Multi-party fair exchange protocol

In cryptography, a multi-party fair exchange protocol is protocol where parties accept to deliver an item if and only if they receive an item in return.

Definition
Matthew K. Franklin and Gene Tsudik suggested in 1998 the following classification:


 * An $$n$$-party single-unit general exchange is a permutation $$\sigma$$ on $$\{1...n\}$$, where each party $$P_i$$ offers a single unit of commodity $$K_i$$ to $$P_{\sigma(i)}$$, and receives a single unit of commodity $$K_{\sigma^{-1}(i)}$$ from $$P_{\sigma^{-1}(i)}$$.
 * An $$n$$-party multi-unit general exchange is a matrix of baskets, where the entry $$B_{ij}$$ in row $$i$$ and column $$j$$ is the basket of goods given by $$P_i$$ to $$P_j$$.