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Multiplicative isogeny estimates [PDF]

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1998
AbstractThe theory of isogeny estimates for Abelian varieties provides ‘additive bounds’ of the form ‘d is at most B’ for the degrees d of certain isogenies. We investigate whether these can be improved to ‘multiplicative bounds’ of the form ‘d divides B’.
openaire   +3 more sources

A subexponential-time, polynomial quantum space algorithm for inverting the CM group action

Journal of Mathematical Cryptology, 2020
We present a quantum algorithm which computes group action inverses of the complex multiplication group action on isogenous ordinary elliptic curves, using subexponential time, but only polynomial quantum space.
Jao David, LeGrow Jason, Leonardi Christopher, Ruiz-Lopez Luis   +3 more
doaj   +1 more source

Towards quantum‐safe blockchain: Exploration of PQC and public‐key recovery on embedded systems

IET Blockchain, Volume 5, Issue 1, January/December 2025.
This paper addresses the need for quantum‐safe blockchain solutions specifically for embedded systems by integrating Post‐Quantum Cryptography (PQC) into blockchain frameworks. We propose a quantum‐secure blockchain architecture using NIST‐standardized PQC algorithms, finding Falcon‐512 to be optimal for embedded environments due to its security and ...
Dominik Marchsreiter
wiley   +1 more source

Optimized SeaSign for Enhanced Efficiency

IEEE Access
This paper optimized SeaSign – an isogeny-based digital signature algorithm that combines the class group actions of CSIDH with the notion of Fiat-Shamir with abort.
Suhri Kim
doaj   +1 more source

Generic Construction of Dual‐Server Public Key Authenticated Encryption With Keyword Search

IET Information Security, Volume 2025, Issue 1, 2025.
In this paper, we propose a generic construction of dual‐server public key authenticated encryption with keyword search (DS‐PAEKS) from PAEKS, public key encryption, and signatures. We also show that previous DS‐PAEKS scheme is vulnerable by providing a concrete attack. That is, the proposed generic construction yields the first DS‐PAEKS schemes.
Keita Emura, Puttamadappa C.
wiley   +1 more source

Cold Boot Attacks on the Supersingular Isogeny Key Encapsulation (SIKE) Mechanism

Applied Sciences, 2020
This research paper evaluates the feasibility of cold boot attacks on the Supersingular Isogeny Key Encapsulation (SIKE) mechanism. This key encapsulation mechanism has been included in the list of alternate candidates of the third round of the National ...
Ricardo Villanueva-Polanco, Eduardo Angulo-Madrid   +1 more
doaj   +1 more source

Constructing Efficient Identity‐Based Signatures on Lattices

IET Information Security, Volume 2025, Issue 1, 2025.
In this work, we explore the recent developments related to lattice‐based signature and preimage sampling, and specify a compact identity‐based signature (IBS) on an ideal lattice for practical use. Specifically, we first propose an ellipsoid version of the G + G signature scheme (Asiacrypt 2023) that achieves slightly better signature size and higher ...
Huiwen Jia, Ying Liu, Chunming Tang, Lin Wang, Qichun Wang   +4 more
wiley   +1 more source

Comprehensive Analysis and Implementation of Isogeny-Based Hash Functions

IEEE Access
This paper analyzes the security and performance of the isogeny-based hash functions. The isogeny-based hash function was first proposed by Charles, Goren, and Lauter, and is referred to as the CGL hash function.
Donghoe Heo, Jeonghwan Lee, Taehoon Kang, Suhri Kim, Seokhie Hong   +4 more
doaj   +1 more source

Mod p points on shimura varieties of parahoric level

Forum of Mathematics, Pi
We study the $\overline {\mathbb {F}}_{p}$ -points of the Kisin–Pappas integral models of Shimura varieties of Hodge type with parahoric level. We show that if the group is quasi-split, then every isogeny class contains the reduction of a CM point,
Pol van Hoften
doaj   +1 more source

Isogeny graphs and Isogeny Volcanoes

, 2020
\textit{Isogeny graphs} are a type of graphs, where the vertices represent elliptic curves and the edges represent isogenies. I will examine some of the structures of these graphs in this thesis. It turns out that the majority of the components of such a graph will be \textit{volcanoes}, see \cref{defn:pvolcano}.
openaire   +1 more source