相关论文: On oriented supersingular elliptic curves

Nodes of sensor networks may be resource-constrained devices, often having a limited lifetime, making sensor networks remarkably dynamic environments. Managing a cryptographic protocol on such setups may require a disproportionate effort…

We discuss the use of elliptic curves in cryptography on high-dimensional surfaces. In particular, instead of a Diffie-Hellman key exchange protocol written in the form of a bi-dimensional row, where the elements are made up with 256 bits,…

We revisit the ordinary isogeny-graph based cryptosystems of Couveignes and Rostovtsev-Stolbunov, long dismissed as impractical. We give algorithmic improvements that accelerate key exchange in this framework, and explore the problem of…

The Deligne-Ogus-Shioda theorem guarantees the existence of isomorphisms between products of supersingular elliptic curves over finite fields. In this paper, we present methods for explicitly computing these isomorphisms in polynomial time,…

Dimension 4 isogenies have first been introduced in cryptography for the cryptanalysis of Supersingular Isogeny Diffie-Hellman (SIDH) and have been used constructively in several schemes, including SQIsignHD, a derivative of SQIsign isogeny…

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…

Based on the detection loophole-free photon key distribution (PKD) compatible with classical optical systems, an optical key distribution (OKD) protocol is presented for unconditionally secured cryptography in fiber-optic communications…

Threshold schemes exist for many cryptographic primitives like signatures, key derivation functions, and ciphers. At the same time, practical key exchange protocols based on Diffie-Hellman (DH) or ECDSA primitives are not designed or…

Isogeny-based cryptography has emerged as a promising postquantum alternative, with CSIDH and its constant-time variants CTIDH and dCTIDH offering efficient group-action protocols. However, CTIDH and dCTIDH rely on dummy operations in…

In this work, a new digital signature based on elliptic curves is presented. We established its efficiency and security. The method, derived from a variant of ElGamal signature scheme, can be seen as a secure alternative protocol if known…

Onion routing provides anonymity by layering encryption so that no relay can link sender to destination. A quantum analogue faces a core obstacle: layered quantum encryption generally requires symmetric encryption schemes, whereas…

This article explores the connection between radical isogenies and modular curves. Radical isogenies are formulas designed for the computation of chains of isogenies of fixed small degree $N$, introduced by Castryck, Decru, and Vercauteren…

In theory, quantum key distribution (QKD) allows secure communications between two parties based on physical laws. However, most of the security proofs of QKD today make unrealistic assumptions and neglect many relevant device…

Hash functions map data of arbitrary length to data of predetermined length. Good hash functions are hard to predict, making them useful in cryptography. We are interested in the elliptic curve CGL hash function, which maps a bitstring to…

We provide theoretical insights around the cutwidth of a graph and the One-Sided Crossing Minimization (OSCM) problem. OSCM was posed in the Parameterized Algorithms and Computational Experiments Challenge 2024, where the cutwidth of the…

An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between elliptic curves efficiently. For ordinary curves of the same…

Consider the problem of efficiently evaluating isogenies $\phi: E \to E/H$ of elliptic curves over a finite field $\mathbb{F}_q$, where the kernel $H = \langle G\rangle$ is a cyclic group of odd (prime) order: given $E$, $G$, and a point…

The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an important tool for computational number theorists and practitioners of elliptic curve cryptography. This…

Elliptic curve cryptography (ECC) is foundational to modern secure communication, yet existing standard curves have faced scrutiny for opaque parameter-generation practices. This work introduces a Selmer-inspired framework for constructing…

Supersingular elliptic curve $\ell$-isogeny graphs over finite fields offer a setting for a number of quantum-resistant cryptographic protocols. The security analysis of these schemes typically assumes that these graphs behave randomly.…