# Perfect secrecy and block ciphers

Consider a block cipher that encrypts bit strings of length $$n$$, where the key-space of the block cipher is of size $$2^{kn}$$, $$k \geq 1$$. My understanding of perfect secrecy is that a system is perfectly secret if (and only if?) the size of the key space is larger than the size of the message space. But then, if the stated block cipher was used to encrypt messages, is it not true that such a block cipher could encrypt $$k$$ messages of length $$n$$ with perfect secrecy? Would this be possible if, after each encrypted message, a nonce was used that changed the key in some way, so that every subsequent message had perfect secrecy?

• – kelalaka May 18 '20 at 10:14
• – kelalaka May 18 '20 at 10:21