Results 11 to 20 of about 4,471 (200)
Simultaneous supersingular reductions of CM elliptic curves [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2022 Abstract We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication. We show – under additional congruence assumptions on the CM order – that the reductions are surjective (and even become equidistributed) on the product of supersingular loci when the discriminant of the order ...
Menny Aka +3 more
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CM liftings of supersingular elliptic curves [PDF]
Journal de théorie des nombres de Bordeaux, 2010 Assuming GRH, we present an algorithm which inputs a prime p and outputs the set of fundamental discriminants D<0 such that the reduction map modulo a prime above p from elliptic curves with CM by 𝒪 D to supersingular elliptic curves in characteristic p is surjective. In the algorithm we first determine an explicit constant D p so that |D|>D p
Kane, Ben
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Perrin-Riou's main conjecture for elliptic curves at supersingular primes [PDF]
Mathematische Annalen, 2016 In 1987, B. Perrin-Riou formulated a Heegner point main conjecture for elliptic curves at primes of ordinary reduction. In this paper, we formulate an analogue of Perrin-Riou's main conjecture for supersingular primes. We then prove this conjecture under mild hypotheses, and deduce from this result a $ $-adic extension of Kobayashi's $p$-adic Gross ...
Francesc Castella, Xin Wan
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Elliptic Curves with Supersingular Reduction over $\Gamma$-extensions [PDF]
, 2012 This is a translation of a research announcement by Anas G. Nasybullin from 1976, in which he states formulas for the p-primary part of the Tate-Shafarevich group of an elliptic curve in cyclotomic $\Z_p$-extensions of number fields.
Igor Minevich, Florian Sprung
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Vietnam Journal of Science, Technology and Engineering, 2022 One option for a digital signature solution for devices with low memory and low bandwidth transmission over channels uses a short digital signature scheme based on Weil bilinear pairing aimed at short processing times, fast computation, and convenient ...
Nhu-Quynh Luc +2 more
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TWO-FACTOR AUTHENTICATION PROTOCOL IN ACCESS CONTROL SYSTEMS
Information and Telecommunication Sciences, 2023 Background. To ensure the protection of the biometric access control system used in unsecured communication channels, it is necessary to exclude the storage and transfer, transfer of biometric data as well as sequences generated on their basis. The paper
Ірина Стрелковська +2 more
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On oriented supersingular elliptic curves [PDF]
Finite Fields and Their Applications, 2021 We revisit theoretical background on OSIDH, that is an isogeny-based key-exchange protocol proposed by Col and Kohel at NutMiC 2019. We give a proof of a fundamental theorem for OSIDH. The theorem was stated by Col and Kohel without proof. Furthermore, we consider parameters of OSIDH, give a sufficient condition on the parameters that the protocol ...
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Improved supersingularity testing of elliptic curves
JSIAM Letters, 2021 Summary: In protocols of isogeny-based cryptosystems, we send data of elliptic curves. Then it is necessary to identify supersingularity of the elliptic curves to guarantee the correctness of protocol. Among deterministic algorithms for the purpose, \textit{A. V. Sutherland} [LMS J. Comput. Math.
Hashimoto, Yuji, Takashima, Katsuyuki
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Batching CSIDH Group Actions using AVX-512
Transactions on Cryptographic Hardware and Embedded Systems, 2021 Commutative Supersingular Isogeny Diffie-Hellman (or CSIDH for short) is a recently-proposed post-quantum key establishment scheme that belongs to the family of isogeny-based cryptosystems.
Hao Cheng +4 more
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The most efficient indifferentiable hashing to elliptic curves of j-invariant 1728
Journal of Mathematical Cryptology, 2022 This article makes an important contribution to solving the long-standing problem of whether all elliptic curves can be equipped with a hash function (indifferentiable from a random oracle) whose running time amounts to one exponentiation in the basic ...
Koshelev Dmitrii
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