摘要
In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N^0.258 ≤ e ≤N^0.854, d 〉 e and satisfies the given conditions, we can perform cryptanalytic attacks based on the LLL lattice basis reduction algorithm. The idea is an extension of Boneh and Durfee's researches on low private key RSA, and provides a new solution to finding weak keys in RSA cryptosystems.
In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N^0.258 ≤ e ≤N^0.854, d 〉 e and satisfies the given conditions, we can perform cryptanalytic attacks based on the LLL lattice basis reduction algorithm. The idea is an extension of Boneh and Durfee's researches on low private key RSA, and provides a new solution to finding weak keys in RSA cryptosystems.
基金
Supported partially by the National Basic Research Program of China (Grant No. 2003CB314805)
the National Natural Science Foundationof China (Grant Nos. 90304014 and 60873249)
the Project funded by Basic Research Foundation of School of Information Science and Technology of Tsinghua