Chebyshev polynomials are used as a reservoir for generating intricate classes of symmetrical and chaotic pattems, and have been used in a vast anaount of applications. Using extended Chebyshev polynomial over finite ...Chebyshev polynomials are used as a reservoir for generating intricate classes of symmetrical and chaotic pattems, and have been used in a vast anaount of applications. Using extended Chebyshev polynomial over finite field Ze, Algehawi and Samsudin presented recently an Identity Based Encryption （IBE） scheme. In this paper, we showed their proposal is not as secure as they chimed. More specifically, we presented a concrete attack on the scheme of Algehawi and Samsudin, which indicated the scheme cannot be consolidated as a real altemative of IBE schemes since one can exploit the semi group property （bilinearity） of extended Chebyshev polynomials over Zp to implement the attack without any difficulty.展开更多
基金Acknowledgements The authors would like to thank the reviewers for their detailed reviews and constructive comments, which have helped improve the quality of this paper. This work was partically supported by National Natural Science Foundation of China under Crants No. 61172085, No. 61103221, No. 61133014, No. 11061130539 and No. 61021004.
文摘Chebyshev polynomials are used as a reservoir for generating intricate classes of symmetrical and chaotic pattems, and have been used in a vast anaount of applications. Using extended Chebyshev polynomial over finite field Ze, Algehawi and Samsudin presented recently an Identity Based Encryption （IBE） scheme. In this paper, we showed their proposal is not as secure as they chimed. More specifically, we presented a concrete attack on the scheme of Algehawi and Samsudin, which indicated the scheme cannot be consolidated as a real altemative of IBE schemes since one can exploit the semi group property （bilinearity） of extended Chebyshev polynomials over Zp to implement the attack without any difficulty.
