Chaotic Root-finding for a Small Class of Polynomials
نویسندگان
چکیده
منابع مشابه
Chaotic Root-Finding for a Small Class of Polynomials
In this paper we present a new closed-form solution to a chaotic difference equation, yn+1 = a2y 2 n + a1yn + a0 with coefficient a0 = (a1 − 4)(a1 + 2)/(4a2), and using this solution, show how corresponding exact roots to a special set of related polynomials of order 2, p ∈ N with two independent parameters can be generated, for any p.
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In this paper we present a new closed-form solution to a chaotic difference equation, yn+1 = a2y 2 n + a1yn + a0 with coefficient a0 = (a1 − 4)(a1 + 2)/(4a2), and using this solution, show how corresponding exact roots to a special set of related polynomials of order 2, p ∈ N with two independent parameters can be generated, for any p.
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Root finding is the most time-consuming stage of McEliece cryptosystem decryption. The best method to find the zeroes of a polynomial for cryptographic parameters is the Berlekamp Trace Algorithm (BTA). Our idea is to mix BTA with ad-hoc methods proposed by Zinoviev. We obtain a significant gain in terms of time complexity for finding roots and so we decrease McEliece decryption time. This pape...
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ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2004
ISSN: 1023-6198,1563-5120
DOI: 10.1080/10236190412331285351