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標題Title: RSA with Balanced Short Exponents and Its Application to Entity Authentication
作者Authors: 楊政達
上傳單位Department: 多媒體與電腦娛樂科學系
上傳時間Date: 2009-11-29
上傳者Author: 楊政達
審核單位Department: 多媒體與電腦娛樂科學系
審核老師Teacher: 楊政達
檔案類型Categories: 論文Thesis
關鍵詞Keyword: RSA, Short Exponent Attack, Lattice Reduction, Entity Authentication
摘要Abstract: In typical RSA, it is impossible to create a key pair (e, d) such that both are simultaneously much shorter than φ(N). This is because if d is selected first, then e will be of the same order of magnitude as φ(N), and vice versa. At Asiacrypt’99, Sun et al. designed three variants of RSA using prime factors p and q of unbalanced size. The first RSA variant is an attempt to make the private exponent d short below N^0.25 and N^0.292 which are the lower bounds of d for a secure RSA as argued
first by Wiener and then by Boneh and Durfee. The second RSA variant is constructed in such a way that both d and e have the same bit-length 1/2 log2 N + 56. The third RSA variant is constructed by such a method that allows a trade-off between the lengths of d and e. Unfortunately, at Asiacrypt’2000, Durfee and Nguyen broke the illustrated instances of the first RSA variant and the third RSA variant by solving small roots to trivariate modular polynomial equations. Moreover, they showed that the instances generated by these three RSA variants with unbalanced p and q in fact become more insecure than those instances, having the same sizes of exponents as the former, in RSA with balanced p and q. In this paper, we focus on designing a new RSA variant with balanced d and e, and balanced p and q in order to make such an RSA variant more secure. Moreover, we also extend this variant to another RSA variant in which allows a trade-off between the lengths of d and e. Based on our RSA variants, an application to entity uthentication for defending the stolen-secret attack is presented.

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2009_11_2a19ad95.pdf 239Kb pdf 419 96
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