Secure Multi-Party Computation via Nil Message Compute

The patent applies preliminary action by pre-generating additive and multiplicative secret sharing schemes along with random values during an offline preprocessing phase. These pre-computed secrets are stored and reused during the actual computation phase, eliminating the need for complex real-time communication protocols while maintaining security. The preprocessing phase prepares all necessary cryptographic materials in advance, so that the online phase requires minimal interaction between parties.

The patent segments the computation into distinct phases: preprocessing phase for generating secret shares and random values, and computation phase for evaluating the arithmetic function. It also segments the secret sharing into additive shares and multiplicative shares, each handled independently. This segmentation allows complex secure computation to be broken down into manageable steps with reduced communication overhead in each phase.

The patent performs all communication-intensive operations during the offline preprocessing phase, including generation of secret shares and random values. During the online computation phase, parties only need to exchange minimal information (such as evaluating pre-computed polynomials at specific points), which significantly reduces communication latency and improves computation speed while maintaining accuracy through the mathematically sound secret sharing framework.

The patent uses polynomial evaluation to compute function values at multiple points simultaneously. By evaluating a polynomial at n points, the system obtains n secret shares without requiring n separate communication rounds. This copying approach, where one polynomial evaluation produces multiple useful outputs (shares), reduces the number of message exchanges needed while ensuring accurate reconstruction of the computation result.