Cryptographic key generation using kummer varieties

A method performed by a certification authority (CA) comprising a computer system, to allow a first computer entity to generate a first private/public key pair, the method comprising:

• generating, by the CA, a first CA key pair for use with a plurality of computer entities including the first computer entity, the first CA key pair comprising a first CA private key and a first CA public key;
• generating, by the CA, a second CA key pair comprising a scalar and a corresponding element of an elliptic curve, wherein the second CA key pair is associated with the first computer entity;
• receiving by the CA, from the first computer entity, an element of the elliptic curve, wherein the received element is to correspond to the first computer entity's secret scalar;
• generating, by the CA, a plurality of values for sending to the first computer entity, the plurality of values comprising:
• a first value of the plurality, the first value corresponding to the sum of:
• (1) the elliptic curve element of the second key pair, and (2) the elliptic curve element received from the first computer entity;
• a second value of the plurality, wherein the second value depends on:
• the scalar of the second CA key pair, the elliptic curve element of the second CA key pair, and an identity associated with the first computer entity;
• sending, by the CA to the first computer entity, the first and second values of the plurality and the elliptic curve element of the second key pair.

A system for generating a first private/public key pair, wherein the first private/public key pair includes a first private key and a corresponding first public key, the system comprising:

• a memory containing machine readable medium storing machine executable code;
• one or more processors coupled to the memory and configured to execute the machine executable code to cause the one or more processors to:
• generate the first private key, wherein the first private key depends on a first scalar, wherein generating the first private key comprises generating the first scalar by using private key material received from a certification authority (CA) and dependent on the CA's private key;
• generate the first public key corresponding to the first private key and dependent on the private key material, wherein generating the first public key comprises computing, by the first computer entity, an element of a Kummer variety of a finite elliptic curve group, the element being dependent on the private key material.