This paper is concerned with the model for security of cryptographic protocols suggested by Dolev and Yao. The Dolev and Yao model deals with a restricted class of protocols, known as Two-Party Ping-Pong Protocols. In such a protocol, messages are exchanged in a memoryless manner. That is, the message sent by each party results from applying a predetermined operator to the message he has received. The Dolev and Yao model is presented, generalized in various directions and the affect of these generalizations is extensively studied. First, the model is trivially generalized to deal with multi-party ping-pong protocols. However, the problems which arise from this generalization are very far from being trivial. In particular, it is no longer clear how many saboteurs (adversaries) should be considered when testing the security of p-party ping-pong protocols. We demonstrate an upper bound of 3(p \Gamma 2) + 2 and a lower bound of 3(p \Gamma 2) + 1 on this number. Thus, for every fixed p, th...