# Perfectly Secure Ciphers known other than the OTP

By Information-Theoretic definitions, the One Time Pad (OTP) is called/was proved to be a Perfectly Secure Cipher. For the sake of completeness, we define

• OTP: An enc/dec function, $f:\mathcal{P} \times \mathcal{K} \rightarrow \mathcal{C}$
• Perfect Security: Given $m, m^* \in \mathcal{M}$, $$P\big(m=m^* \mid E_\mathcal{K}(m) = c\big) = P(m=m^*)$$

I ask, Are there any more Perfectly Secure Ciphers known other than the OTP?

• Look at Shannon's paper Communication Theory of Secrecy Systems. He proves that for perfect secrecy you must have that "the number of different keys is at least as great as the number of M's [messages]". Sep 20 '13 at 18:16