Title: asymptotic granularity reduction and its application
Author: Su Shenghui
; L&#
; Shuwang
; Fan Xiubin
Keyword: Algebra
; Asymptotic analysis
; Public key cryptography
Source: Theoretical Computer Science
Issued Date: 2011
Volume: 412, Issue: 39, Pages: 5374-5386 Indexed Type: ei
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
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. Language: 英语
WOS ID: WOS:000294592500022
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Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/14063
Appears in Collections: 软件所图书馆_期刊论文
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Recommended Citation:
Su Shenghui,L&#,Shuwang,et al. asymptotic granularity reduction and its application[J]. Theoretical Computer Science,2011-01-01,412(39):5374-5386.
