About one algorithm of calculation of inverses in finite fields
In work are two algorithms of calculation of inverses in a finite field qn F developed, where q is power of the prime number. They are received by generalisation of algorithm of Wong for a field F2n with use of the main idea for fast algorithm of calculation of inverses in the field 2 F n .
1. Handbook of elliptic ...
About generations of curves of genus 2 of p-rank 1 over finite fields
Explicit methods of ge nerations of curves of genus 2 of p-rank 1 over finite fields are produced.
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2. Serre J. P. ...
About pairing on abelian varieties p-rank one and their cryptographic applications
... Vol. 5011. P. 60—73.
4. Galbraith S. D., Hess F., Vercauteren F. Hyperelliptic pairing // Pairing 2007. LNCS 4575. 2007. P. 108—131.
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6. Granger R., Hess F. et al. Ate pairing on hyperelliptic curves // Advance in Cryptology–EUROCRYPT’2007. LNCS 4515. 2007. P. 430—447.
7. Granger R., Page D., Smart N. P. High security ...
Algebraic-geometric code is associated with a curve of genus 3 over finite field with discriminant 19
The construction of an AG-code and the process of decoding are described by the Rimann-Roch spaces.
Optimal curves of genus 3 over finite fields with discriminant
19 // arXiv: 0902.1091v1 [math. AG
С., Алешников С.
И., Зайцев А.
Общие уравнения оптимальных кривых над конечным ...
Overview of effective point counting algorithms for Jacobian of hyperelliptic curve over finite field
... hyperelliptic curves of type.....
Furukawa E., Kawazoe M., Takahashi T.
Counting points for hyperelliptic curves of type.....
// Ibid. 2002.
The minimum and maximum number of rational points on jacobian surfaces over finite fields. URL: http://arxiv. org/abs/1002.3683.2010.
Ravnshoj C. R.
Generators of Jacobians of genus two curves // Cryptology ePrint Archive. 2008.
Ravnshoj C. R.
Non-cyclic subgroups of Jacobians of genus two curves // Ibid.
A review of the existing generalizations of the Deuring Reduction Theorem
... 5671. Springer, 2009. P. 52—65.
2. Blake C. A Deuring criterion for abelian varieties // Bulletin of the London Mathematical Society. Dec. 2014. Vol. 46, issue 6. P. 1256.
3. Bradford J. Commutative Endomorphism Rings of Simple Abelian Varieties over Finite Fields. Ph. D. Thesis, University of Maryland, 2012.
4 Clark P. L. Bounds for torsion on abelian varieties with integral moduli // arXiv:math/0407264, 2004.
5. Clark P. L., Xarles X. Local bounds for torsion points on abelian varieties // Canad. J. Math....
The closed piecewise uniform string revisited
... plasma shell // J. Phys. A: Math. Gen. 2018. Vol. 51. 455001.
22. Bordag M. Entropy in some simple one-dimensional configurations. 2018. ArXiv: 1807.10354quant-ph.
23. Bordag M., Munoz-Castaneda J. M., Santamaría-Sanz L. Free energy and entropy for finite temperature quantum field theory under the influence of periodic backgrounds // Eur. Phys. J. C. 2020. Vol. 80 (3).
24. Brevik I., Sollie R. On the Casimir energy for a 2N-piece relativistic string // J. of Mathematical Physics. 1997. Vol. 38 (6). P. 2774—2785.
25. Griffiths ...
An efficient implementation of an exponential point-counting algorithm on Jacobians of genus 2 hyperelliptic curves
... CRT (polynomial-time part); 2) restoring the number of points utilizing modular data using algorithms based on birthday paradox (exponential-time part). Theoretically, the algorithm terminates after the first stage with time-complexity, where is a finite field modulus. However, in practice we terminate the polynomial-time part (due to high memory consumption), and we proceed to the second, memory-efficient, exponential-time part. This article presents a multithreaded C++ implementation of exponential ...