Authentication codes and plaintext attack

We study authentication codes (A-codes) and obtain lower bounds on the probability of success and number of encoding rules when the enemy uses plaintext or chosen plaintext attack. A-codes with minimum number of encoding rules that provide perfect protection for impersonation and substitution in these attacks are characterized and a general method of constructing A-codes that provide perfect protection for these attacks, using A-codes that provide perfect protection in its traditional sense, are given. The constructions are optimal as they produce A-codes with minimum number of encoding rules if the original A-code has the same property