Cyclicity statistics for elliptic curves over finite fields

DOI10.1006/ffta.1998.0225zbMath0927.11032OpenAlexW38060680MaRDI QIDQ1284208

S. G. Vleduts

Publication date: 12 December 1999

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/ffta.1998.0225

zbMATH Keywords

elliptic curvesfinite fields

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15)

Related Items (16)

Sums of Euler products and statistics of elliptic curves ⋮ Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height ⋮ Small exponent point groups on elliptic curves ⋮ On the cyclicity of the rational points group of abelian varieties over finite fields ⋮ The distribution of the number of points modulo an integer on elliptic curves over finite fields ⋮ Elliptic curve analogue of Legendre sequences ⋮ Primes, elliptic curves and cyclic groups ⋮ On the elliptic curve analogue of the sum-product problem ⋮ Corrigendum to: ``Local cyclicity of isogeny classes of abelian varieties defined over finite fields ⋮ Pseudo-Randomness of Discrete-Log Sequences from Elliptic Curves ⋮ A Digital Signature Scheme Based on Two Hard Problems ⋮ Constants in Titchmarsh divisor problems for elliptic curves ⋮ Local cyclicity of isogeny classes of abelian varieties defined over finite fields ⋮ Cyclic abelian varieties over finite fields in ordinary isogeny classes ⋮ On the linear complexity and multidimensional distribution of congruential generators over elliptic curves ⋮ Pseudorandom vector generation using elliptic curves and applications to Wiener processes

Cites Work

• Cyclicity and generation of points mod \(p\) on elliptic curves
• Factoring integers with elliptic curves
• Nonsingular plane cubic curves over finite fields
• Primitive points on elliptic curves
• Abelian varieties over finite fields
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