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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
On the supersingular GPST attack
Journal of Mathematical Cryptology, 2021 The main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange.
Basso Andrea, Pazuki Fabien
doaj +1 more source
Supersingular Elliptic Curves and Moonshine [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 We generalize a theorem of Ogg on supersingular $j$-invariants to supersingular elliptic curves with level. Ogg observed that the level one case yields a characterization of the primes dividing the order of the monster. We show that the corresponding analyses for higher levels give analogous characterizations of the primes dividing the orders of other ...
openaire +3 more sources
A Blockchain‐Assisted Electronic Medical Records by Using Proxy Reencryption and Multisignature
Security and Communication Networks, Volume 2022, Issue 1, 2022., 2022 Electronic medical records (EMR) have been commonly used in medical institutions in recent years. In particular, the combination of EMR and the cloud server has significantly improved the work efficiency and therapeutic level of the hospital. It also raises some security concerns, e.g., the information leaks.
Xiaoguang Liu +4 more
wiley +1 more source
Optimized CSIDH Implementation Using a 2-Torsion Point
Cryptography, 2020 The implementation of isogeny-based cryptography mainly use Montgomery curves, as they offer fast elliptic curve arithmetic and isogeny computation. However, although Montgomery curves have efficient 3- and 4-isogeny formula, it becomes inefficient when ...
Donghoe Heo +4 more
doaj +1 more source
Identifying supersingular elliptic curves [PDF]
LMS Journal of Computation and Mathematics, 2012 AbstractGiven an elliptic curve E over a field of positive characteristic p, we consider how to efficiently determine whether E is ordinary or supersingular. We analyze the complexity of several existing algorithms and then present a new approach that exploits structural differences between ordinary and supersingular isogeny graphs.
openaire +2 more sources
Privacy‐Preserving Task Distribution Mechanism with Cloud‐Edge IoT for the Mobile Crowdsensing
Security and Communication Networks, Volume 2022, Issue 1, 2022., 2022 Mobile crowdsensing under big data provides an efficient, win‐win, and low‐budget data collection solution for IoT applications such as the smart city. However, its open and all access scenarios raise the threat of data security and user privacy during task distribution of mobile crowdsensing.
Liquan Jiang, Zhiguang Qin, Jinbo Xiong
wiley +1 more source
Dynamics on supersingular K3 surfaces [PDF]
, 2015 For any odd characteristic p=2 mod 3, we exhibit an explicit automorphism on the supersingular K3 surface of Artin invariant one which does not lift to any characteristic zero model.
Schuett, Matthias
core +3 more sources
On the Deuring Polynomial for Drinfeld Modules in Legendre Form [PDF]
, 2018 We study a family $\psi^{\lambda}$ of $\mathbb F_q[T]$-Drinfeld modules, which is a natural analog of Legendre elliptic curves. We then find a surprising recurrence giving the corresponding Deuring polynomial $H_{p(T)}(\lambda)$ characterising ...
Bassa, Alp, Beelen, Peter
core +2 more sources
A Comparison of Security and its Performance for Key Agreements in Post-Quantum Cryptography
IEEE Access, 2020 Nowadays, we are surrounded by devices collecting and transmitting private information. Currently, the two main mathematical problems that guarantee security on the Internet are the Integer Factorization Problem and the Discrete Logarithm Problem ...
Fabio Borges +2 more
doaj +1 more source