On the Existence of Multiple RSA Private Keys
Chuan-Kun Wu, Bin L. Zhao · Security and Communication Networks · 2022
It is known that, given an RSA modulus, n = p q , the public key e and the corresponding private key d satisfy the modulo congruence e d ≡ 1 mod ϕ n , where ϕ n = p − 1 q − 1 . Usually, the private key d can be computed efficiently using the extended Euclidean algorithm, and it is common knowledge that the private key is unique in the sense of modular ϕ n . This paper shows that there exist multiple private keys d ; they all satisfy that d < ϕ n . This paper also presents the exact relationship between an RSA public key and a corresponding private key.