[Resource Topic] 2024/205: A Generalized Distributed RSA Key Generation

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A Generalized Distributed RSA Key Generation

Authors: ChihYun Chuang, IHung Hsu, TingFang Lee


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.

ePrint: https://eprint.iacr.org/2024/205

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