Wei Jiang, "Efficient and Constant-Round Secure Comparison through Function Transformation, Dynamic Group Switching and Asymmetric Computation"

Within recent years, secure comparison protocols have been proposed
using binary decomposition and properties of algebraic fields.
These protocols have become increasingly efficient, but their
performance has seemingly reached a plateau. We propose a new
approach to this problem that transforms the comparison function
into comparing specialized summations and takes advantage of
dynamically switching domains of secret shares and asymmetric
computations for intermediate calculations among the participating
parties. As a consequence, according to our analysis, communication
and computation costs have been brought to a very low and efficient
level. Particularly, the communication costs have been considerably
reduced both in order as well as the dominating term’s order of
magnitude. In addition, we propose a secure protocol under the
malicious setting which maintains our transformation and is more
efficient than the existing work for common domain sizes.