Polynomial Analysis of DH Secrete Key and Bit Security

In this paper, we lower the upper bound of the number of solutions of oracle transformation polynomial F(x) over GF(q). So one can also recover all the secrete keys with fewer calls. We use our generalized ““““““““even-and-odd test““““““““ method to recover the least significant p-adic ‘bits‘ of representations of the Lucas Cryptosystem secret keys x. Finally, we analyze the Efficient Compact Subgroup Trace Representation (XTR) Diffie-Hellmen secrete keys and point out that if the order of XTR subgroup has a special form then all the bits of the secrete key of XTR can be recovered form any bit of the exponent x.

Polynomial analysis of DH secrete key and bit security

In this paper, we lower the upper bound of the number of solutions of oracle transformation polynomialF(x) overGF(q). So one can also recover all the secrete keys with fewer calls. We use our generalized “even-and-odd test” method to recover the least significantp-adic ‘bits’ of representations of the Lucas Cryptosystem secret keysx. Finally, we analyze the Efficient Compact Subgroup Trace Representation (XTR) Diffie-Hellmen secrete keys and point out that if the order of XTR-subgroup has a special form then all the bits of the secrete key of XTR can be recovered form any bit of the exponentx. Foundation item: Supported by the Special Funds for Major State Basic Research Program of China (973 Program) (G1999035804) Biography: JIANG Zheng-tao (1976-), male, Ph.D candidate, research direction: the theory of public-key cryptography, network security, number theory and its application.