| asymptotic granularity reduction and its application |
| Su Shenghui; L&#; Shuwang; Fan Xiubin
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| 2011
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| 发表期刊 | Theoretical Computer Science
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| ISSN | 3043975
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| 卷号 | 412期号:39页码:5374-5386 |
| 摘要 | It is well known that the inverse function of y=x with the derivative y′=1 is x=y, the inverse function of y=c with the derivative y′=0 is nonexistent, and so on. Hence, on the assumption that the noninvertibility of the univariate increasing function y=f(x) with x>0 is in direct proportion to the growth rate reflected by its derivative, the authors put forward a method of comparing difficulties in inverting two functions on a continuous or discrete interval called asymptotic granularity reduction (AGR) which integrates asymptotic analysis with logarithmic granularities, and is an extension and a complement to polynomial time (Turing) reduction (PTR). Prove by AGR that inverting y≡xx(modp) is computationally harder than inverting y≡gx(modp), and inverting y≡gxn(modp) is computationally equivalent to inverting y≡gx(modp), which are compatible with the results from PTR. Besides, apply AGR to the comparison of inverting y≡xn(modp) with y≡gx(modp), y≡gg1x(modp) with y≡gx(modp), and y≡xn+x+1(modp) with y≡xn(modp) in difficulty, and observe that the results are consistent with existing facts, which further illustrates that AGR is suitable for comparison of inversion problems in difficulty. Last, prove by AGR that inverting y≡xngx(modp) is computationally equivalent to inverting y≡gx(modp) when PTR cannot be utilized expediently. AGR with the assumption partitions the complexities of problems more detailedly, and finds out some new evidence for the security of cryptosystems. © 2011 Elsevier B.V. All rights reserved. |
| 收录类别 | ei
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| 关键词 | Algebra
Asymptotic Analysis
Public Key Cryptography
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| 部门归属 | (1) College of Computer, Beijing University of Technology, Beijing 100124, China; (2) Graduate School, Chinese Academy of Sciences, Beijing 100039, China; (3) Institute of Software, Chinese Academy of Sciences, Beijing 100080, China
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| 语种 | 英语
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| WOS记录号 | WOS:000294592500022
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| 引用统计 |
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| 内容类型 | 期刊论文
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| URI标识 | http://ir.iscas.ac.cn/handle/311060/14063
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| 专题 | 中国科学院软件研究所
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推荐引用方式
GB/T 7714 |
Su Shenghui,L&#,Shuwang,et al. asymptotic granularity reduction and its application[J]. Theoretical Computer Science,2011,412(39):5374-5386.
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| APA |
Su Shenghui,L&#,Shuwang,&Fan Xiubin.(2011).asymptotic granularity reduction and its application.Theoretical Computer Science,412(39),5374-5386.
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| MLA |
Su Shenghui,et al."asymptotic granularity reduction and its application".Theoretical Computer Science 412.39(2011):5374-5386.
|
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