US Patent 10116443 Pairing verification in supersingular isogeny-based cryptographic protocols

In a general aspect, a supersingular isogeny-based cryptography process is performed. In some aspects, a secret integer of a first entity is obtained. A public key of a second entity includes a first image curve and a first pair of elliptic curve points. A first pairing value is computed based on a second pair of elliptic curve points defined by a supersingular isogeny-based cryptosystem. A second pairing value is computed based on the first pair of elliptic curve points. Validating the public key includes verifying whether the first pairing value matches the second pairing value. A second image curve is computed based on the secret integer and the first pair of elliptic curve points. A shared secret value, shared by the first entity and the second entity, is computed based on the second image curve.