Results 11 to 20 of about 42,992 (209)
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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An Efficient Signature Scheme From Supersingular Elliptic Curve Isogenies
IEEE Access, 2019 Since supersingular elliptic curve isogenies are one of the several candidate sources of hardness for building post-quantum cryptographic primitives, the research of efficient signature schemes based on them is still a hot topic.
Yan Huang +3 more
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Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
Journal of Mathematical Cryptology, 2014 We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases
De Feo Luca, Jao David, Plût Jérôme
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Computational problems in supersingular elliptic curve isogenies
Quantum Information Processing, 2018 We present an overview of supersingular isogeny cryptography and how it fits into the broad theme of post-quantum public-key crypto. The paper also gives a brief tutorial of elliptic curve isogenies and the computational problems relevant for supersingular isogeny crypto.
Galbraith, Steven D. +1 more
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Minimal CM Liftings of Supersingular Elliptic Curves [PDF]
Pure and Applied Mathematics Quarterly, 2008 In this paper, we prove that if every supersingular elliptic curve over Fp can be lifted to a CM elliptic curve by an imaginary order OD for some D ? pθ, then θ ≥ 1 2 . We also prove that if every supersingular elliptic curve over Fp can be lifted to a CM elliptic curve by an imaginary order OD for some D ? pθ, then θ ≥ 23 as suggested by Elkies.
Tonghai Yang
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A BOUND ON THE $\mu$ -INVARIANTS OF SUPERSINGULAR ELLIPTIC CURVES
Canadian Mathematical BulletinAbstract Let $E/\mathbb {Q}$ be an elliptic curve and let p be a prime of good supersingular reduction. Attached to E are pairs of Iwasawa invariants $\mu _p^\pm $ and $\lambda _p^\pm $ which encode arithmetic properties of E along the cyclotomic
Rylan Gajek-Leonard
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Supersingular zeros of divisor polynomials of elliptic curves of prime conductor [PDF]
Research in the Mathematical Sciences, 2016 For a prime number $p$ we study the zeros modulo $p$ of divisor polynomials of rational elliptic curves $E$ of conductor $p$. Ono made the observation that these zeros of are often $j$-invariants of supersingular elliptic curves over $\overline{\mathbb{F}_p}$.
Matija Kazalicki, Daniel P. Kohen
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On the Search for Supersingular Elliptic Curves and Their Applications
MathematicsElliptic curves with the special quality known as supersingularity have gained much popularity in the rapidly developing field of cryptography. The conventional method of employing random search is quite ineffective in finding these curves. This paper analyzes the search of supersingular elliptic curves in the space of curves over Fp2.
Ismel Martinez-Diaz +2 more
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THE ANTICYCLOTOMIC MAIN CONJECTURE FOR ELLIPTIC CURVES AT SUPERSINGULAR PRIMES [PDF]
Journal of the Institute of Mathematics of Jussieu, 2007 The Main Conjecture of Iwasawa theory for an elliptic curve is a prime of supersingular reduction. The foundational study of supersingular main conjectures carried out by Perrin-Riou, Pollack, Kurihara, Kobayashi and Iovita and Pollack are required to handle this case in which many of the simplifying features of the ordinary setting break down.
Henri Darmon, Adrian Iovita
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The SEA algorithm for endomorphisms of supersingular elliptic curves [PDF]
For a prime $p{\,>\,}3$ and a supersingular elliptic curve $E$ defined over $\mathbb{F}_{p^2}$ with ${j(E)\notin\{0,1728\}}$, consider an endomorphism $α$ of $E$ represented as a composition of $L$ isogenies of degree at most $d$. We prove that the trace of $α$ may be computed in $O(n^4(\log n)^2 + dLn^3)$ bit operations, where $n{\,=\,}\log(p ...
Travis Morrison +3 more
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