相关论文: Accelerating the Couveignes Rostovtsev Stolbunov k…

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…

Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the…

We describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n >= 2. Our approach is based on the problem of computing isogenies between isogenous elliptic curves, which is…

The problem of computing an explicit isogeny between two given elliptic curves over F_q, originally motivated by point counting, has recently awaken new interest in the cryptology community thanks to the works of Teske and Rostovstev &…

Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to be computationally difficult. The fastest…

Isogenies occur throughout the theory of elliptic curves. Recently, the cryptographic protocols based on isogenies are considered as candidates of quantum-resistant cryptographic protocols. Given two elliptic curves $E_1, E_2$ defined over…

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…

The widespread use of wireless sensor networks (WSNs) that are consisted of resource-constrained sensor nodes in communication with gateways in open-space environments and industries has highlighted the need for a secure yet fast…

We present e cient algorithms for computing isogenies between hyperelliptic curves, leveraging higher genus curves to enhance cryptographic protocols in the post-quantum context. Our algorithms reduce the computational complexity of isogeny…

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,…

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…

We present a new key exchange protocol based on circulant matrices acting on matrices over a congruence-simple semiring. We describe how to compute matrices with the necessary properties for the implementation of the protocol. Additionally,…

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…

Cryptography is the study of techniques for ensuring the secrecy and authentication of the information. Public-key encryption schemes are secure only if the authenticity of the public-key is assured. Elliptic curve arithmetic can be used to…

We investigate stable operations in supersingular elliptic cohomology using isogenies of supersingular elliptic curves over finite fields. Our main results provide a framework in which we give a conceptually simple proof of an elliptic…

The increasing deployment of the Internet of Things (IoT) edge devices in modern smart grid environments requires secure and efficient communication protocols specifically designed for resource-constrained environments. However, most…

In this paper, we study the problem of sampling random supersingular elliptic curves with unknown endomorphism rings. This problem has recently gained considerable attention as many isogeny-based cryptographic protocols require such…

The rapid development of computer technology will be the whole world as a whole, the widespread application of instant messaging technology to bring great convenience to people's lives, while privacy protection has become a more significant…

We examine two public key exchange protocols proposed recently by Grigoriev and Shpilrain (arXiv:1811.06386), which use tropical algebra. We introduce a fast attack on the first protocol, and we show that the second protocol cannot be…

Elliptic curve cryptography (ECC) is a remarkable mathematical tool that offers the same level of security as traditional public-key cryptography (PKC) with a significantly smaller key size and lower computational requirements. The use of…