Millions of Millionaires: Multiparty Computation in Large Networks

We describe a general Multi-Party Computation (MPC) protocol for arithmetic circuitsthat is secure against a static malicious adversary corrupting up to a 1/7 fraction of theparties. The protocol requires each party to send an average of O(mn log 3 n)bits, and computeO(mn log 4 n)operations in a network of size n, where m is the size of circuit. This is achieved byincreasing latency from constant to O(d), where d is the depth of the circuit. Our protocol hasa setup phase that is independent of the circuit and relies on Threshold Fully HomomorphicEncryption (TFHE). The setup requires each party to send Õ(κ) messages and compute Õ(κ)operations, where κ is the security parameter. We provide results from microbenchmarksconducted over a sorting network showing that our protocol may be practical for deploymentin large networks. For example, we consider a network of size 2 (over 33 million) where eachparty has an input item of size 20 bytes. To securely sort the items, our protocol requires eachparty on average to send 5 kilobytes per item sorted.