A method for providing Cheon-resistance security for a static elliptic curve Diffie- Hellman cryptosystem (ECDH), the method including providing a system for message communication between a pair of correspondents, a message being exchanged in accordance with ECDH instructions executable on computer processors of the respective correspondents, the ECDH instructions using a curve selected from a plurality of curves, the selecting including choosing a range of curves; selecting, from the range of curves, curves matching a threshold efficiency; excluding, within the selected curves, curves which may include intentional vulnerabilities; and electing, from non-excluded selected curves, a curve with Cheon resistance, the electing comprising a curve from an additive group of order q , wherein q is prime, such that q-1 = cr and q +1 = ds , where r and s are primes and c and d are integer Cheon cofactors of the group, such that cd ≤ 48.