Asymptotic formula for Tate-Shafarevich groups of $p$-supersingular elliptic curves over anticyclotomic extensions [PDF]
, 2022 Antonio Lei +2 more
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Supersingular Elliptic Curves, Quaternion Algebras and Applications to Cryptography
This paper contains a survey of supersingular isogeny graphs associated to supersingular elliptic curves and their various applications to cryptography. Within limitation of space, we attempt to address a broad audience and make this part widely accessible. For those graphs we also present three recent results and sketch their proofs. We then discuss a
Goren, Eyal Z., Love, Jonathan R.
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APPROACH TO CHECKING THE SUPERSINGULARITY OF ELLIPTIC CURVES AND CALCULATING THEIR ORDER
, 2021 Ruslan SKURATOVSKYI
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Non-Invertible Public Key Certificates. [PDF]
Entropy (Basel), 2021 Lizama-Perez LA, López R JM.
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The Iwasawa Main Conjecture for elliptic curves at odd supersingular\n primes [PDF]
, 2016 Florian Sprung
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Post-quantum distributed ledger technology: a systematic survey. [PDF]
Sci Rep, 2023 Parida NK +4 more
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Supersingular elliptic curves, theta series and weight two modular forms [PDF]
, 2002 Matthew Emerton
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Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs
Journal de théorie des nombres de BordeauxIn this paper, we add the information of level structure to supersingular elliptic curves and study these objects with the motivation of isogeny-based cryptography. Supersingular elliptic curves with level structure map to Eichler orders in a quaternion algebra, just as supersingular elliptic curves map to maximal orders in a quaternion algebra via the
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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 ...
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Resilience Optimization of Post-Quantum Cryptography Key Encapsulation Algorithms. [PDF]
Sensors (Basel), 2023 Farooq S +6 more
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