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| asymptotic granularity reduction and its application | |
| Su Shenghui; L&#; Shuwang; Fan Xiubin | |
| 2011 | |
| Source | Theoretical Computer Science
 |
| ISSN | 3043975 |
| Volume | 412Issue:39Pages:5374-5386 |
| English Abstract | 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. |
| Indexed Type | ei |
| Keyword | Algebra Asymptotic Analysis Public Key Cryptography |
| Department | (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 |
| Language | 英语 |
| WOS ID | WOS:000294592500022 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/14063 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Su Shenghui,L&#,Shuwang,et al. asymptotic granularity reduction and its application[J]. Theoretical Computer Science,2011,412(39):5374-5386. |
| APA | Su Shenghui,L&#,Shuwang,&Fan Xiubin.(2011).asymptotic granularity reduction and its application.Theoretical Computer Science,412(39),5374-5386. |
| MLA | Su Shenghui,et al."asymptotic granularity reduction and its application".Theoretical Computer Science 412.39(2011):5374-5386. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| Asymptotic granulari（253KB） | 开放获取 | -- | Application Full Text | |||
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