English
Related papers

Related papers: Elliptic-Curves Cryptography on High-Dimensional S…

200 papers

Most modern cryptographic systems, such as RSA and the Diffie-Hellman Key Exchange, rely on "trapdoor" mathematical functions that are presumed to be computationally difficult with existing tools. However, quantum computers will be able to…

Cryptography and Security · Computer Science 2025-05-15 Alexander Meyer

We use matrices over bit strings as platforms for Diffie-Hellman-like public key exchange protocols. When multiplying matrices like that, we use Boolean OR operation on bit strings in place of addition and Boolean AND operation in place of…

Cryptography and Security · Computer Science 2021-06-03 Nael Rahman , Vladimir Shpilrain

In this paper we present a key exchange protocol in which Alice and Bob have secret keys given by quadric surfaces embedded in a large ambient space by means of the Veronese embedding and public keys given by hyperplanes containing the…

Cryptography and Security · Computer Science 2020-05-29 Daniele Di Tullio , Manoj Gyawali

Nowadays, predominant asymmetric cryptographic schemes are considered to be secure because discrete logarithms are believed to be hard to be computed. The algorithm of Shor can effectively compute discrete logarithms, i.e. it can brake such…

Cryptography and Security · Computer Science 2025-04-01 Johanna Barzen , Frank Leymann

In this paper we present a new primitive for a key exchange protocol based on multivariate non-commutative polynomial rings, analogous to the classic Diffie-Hellman method. Our technique extends the proposed scheme of Boucher et al. from…

Cryptography and Security · Computer Science 2015-05-20 Reinhold Burger , Albert Heinle

Cryptographic Protocols (CP) are distributed algorithms intended for secure communication in an insecure environment. They are used, for example, in electronic payments, electronic voting procedures, systems of confidential data processing,…

Cryptography and Security · Computer Science 2021-09-21 Andrew M. Mironov

We present an elementary proof of the group properties of the elliptic curve known as "Curve25519", as a component of a comprehensive proof of correctness of a hardware implementation of the associated Diffie-Hellman key agreement…

Cryptography and Security · Computer Science 2017-05-04 David M. Russinoff

Today's information society relies on cryptography to achieve security goals such as confidentiality, integrity, authentication, and non-repudiation for digital communications. Here, public-key cryptosystems play a pivotal role to share…

Cryptography and Security · Computer Science 2024-12-19 Paul Staat , Meik Dörpinghaus , Azadeh Sheikholeslami , Christof Paar , Gerhard Fettweis , Dennis Goeckel

It is well-known that the linear secret-sharing scheme (LSSS) can be constructed from linear error-correcting codes (Brickell [1], R.J. McEliece and D.V.Sarwate [2],Cramer, el.,[3]). The theory of linear codes from algebraic-geometric…

Cryptography and Security · Computer Science 2007-07-13 Hao Chen

The Stealth Address Protocol (SAP) allows users to receive assets through stealth addresses that are unlinkable to their stealth meta-addresses. The most widely used SAP, Dual-Key SAP (DKSAP), and the most performant SAP, Elliptic Curve…

Cryptography and Security · Computer Science 2025-01-24 Marija Mikic , Mihajlo Srbakoski , Strahinja Praska

We offer a public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over Z_p. One of the (semi)groups is additive, the other one multiplicative. This allows us to take advantage of both operations on…

Cryptography and Security · Computer Science 2021-03-12 Nael Rahman , Vladimir Shpilrain

Key establishment is one fundamental issue in wireless security. The widely used Diffie-Hellman key exchange is vulnerable to the man-in-the-middle attack. This paper presents a novel in-band solution for defending the man-in-the-middle…

Cryptography and Security · Computer Science 2019-01-29 Wenlong Shen , Yu Cheng , Bo Yin , Kecheng Liu , Xianghui Cao

Homomorphic encryption (HE) is a promising cryptographic technique for enabling secure collaborative machine learning in the cloud. However, support for homomorphic computation on ciphertexts under multiple keys is inefficient. Current…

Cryptography and Security · Computer Science 2019-11-12 Asma Aloufi , Peizhao Hu

We analyze the security of two-way quantum key distribution using arbitrary finite-dimensional systems, considering both individual and collective eavesdropping attacks, without the effective use of entangled states, by incorporating two…

Quantum Physics · Physics 2026-04-14 Abhishek Muhuri , Ayan Patra , Rivu Gupta , Tamoghna Das , Aditi Sen De

Loops and cycles play an important role in computing endomorphism rings of supersingular elliptic curves and related cryptosystems. For a supersingular elliptic curve $E$ defined over $\mathbb{F}_{p^2}$, if an imaginary quadratic order $O$…

Number Theory · Mathematics 2023-12-12 Guanju Xiao , Lixia Luo , Yingpu Deng

Quantum cryptographic protocols solve the longstanding problem of distributing a shared secret string to two distant users by typically making use of one-way quantum channel. However, alternative protocols exploiting two-way quantum channel…

Quantum Physics · Physics 2015-05-01 Jesni Shamsul Shaari , Stefano Mancini

We present a cryptanalysis of a key exchange protocol based on the digital semiring. For this purpose, we find the maximal solution of a linear system over such semiring, and use the properties of circulant matrix to demonstrate that the…

Cryptography and Security · Computer Science 2025-06-18 Alvaro Otero Sanchez

Historically, Elliptic Curve Cryptography (ECC) is an active field of applied cryptography where recent focus is on high speed, constant time, and formally verified implementations. While there are a handful of outliers where all these…

Cryptography and Security · Computer Science 2021-08-02 Dmitry Belyavsky , Billy Bob Brumley , Jesús-Javier Chi-Domínguez , Luis Rivera-Zamarripa , Igor Ustinov

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…

Number Theory · Mathematics 2014-02-12 David Jao , Vladimir Soukharev

Specific quantum algorithms exist to-in theory-break elliptic curve cryptographic protocols. Implementing these algorithms requires designing quantum circuits that perform elliptic curve arithmetic. To accurately judge a cryptographic…

Quantum Physics · Physics 2025-07-16 Francis P. Papa