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Application of periodic orbit theory in chaos-based security analysis 被引量:3
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作者 龙敏 丘水生 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第8期2254-2258,共5页
Chaos-based encryption schemes have been studied extensively, while the security analysis methods for them are still problems to be resolved. Based on the periodic orbit theory, this paper proposes a novel security an... Chaos-based encryption schemes have been studied extensively, while the security analysis methods for them are still problems to be resolved. Based on the periodic orbit theory, this paper proposes a novel security analysis method. The periodic orbits theory indicates that the fundamental frequency of the spiraling orbits is the natural frequency of associated linearized system, which is decided by the parameters of the chaotic system. Thus, it is possible to recover the plaintext of secure communication systems based on chaotic shift keying by getting the average time on the spiraling orbits. Analysis and simulation results show that the security analysis method can break chaos shift keying secure communication systems, which use the parameters as keys. 展开更多
关键词 periodic orbit theory secure communication chaos-based security analysis
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LIMIT CYCLES OF THE GENERALIZED POLYNOMIAL LINARD DIFFERENTIAL SYSTEMS
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作者 Amel Boulfoul Amar Makhlouf 《Annals of Applied Mathematics》 2016年第3期221-233,共13页
Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y + εhl1(x) + ε2hl2(x),y=-x- ε(fn1(x)y(2p+1) + gm1(x))... Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y + εhl1(x) + ε2hl2(x),y=-x- ε(fn1(x)y(2p+1) + gm1(x)) + ∈2(fn2(x)y(2p+1) + gm2(x)),which bifurcate from the periodic orbits of the linear center x = y,y=-x,where ε is a small parameter.The polynomials hl1 and hl2 have degree l;fn1and fn2 have degree n;and gm1,gm2 have degree m.p ∈ N and[·]denotes the integer part function. 展开更多
关键词 limit cycle periodic orbit Li′enard differential system averaging theory
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