Legendre Polynomial over Finite Fields and Factorization of Integers

Kanji Namba

A chapter in International Symposium in Memory of Hua Loo Keng, 1991, pp 209-223 from Springer

Abstract: Abstract We consider elliptic curves of the form: % MathType!MTEF!2!1!+- % feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaCa % aaleqabaGaaGOmaaaakiabg2da9iaadIhadaahaaWcbeqaaiaaioda % aaGccqGHRaWkcaWGHbGaamiEamaaCaaaleqabaGaaGOmaaaakiabgU % caRiaadkgacaWG4bGaey4kaSIaam4yaaaa!4325! $${y^2} = {x^3} + a{x^2} + bx + c$$ over finite field F p , and abelean groups associated to the curve. The order of the group suitably parametrized satisfies so-called Gaussian differential equation.

Keywords: Abelian Group; Prime Number; Elliptic Curve; Finite Field; Elliptic Curf (search for similar items in EconPapers)
Date: 1991
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DOI: 10.1007/978-3-662-07981-2_11

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