A method of generating a first and a second root private key (k CAroot) and establishing a first (IC 1 CAroot) and a second (IC 2 CAroot) self-signed implicit certificate that can be operated on to obtain a first and a second corresponding root public key (Q 1 CAroot, Q 2 CAroot), said first public key corresponding to a first security domain and said second public key corresponds to a second security domain, said method being performed by a certification authority device that issues certificates in a cryptographic system based on an underlying elliptic group of order n, said certification authority device having a cryptographic unit, said method comprising: the certification authority device obtaining a long-term private key, r CAroot, and a corresponding public-key reconstruction value, B CA, where B CA =r CAroot G and G is the base point on the underlying elliptic curve; the certification authority device obtaining a first (I CA1) and a second (I CA2) certificate data; the certification authority device operating on said public-key reconstruction value and said first certificate data (I CA1) to obtain said first self-signed implicit certificate (IC 1 CAroot); the certification authority device operating on said public-key reconstruction value and said second certificate data (I CA2) to obtain said second self-signed implicit certificate (IC 2 CAroot); the certification authority device operating on said long-term private key and said first self-signed implicit certificate to obtain said first root private key; and the certification authority device operating on said long-term private key and said second self-signed implicit certificate to obtain said second root private key; wherein each of said first and second root private keys are an integer of the form k CAroot =e.r CAroot +r (mod n); wherein e is an integer derived using a hash of said respective first or second self-signed implicit certificate, and r is an integer, and wherein said integer r is either 0, 1, or r CAroot. the certification authority device obtaining a long-term private key, r CAroot, and a corresponding public-key reconstruction value, B CA, where B CA =r CAroot G and G is the base point on the underlying elliptic curve; the certification authority device obtaining a first (I CA1) and a second (I CA2) certificate data; the certification authority device operating on said public-key reconstruction value and said first certificate data (I CA1) to obtain said first self-signed implicit certificate (IC 1 CAroot); the certification authority device operating on said public-key reconstruction value and said second certificate data (I CA2) to obtain said second self-signed implicit certificate (IC 2 CAroot); the certification authority device operating on said long-term private key and said first self-signed implicit certificate to obtain said first root private key; and the certification authority device operating on said long-term private key and said second self-signed implicit certificate to obtain said second root private key; wherein each of said first and second root private keys are an integer of the form k CAroot =e.r CAroot +r (mod n); wherein e is an integer derived using a hash of said respective first or second self-signed implicit certificate, and r is an integer, and wherein said integer r is either 0, 1, or r CAroot.