A new Identity Based Encryption (IBE) scheme using extended Chebyshev polynomial over finite fields ZpZp

We present a method to extract key pairs needed for the Identity Based Encryption (IBE) scheme from extended Chebyshev polynomial over finite fields ZpZp. Our proposed scheme relies on the hard problem and the bilinear property of the extended Chebyshev polynomial over ZpZp. The proposed system is applicable, secure, and reliable.