Cryptographic key generation using kummer varieties
An authenticated, ID-based private/public key pair, with a self-certified public key, is generated using Kummer arithmetic without bilinear pairings. Two or more parties can generate such key pairs and use them as their respective long-term key pairs which, when combined with the parties' short-term key pairs, can allow the parties to establish an authenticated, short-term shared key. Some embodiments are suitable for connected vehicles communicating with each other and/or with other systems. Other features are also provided.
1. 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.
2. The method of claim 1 wherein generating the first value of the plurality comprises:
generating, in a projective space, 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; and
generating the first value of the plurality as affine (x,y) coordinates of the sum, the affine (x, y) coordinates corresponding to a polynomial equation defining the elliptic curve, the polynomial equation having a second degree in coordinate y and a third degree in coordinate x.