Fast algorithms for solving equations of degree \(\le 4\) in some finite fields

DOI10.3103/S0027132221030049zbMath1481.12002OpenAlexW3201310957MaRDI QIDQ2666933

Sergey B. Gashkov

Publication date: 23 November 2021

Published in: Moscow University Mathematics Bulletin (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s0027132221030049

zbMATH Keywords

solving equationsbit complexitystandard and normal basestower of finite fields

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Finite fields (field-theoretic aspects) (12E20) Computational methods for problems pertaining to field theory (12-08)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Formulas for cube roots in \(\mathbb F_{3^m}\)
• Fast algorithm of square rooting in some finite fields of odd characteristic
• Computing in degree \(2^k\)-extensions of finite fields of odd characteristic
• Faster polynomial multiplication over finite fields using cyclotomic coefficient rings
• Efficient computation of roots in finite fields
• The complexity and depth of Boolean circuits for multiplication and inversion in some fields \(\mathrm{GF}(2^{n})\)
• On complexity and depth of Boolean circuits for multiplication and inversion over finite fields of characteristic 2
• Taking roots over high extensions of finite fields
• Fast Polynomial Factorization and Modular Composition
• Formulas for the solutions of quadratic equations over<tex>GF(2^m)</tex>(Corresp.)
• Faster integer multiplication using plain vanilla FFT primes
• On a quick multiplication in normal bases of finite fields
• An application of the method of additive chains to inversion in finite fields
• On the solution of algebraic equations over finite fields
• Hybrid methods for finding roots of a polynomial - With application to BCH decoding (Corresp.)
• A note on square roots in finite fields