Results 11 to 20 of about 4,610 (199)
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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Torsion point attacks on ‘SIDH‐like’ cryptosystems
IET Information Security, 2023 Isogeny‐based cryptography is a promising approach for post‐quantum cryptography. The best‐known protocol following that approach is the supersingular isogeny Diffie–Hellman protocol (SIDH); this protocol was turned into the CCA‐secure key encapsulation ...
Péter Kutas, Christophe Petit
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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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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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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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Concentration of closed geodesics in the homology of modular curves
Forum of Mathematics, Sigma, 2023 We prove that the homology classes of closed geodesics associated to subgroups of narrow class groups of real quadratic fields concentrate around the Eisenstein line.
Asbjørn Christian Nordentoft
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Extended supersingular isogeny Diffie–Hellman key exchange protocol: Revenge of the SIDH
IET Information Security, 2021 The supersingular isogeny Diffie–Hellman key exchange protocol (SIDH) was introduced by Jao and De Feo in 2011. SIDH operates on supersingular elliptic curves defined over Fp2, where p is a large prime number of the form p=4eA3eB−1 and eA and eB are ...
Daniel Cervantes‐Vázquez +2 more
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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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