Secure rational numbers equivalence test based on threshold cryptosystem with rational numbers

In this study, we consider an equivalence test on rational numbers in a scenario with K+2 distributed parties, Alice, Bob, P1,P2,…,PK, where Alice has a private rational number xa, Bob has a private rational number xb, and party Pi has a secret si, where i∈{1,2,…,K},K ≥ 2. The parties want to cooperatively detect whether xa=xb without revealing any information about their secrets. This problem has many applications in online collaboration, such as e-voting, which requires public verifiability. First, we develop a provably secure threshold cryptosystem for rational numbers. Next, based on the proposed threshold scheme, we construct a distributed plaintext equivalence test protocol in an honest majority environment. We prove that the proposed protocol is secure and robust in the standard (ideal/real) model.