New answers tagged perfect-secrecy
Add the two numbers, and keep only the lower 4 digits. To reverse, add 10000 then subtract the second number and keep only the lower 4 digits again. Works like a charm.
Expand the key using a pseudo random generator and then add each digit mod 10 together, similar to Vigenère cipher and OTP.
Jean-François Gagnon's answer is fine and would serve as an obvious proof that this scheme does not provide perfect secrecy. Now the fault in your thought process is actually that an attacker doesn't know that the key is "copied". This is a simple form of a key schedule which is assumed to be known to the attacker along with the encryption and decryption ...
Xor-ing the first half of the encrypted message with the second gives the same result as xor-ing the first and second half of the original message. (When the key is duplicated). This contradicts perfect secrecy as some information can be obtained from the cyphertext.
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