We investigate the possibilities of building a Multivariate Identity-Based Encryption (IBE) Scheme, such that for each identity the obtained Public Key Encryption Scheme is Multivariate Quadratic (MQ). The biggest problem in creating an IBE with classical MQ properties is the possibility of collusion of polynomial number of users against the master key or the keys of other users. We present a solution that makes the collusion of polynomial number of users computationally infeasible, although still possible. The proposed solution is a general model for a Multivariate IBE Scheme with exponentially many public-private keys that are instances of an MQ public key encryption scheme.
Identity-Based Encryption (IBE) Public Key Encryption Schemes Multivariate Quadratic Schemes (MQ schemes)