciphers are there?
Answers
Since, for the standard alphabet, there are 12 numbers less than 26 which are coprime to 26, and for each of these there are 26 possibilities for the value of b, we have a total of 12 x 26 = 312 possible keys for the Affine Cipher.
Answer:
There are 676 one-to-one affine Caesar ciphers.
If considering the co-prime factors, then there are: 312.
Explanation:
An affine Caesar cipher is a type of encryption algorithm that combines the principles of a Caesar cipher with the mathematical concept of an affine transformation. In a one-to-one affine Caesar cipher, each letter in the plaintext is mapped to a unique letter in the ciphertext, and the mapping is determined by an affine function that includes two variables, a and b.
There are 26 possible choices for a and 26 possible choices for b, since each variable can be any integer from 1 to 25 (excluding 0, which would result in a null cipher). Therefore, the total number of possible one-to-one affine Caesar ciphers is the product of these two values, or 26 x 26 = 676.
The Affine cipher consists of two parts, b or the additive part (Shift), m or the multiplicative part. There are 26 alphabets so 26 choices for b.
There are 12 numbers, which are coprime to 26 and less than 26. So, for each of the 12 numbers, we can generate 26 caesar ciphers.
So, we can see the number of possible ciphers = 12 x 26 = 312.
However, some of these ciphers may not be useful, as certain combinations of a and b may result in the same cipher as other combinations. Nevertheless, there are 676 possible one-to-one affine Caesar ciphers that can be created using any combination of a and b.
For more such question: https://brainly.in/question/1670949
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