UFOs: An Ultra-Fast Toolkit for Multiparty Computation on Small Elements

In many secure multiparty computation (MPC) applications, the semantic domains of some operands are much smaller than the underlying arithmetic field or ring. The arithmetic domain is typically chosen to meet computation and security requirements (e.g., a 128-bit prime field), whereas the actual data may consist of only a few bits, such as 4-bit values in a 16-category classification task. This mismatch can lead to substantial communication and computation overhead in existing MPC protocols, which typically treat data of different ranges uniformly. We introduce UFOs, an ultra-fast toolkit for MPC on small elements, with optimized protocols for one-hot encoding, comparison, and digit decomposition. For $t=2^{k}$ , our random one-hot vector generator attains, in the fan-in-two arithmetic-circuit model, the lower bounds of $t-\log t-1$ multiplication gates and $\lceil \log \log t\rceil $ multiplication depth. Our comparison protocol applies to any public small domain, while DigitDecomp avoids binary expansion and supports any public base $t\gt 1$ . Using these primitives, we construct a higher-radix sorting protocol for large field elements. Experiments confirm the resulting gains in random one-hot vector generation, digit decomposition, and sorting. In particular, our sorting protocol achieves a $3.4\times $ online and $1.4\times $ offline speedup over Hamada et al.’s radix-sort baseline when sorting $2^{16}$ elements among five parties.