Pitfalls in identity based encryption using extended chebyshev polynomial

Chebyshev polynomials are used as a reservoir for generating intricate classes of symmetrical and chaotic patterns, and have been used in a vast amount of applications. Using extended Chebyshev polynomial over finite field Z _p, Algehawi and Samsudin presented recently an Identity Based Encryption (IBE) scheme. In this paper, we showed their proposal is not as secure as they claimed. More specifically, we presented a concrete attack on the scheme of Algehawi and Samsudin, which indicated the scheme cannot be consolidated as a real alternative of IBE schemes since one can exploit the semi group property (bilinearity) of extended Chebyshev polynomials over Z _p to implement the attack without any difficulty.