In search of secure domain parameters under strong diffie-hellman and related assumptions

In the literature, many cryptosystems are based on the Strong Diffie-Hellman (SDH) and related problems. If cryptosystems based on the SDH problem use general domain parameters, this leads to a significant security loss. However, domain parameters in standards (e.g., SEC 2, ANSI X9.62/63, IEEE 1363, NIST SP 800-56) are susceptible to Cheon´s algorithm [10], [11]. In this paper, we propose an algorithmic procedure based on some observations, and then show simulation results for secure elliptic curve domain parameters resistant to Cheon´s algorithm [10], [11].