Twelve new primitive binary trinomials

Richard Brent 1 Paul Zimmermann 2
2 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry, Inria Nancy - Grand Est
Abstract : We exhibit twelve new primitive trinomials over GF(2) of record degrees 42 643 801, 43 112 609, and 74 207 281. In addition we report the first Mersenne exponent not ruled out by Swan's theorem [10] — namely 57 885 161 — for which none primitive trinomial exists. This completes the search for the currently known Mersenne prime exponents.
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https://hal.inria.fr/hal-01378493
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Submitted on : Monday, October 10, 2016 - 11:44:10 AM
Last modification on : Tuesday, December 18, 2018 - 4:18:26 PM
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  • HAL Id : hal-01378493, version 1
  • ARXIV : 1605.09213

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Richard Brent, Paul Zimmermann. Twelve new primitive binary trinomials. 2016. ⟨hal-01378493⟩

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