Self-signed implicit certificates

A method of obtaining a public key from a self-signed implicit certificate, the method being performed in a computing device in a cryptographic system based on an underlying group of order n;

• the computing device having a cryptographic unit;
• the method comprising:
• the device operating on said self-signed implicit certificate to obtain a public-key reconstruction value;
• and
• the device operating on said self-signed implicit certificate and said public-key reconstruction value in said cryptographic unit to obtain said public key, said public key corresponding to a private key generated by an issuer of the self-signed implicit certificate.

A method of generating a root private key kCA root and establishing a self-signed implicit certificate ICCA root that can be operated on to obtain a corresponding root public key, the method being performed in a certification authority in a cryptographic system, the cryptographic system based on an underlying elliptic curve group of order n;

• the certification authority having a cryptographic unit;
• the method comprising:
• the certification authority generating an integer representing an ephemeral private key dCA, and operating on said ephemeral private key dCA to compute in said cryptographic unit an element of said elliptic curve group representing a corresponding public-key reconstruction value BCA;
• the certification authority deriving a string from said public-key reconstruction value BCA;
• the certification authority obtaining certificate data ICA;
• the certification authority operating on said string and said certificate data ICA to obtain said self-signed implicit certificate ICCA root;
• the certification authority computing in said cryptographic unit a hash H of said self-signed implicit certificate ICCA root and operating on said hash H to derive an integer e;
• and
• the certification authority operating on said integer e and said ephemeral private key dCA in said cryptographic unit to obtain said root private key kCA root.

A method of obtaining a root public key QCA root from a self-signed implicit certificate ICCA root established by a certification authority in a cryptographic system, the cryptographic system based on an underlying elliptic curve group of order n;

• the method being performed in a computing device having a cryptographic unit;
• the method comprising:
• the device computing a hash H of said self-signed implicit certificate ICCA root in said cryptographic unit and operating on said hash H to derive an integer e;
• the device verifying the contents of said self-signed implicit certificate ICCA root;
• the device operating on said self-signed implicit certificate ICCA root to derive a string representing a public-key reconstruction value BCA;
• the device obtaining said public-key reconstruction value BCA from said string;
• the device verifying the validity of said public-key reconstruction value BCA;
• and
• the device operating on said integer e and said public-key reconstruction value BCA in said cryptographic unit to obtain said root public key QCA root said root public key QCA root corresponding to a root private key generated by said certification authority.