Results 31 to 40 of about 38,603 (168)
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 endomorphism rings of supersingular elliptic curves and connections to path-finding in isogeny graphs [PDF]
The Open Book Series, 2020 Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of the recently proposed isogeny-based cryptosystems.
Kirsten Eisentraeger +4 more
semanticscholar +1 more source
Torsion point attacks on ‘SIDH‐like’ cryptosystems
IET Information Security, Volume 17, Issue 2, Page 161-170, March 2023., 2023 Abstract 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 mechanism SIKE, which was submitted to and remains in the third round of NIST's post ...
Péter Kutas, Christophe Petit
wiley +1 more source
Quantum algorithms for attacking hardness assumptions in classical and post‐quantum cryptography
IET Information Security, Volume 17, Issue 2, Page 171-209, March 2023., 2023 Abstract In this survey, the authors review the main quantum algorithms for solving the computational problems that serve as hardness assumptions for cryptosystem. To this end, the authors consider both the currently most widely used classically secure cryptosystems, and the most promising candidates for post‐quantum secure cryptosystems.
J.‐F. Biasse +4 more
wiley +1 more source
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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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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International Journal of Intelligent Systems, Volume 2023, Issue 1, 2023., 2023 With the rapid development of Internet of Things (IoT), designing a secure two‐factor authentication scheme for IoT is becoming increasingly demanding. Two‐factor protocols are deployed to achieve a higher security level than single‐factor protocols.
Behnam Zahednejad +4 more
wiley +1 more source
Towards Isogeny-Based Password-Authenticated Key Establishment
Journal of Mathematical Cryptology, 2020 Password authenticated key establishment (PAKE) is a cryptographic primitive that allows two parties who share a low-entropy secret (a password) to securely establish cryptographic keys in the absence of public key infrastructure.
Taraskin Oleg +3 more
doaj +1 more source
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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Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 Scalar multiplications are considered an essential aspect of implementations of isogeny‐based cryptography. The efficiency of scalar multiplication depends on the equation of the underlying elliptic curves and the addition chain employed. Bos and Friedberger recently stated that, for larger scalar multiplication, addition‐subtraction chains will become
Sookyung Eom +3 more
wiley +1 more source