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Showing 1 to 3 of 3 for “"Lucas sequences"”.
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Higher-Order Lucas Sequences and Dickson Polynomials
In this paper we determine when there exists a matrix M in PGL2(F), and its form, such that L_k = D^M_k where D^M_k is a higher-order Dickson polynomial. We first examine the cases where M has projective orders 3, 4, and 6. For the order 3 case, we find that M has entries in, at worst, a quadratic …
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Security systems based on Gaussian integers : Analysis of basic operations and time complexity of secret transformations
… to two other well known problems: DLP for Lucas sequences and the real integer DLP. Additionally, a novel exponentiation algorithm for Gaussian integers, called Lucas sequence Exponentiation of Gaussian integers (LSEG) is introduced and its performance assessed, both analytically and …