Security vulnerability of ID-based key sharing schemes

Recently, several ID-based key sharing schemes have been proposed, where an initiation phase generates users' secret key associated with identities under the hardness of integer factorization. In this letter, we show that, unfortunately any key sharing scheme with this initiation phase is intrinsically insecure in the sense that the collusion of some users enables them to derive master private keys and hence, generating any user's secret key.