The following technical report is available from http://aib.informatik.rwth-aachen.de/: Zinaida Benenson, Felix C. Gärtner, Dogan Kesdogan Secure Multi-Party Computation with Security Modules 2004-10 We consider the problem of secure multi-party computation (SMC) in a new model where individual processes contain a tamper-proof security module. Security modules can be trusted by other processes and can establish secure channels between each other. However, their availability is restricted by their host, i.e., a corrupted party can stop the computation of its own security module as well as drop any message sent by or to its security module. In this model we show that SMC is solvable if and only if a majority of processes is correct. We prove this by relating SMC to the problem of Uniform Interactive Consistency among security modules (a variant of the Byzantine Generals Problem from the area of fault-tolerance). The obtained solutions to SMC for the first time allow to compute any function securely with a complexity which is polynomial only in the number of processes (i.e., the complexity does not depend on the function which is computed). We conclude that adding secure hardware does not improve the resilience of SMC but can effectively improve the efficiency. Regards, Volker