Results 21 to 30 of about 42,992 (209)
On supersingular primes of the Elkies' elliptic curve
Functiones et Approximatio Commentarii Mathematici, 2019 Let $E$ be the elliptic curve $y^2=x^3+(i-2)x^2+x$ over the imaginary quadratic field $\mathbb{Q}(i)$. In this paper, we investigate the supersingular primes of $E$. We introduce the curve $C$ of genus two over $\mathbb{Q}$ covering a quotient of $E$ and for any prime number $p$, we state a condition (over $\mathbb{F}_p$) about the reduction of the ...
N. Murabayashi
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A singular property of the supersingular elliptic curve in characteristic 2
, 2010 In the first version of the paper, the quest for simplicity in the exposition leaded the author to a major oversight (the notion of signature), inducing some wrong assertions, which are now corrected. In this new version, the results and their proofs are almost unchanged.
Leonardo Zapponi
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Computing Isomorphisms between Products of Supersingular Elliptic Curves [PDF]
The Deligne-Ogus-Shioda theorem guarantees the existence of isomorphisms between products of supersingular elliptic curves over finite fields. In this paper, we present methods for explicitly computing these isomorphisms in polynomial time, given the endomorphism rings of the curves involved.
Pierrick Gaudry +2 more
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APPROACH TO CHECKING THE SUPERSINGULARITY OF ELLIPTIC CURVES AND CALCULATING THEIR ORDER
INFORMATION TECHNOLOGY AND SOCIETY, 2021 Ruslan SKURATOVSKYI
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Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems [PDF]
Journal of Cryptology, 2004 Eric R. Verheul
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Earthline Journal of Mathematical Sciences, 2023 Several research works propose the use of Elliptic Curve Cryptography (ECC) to provide security for the Internet of Things (IoT) and cloud computing due to its shorter key requirement of approximately 160-571 bits vs.
Zakaria Abukari +2 more
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A remark on the characteristic elements of anticyclotomic Selmer groups of elliptic curves with complex multiplication at supersingular primes [PDF]
Quarterly Journal of Mathematics, 2023 Let $p\ge5$ be a prime number. Let $E/\mathbb{Q}$ be an elliptic curve with complex multiplication by an imaginary quadratic field K such that p is inert in K and that E has good reduction at p.
Antonio Lei
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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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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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