摘要
This paper presents an algebraic method to attack the projected C*? cryptographic scheme.The attack applies the affine parts of the private keys and the weakness caused by the structures of the private keys to find a large number of linear equations.The attack can recover the private keys efficiently when the parameters are small enough.Meanwhile,the weak keys of the scheme are found and the private keys can be recovered efficiently once the weak keys are used.The paper also proposes a new modification of C*? cryptographic scheme,which is not only as efficient as original projected C*? scheme,but also resistant to the differential attack and the attack proposed in this paper.
This paper presents an algebraic method to attack the projected C＊ cryptographic scheme. The attack applies the affine parts of the private keys and the weakness caused by the structures of the private keys to find a large number of linear equations. The attack can recover the private keys efficiently when the parameters are small enough. Meanwhile, the weak keys of the scheme are found and the private keys can be recovered efficiently once the weak keys are used. The paper also proposes a new modification of C＊ cryptographic scheme, which is not only as efficient as original projected C＊- scheme, but also resistant to the differential attack and the attack proposed in this paper.
基金
This work is supported by the National Natural Science Foundation of China under Grants No.60970119 and No.60803149, the Youth Science and Technology Foundation of Xi＇an University of Architecture and Technology （QN0831）, and the National Basic Research Program （973 Program） of China under Grants No.2007CB311201.
