Method and system for Cheon resistant static Diffie-Hellman security

A computing device for providing Cheon-resistance security for a static elliptic curve Diffie-Hellman cryptosystem (ECDH), the computing device comprising a hardware processor for executing program instructions configured to:

• receive, at the computing device and from a first computing device, a public key for the first computing device along with curve parameters of a curve with Cheon resistance, the curve with Cheon resistance comprising a curve chosen from a range of curves matching a threshold efficiency and excluding curves which may include intentional vulnerabilities, and being elected 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;
• select a private key for the computing device;
• compute a public key for the computing device based on the curve parameters and the private key for the computing device;
• transmit the public key for the computing device to the first computing device;
• compute a shared secret based on the public key for the first computing device and the private key for the computing device;
• and
• communicating with the first computing device using the shared secret.

A non-transitory computer readable medium for storing instruction code for providing Cheon-resistance security for a static elliptic curve Diffie-Hellman cryptosystem (ECDH), the instruction code, when executed by a processor of a second computing device causing the second computing device to:

• receive, at a second computing device and from a first computing device, a public key for the first computing device along with curve parameters of a curve with Cheon resistance, the curve with Cheon resistance comprising a curve chosen from a range of curves matching a threshold efficiency and excluding curves which may include intentional vulnerabilities, and being elected 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;
• select a private key for the second computing device;
• compute a public key for the second computing device based on the curve parameters and the private key for the second computing device;
• transmit the public key for the second computing device to the first computing device;
• compute a shared secret based on the public key for the first computing device and the private key for the second computing device;
• and
• communicate with the first computing device using the shared secret.