Partial Exposure Attacks Against a Family of RSA-like Cryptosystems
George Teşeleanu · Cryptography · 2024
An RSA generalization using complex integers was introduced by Elkamchouchi, Elshenawy and Shaban in 2002. This scheme was further extended by Cotan and Teșeleanu to Galois fields of order n≥1. In this generalized framework, the key equation is ed−k(pn−1)(qn−1)=1, where p and q are prime numbers. Note that the classical RSA and Elkamchouchi et al.’s key equations are special cases, namely, when n=1 and n=2. In addition to introducing this generic family, Cotan and Teșeleanu described a continued fractions attack capable of recovering the secret key d if d