ELEMENTS OF HIGH ORDER ON FINITE FIELDS FROM ELLIPTIC CURVES

DOI10.1017/S0004972709001075zbMath1221.11145MaRDI QIDQ3564907

José Felipe Voloch

Publication date: 26 May 2010

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

elliptic curvesfinite fieldsmultiplicative group

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Polynomials over finite fields (11T06) Finite ground fields in algebraic geometry (14G15)

Related Items (11)

On division polynomial PIT and supersingularity ⋮ SUM–PRODUCT ESTIMATES AND MULTIPLICATIVE ORDERS OFγANDγ+γ⁻¹IN FINITE FIELDS ⋮ Factor base discrete logarithms in Kummer extensions ⋮ High order elements in finite fields arising from recursive towers ⋮ On solutions of Aczél's equation and some related equations ⋮ Subgroups generated by rational functions in finite fields ⋮ Sharpening of the explicit lower bounds for the order of elements in finite field extensions based on cyclotomic polynomials ⋮ Orders of points in families of elliptic curves ⋮ ELEMENTS OF LARGE ORDER IN PRIME FINITE FIELDS ⋮ Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture ⋮ Elements of large order on varieties over prime finite fields

Cites Work

• Finite field elements of high order arising from modular curves
• The explicit construction of irreducible polynomials over finite fields
• Elements of provable high orders in finite fields

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