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.

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

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

Secure multi-party computation