The first protocol is based on a trusted consolidator who acts on behalf of the merchants performing the cryptographic actions and distributing the information to the merchants. The computational costs of this protocol are 4m + 17 1024-bit exponentiations compared to 19n 1024-bit ex- ponentiations in the traditional SET scenario. The communication over- head is reduced from 12m kbit to 5m + 8 kbit.

The second protocol is based on a (n; k)-threshold scheme set up among the merchants which allows all sets of k merchants to perform a crypto- graphic action together. It does not require a trusted party. The compu- tational costs of this protocol are 6m+2k+12 1024-bit exponentiations. The communication overhead is to 6m + 5k + 7 kbit.