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Show that if only a single character is encrypted, then the shift cipher is perfectly secret

Show that if only a single character is encrypted, then the shift cipher is perfectly secret

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Answer #1

Shift cipher, also known as Ceasar cipher replaces each letter in the message with the letter obtained by shifting the letter by a key value.

Eg: plain-text = "ABC" key = 3

       cipher-text = "DEF"

Since there are 26 distinct alphabets, there 26 possibilities for a key.

Perfect secrecy that is to make a message unable to read without the value of a key can be attained if we encrypt each character in the message with different(random of 26) key value. Ceasar cipher ususally uses single key value for the encryption of the total message.

Therefore, if each character is encrypted using different key value, then each(of 26 alphabets) character will have their own key value(1 to 26). It is very very difficult to decrypt because there are 26N (N is the size of plain-text) possible keys.

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