Blinded semi-static elliptic curve diffie-hellman authentication protocol

A data processing system comprising instructions embodied in a non-transitory computer readable medium, the instructions for an elliptic curve cryptography authentication method based on an elliptic curve in a processor, the instructions, comprising:

• receiving, by a prover, an x-coordinate of R, wherein R=r·G, where r a random challenge generated by a verifier and G is a basepoint;
• generating, by the prover, two shares q1, q2 of the private key q of the prover such that q=q1−q2;
• calculating P1=q1·R,
• calculating P2=q2·R;
• and
• sending an x-coordinate of P1 and an x-coordinate of P2 to the verifier.

An elliptic curve cryptography authentication method based on an elliptic curve, comprising:

• generating, by a verifier, a random challenge r;
• multiplying, by the verifier, the random challenge r by a basepoint G to produce R;
• sending an x coordinate of R to a prover;
• receiving an x-coordinate of a first point P1 and a second point P2 from the prover, wherein P1 is based on a random share q1 of the private key q of the prover and R, and wherein P2 is based on a random share q2 of the private key q and R;
• where q=q1−q2;
• finding a point P1′ on the elliptic curve having an x-coordinate of the first point P1;
• finding a point P2′ on the elliptic curve having an x-coordinate of the second point P2;
• and
• authenticating the prover when an x-coordinate of one of (P1′+P2′) and (P1′−P2′) matches an x-coordinate of r·Q, wherein Q is a public key of the prover.

An elliptic curve cryptography authentication method based on an elliptic curve, comprising:

• receiving, by a prover, an x-coordinate of R, wherein R=r·G, where r a random challenge generated by a verifier and G is a basepoint;
• generating, by the prover, two shares q1, q2 of the private key q of the prover such that q=q1−q2;
• calculating P1=q1·R,
• calculating P2=q2·R;
• and
• sending an x-coordinate of P1 and an x-coordinate of P2 to the verifier.