International Association
for Cryptologic Research

Secure computation has become a necessity in the modern world. Its applications are widespread: from allowing medical researchers to compute statistics over private patient data without violating HIPAA to helping large companies like Meta and Google avoid GDPR fines. A ubiquitous and popular choice for secure computation is Multi-party Computation (MPC). Most MPC protocols work over finite fields or rings, which means that encoding techniques are required to map rational-valued data into the algebraic structure being used. Leveraging an encoding technique introduced in "$\mathsf{PIE}$ : $p$-adic Encoding for High-Precision Arithmetic in Homomorphic Encryption", we present $\mathsf{Mercury}$ - a family of protocols for addition, multiplication, subtraction, and division of rational numbers. Notably, the output of our division protocol is exact (i.e., it does not use iterative methods). Our protocols offer significant improvements in both round complexity and communication complexity when compared with prior art, and are secure for a dishonest minority of semi-honest parties. We emphasize that the encoding technique our protocols are based on is composable, so it can be paired with any MPC protocol over a prime-order field.