# What happen if a asymmetric crypto-system deals with only one key

Assume there is a crypto algorithm that deals with matrices to encrypt and decrypt. Regardless of the specification of such algorithm, what if the algorithm assumes that two parties can securely agree on a matrix and use it along with its inverse to encrypt and decrypt? What I am trying to understand, is that, such thing plays excatly the same role of asymmetric/public key cryptosystem. However, in this algorithm (unknown), there is only one key to encrypt and decrypt messages and is known to two parties who have never met before (agreed on it through a public channel). I would like to know in point of security, and consideration of public key cryptoo

-
What was your last sentence supposed to say? $\:$ –  Ricky Demer Apr 24 '13 at 3:57
In a sense, knowing the public key gives you the private key. Thus, anyone know can encrypt can also decrypt. This isn't really asymmetric crypto. In asymmetric crypto, knowing the public key should not yield the private key. –  mikeazo Apr 24 '13 at 11:19