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Showing 1 to 3 of 3 for “"primitive polynomials"”.
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Existence problems of primitive polynomials over finite fields
This thesis concerns existence of primitive polynomials over finite fields with one coefficient arbitrarily prescribed. It completes the proof of a fundamental conjecture of Hansen and Mullen (1992), which asserts that, with some explicable general exceptions, there always exists a primitive …
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Testing Primitive Polynomials for Generalized Feedback Shift Register Random Number Generators
… The poor performance may be due to the choice of primitive polynomials used in the generators, rather than inherent flaws in the method. The original GFSR generators were all based on primitive trinomials. This project examines several alternative choices of primitive polynomials with more than …
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Exploring fields with shift registers
… implementation, and efficient attacks. Different polynomials can be used to generate the fields, and we explore the set of polynomials x^ 2 + x + a^J over GF(2^n) where a is a primitive element of GF(2^n). The results of this work are the first steps towards a full understanding of the field that …