International Association
for Cryptologic Research

In this paper, we propose a novel bi-primality test to determine whether $N=pq$ is the product of two primes on any RSA modulus in which we relaxed the restriction, $p\equiv q \equiv 3 \mbox{ (mod } 4)$, that was assumed in most of current bi-primality tests. Our bi-primality test is generalized from Lucas primality test to the bi-prime case. Our test always accepts when $p$ and $q$ are both prime, and otherwise accepts with probability at most $1/2$. In addition, we also prove that the Boneh-Franklin's bi-primality test accepts composite with probability at most $1/4$ instead of $1/2$, if we add an additional condition $\gcd(N, p+q-1)=1$. Moreover, we design a multiparty protocol against of static semi-honest adversaries in the hybrid model and provide a security proof. We then implement the proposed protocol and run in a single thread on a laptop which turned out with average 224 seconds execution time, given that $N$ is around $2048$-bit.