Method and system for cheon resistant static diffie-hellman security

A method for providing Cheon-resistance security for a static elliptic curve Diffie-Hellman cryptosystem (ECDH), the method comprising:

• 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 comprising:
• 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;
• an affine equation in the form y2=x3+ix, where i=√{square root over (−1)};
• a length of 454 bits;
• a field size p=2454+(3×17×11287)2;
• an order q=2452+(7×41117)2;
• r=(q−1)/8;
• and
• s=(q+1)/6.

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

• provide 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 comprising:
• choose a range of curves;
• select, from the range of curves, curves matching a threshold efficiency;
• exclude, within the selected curves, curves which may include intentional vulnerabilities;
• and
• elect, from non-excluded selected curves, a curve with Cheon resistance, the electing comprising electing 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.

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

• 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 comprising:
• 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;
• an affine equation in the form y2=x3+ix, where i=√{square root over (−1)};
• a length of 454 bits;
• a field size p=2454+(3×17×11287)2;
• an order q=2452+(7×41117)2;
• r=(q−1)/8;
• and
• s=(q+1)/6.