Efficient Root Finding of Polynomials over Fields of Characteristic 2
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چکیده
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 paper contains both theoretical and experimental study of this technique.
منابع مشابه
Character Sums and Deterministic Polynomial Root Finding in Finite Fields
Let Fq be a finite field of q elements of characteristic p. The classical algorithm of Berlekamp [1] reduces the problem of factoring polynomials of degree n over Fq to the problem of factoring squarefree polynomials of degree n over Fp that fully split in Fp, see also [8, Chapter 14]. Shoup [15, Theorem 3.1] has given a deterministic algorithm that fully factors any polynomial of degree n over...
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تاریخ انتشار 2009