Remarks on the bounds for cryptanalysis of low private key RSA |
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Authors: | Haijian Zhou Ping Luo Daoshun Wang Yiqi Dai |
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Institution: | 1. Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China 2. School of Software, Tsinghua University, Beijing 100084, China |
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Abstract: | Boneh and Durfee have developed a cryptanalytic algorithm on low private key RSA. The algorithm is based on lattice basis reduction and breaks RSA with private key d<N0.292. Later on, an improved version by Blömer and May enhanced the efficiency, while reaching approximately this same upper bound. Unfortunately, in both the algorithms, there is a critical error in theoretical analysis, leading to the overestimated upper bound N0.292. In this paper we present a more precise analytical model, with which the theoretical upper bound on d is modified to approximately d<N0.277 for ordinary RSA systems with a 1024-bit public key (N,e). |
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Keywords: | RSA Cryptanalysis Low private key Lattice basis reduction |
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