Endomorphism rings of reductions of Drinfeld modules

Garai, Sumita; Papikian, Mihran

doi:10.48550/arxiv.1804.07904

Cited by 1 publication

(2 citation statements)

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“…From this, Hsia and Yu [17] and Garai and Papikian [9] sketched algorithms that compute A. When φ p is computed in a direct manner, they take Θ(n 2 ) additions, multiplications and Frobenius applications in L, so Ω(n 3 ) bit operations.…”

Section: The Case L = Kmentioning

confidence: 99%

“…Based in part on these similarities, Drinfeld modules have recently started being considered under the algorithmic viewpoint. For instance, they have been proved to be unsuitable for usual forms of public key cryptography [34]; they have also been used to design several polynomial factorization algorithms [7,29,30,38]; recent work by Garai and Papikian discusses the computation of their endomorphism rings [9]. Our goal is to study in detail the complexity of computing the characteristic polynomial of a rank two Drinfeld module over a finite field.…”

Section: Introductionmentioning

confidence: 99%

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Computing the Characteristic Polynomial of a Finite Rank Two Drinfeld Module

Musleh

Schost

2019

Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation

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Motivated by finding analogues of elliptic curve point counting techniques, we introduce one deterministic and two new Monte Carlo randomized algorithms to compute the characteristic polynomial of a finite rank-two Drinfeld module. We compare their asymptotic complexity to that of previous algorithms given by Gekeler, Narayanan and Garai-Papikian and discuss their practical behavior. In particular, we find that all three approaches represent either an improvement in complexity or an expansion of the parameter space over which the algorithm may be applied. Some experimental results are also presented.

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Section: The Case L = Kmentioning

confidence: 99%