Efficient Generation of Shared RSA keys

In Public key Cryptosystems, exchanging public keys among the communicating parties is very important. Since an adversary can impersonate a legitimate user and send his own public key instead of the legitimate user’s one. So that, the idea of another trusted third party that can authenticate the legitimate parties appeared. This trusted party is often called the Certification Authority (CA) [6]. The CA issues certificates that carry users’ identities along with their public keys. The CA also signs (using its private key) the certificates so that the users can trust each other. When Bob sends his certificate (which he got from the CA) to Alice, she can verify the signature appended to this certificate and make sure that it’s Bob whom she is communication with, assuming that none can forge the signature generated by the CA. Shared keys can be used to protect sensitive private keys, such as Certification Authority keys. In this case, the CA generates the private key and distributes it over several parties (servers) in such a way that each one of them will have a share of the private key but can not construct the whole key. This approach makes it harder for an adversary to break the security system (since he needs now to crack several servers not only one.) However, it still has a single point of attack, which is the party that generates the private key. So, if a hacker compromised the security of this party, he will have the private key.