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We present a polynomial time attack of a rank metric code based encryption scheme due to Loidreau for some parameters.

Information Theory · Computer Science 2020-07-13 Daniel Coggia , Alain Couvreur

After some excitement generated by recently suggested public key exchange protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al., it is a prevalent opinion now that the conjugacy search problem is unlikely to provide sufficient level of…

Group Theory · Mathematics 2007-05-23 Vladimir Shpilrain , Gabriel Zapata

Garber, Kahrobaei, and Lam studied polycyclic groups generated by number field as platform for the AAG key-exchange protocol. In this paper, we discuss the use of a different kind of polycyclic groups, Heisenberg groups, as a platform group…

Cryptography and Security · Computer Science 2014-03-18 Delaram Kahrobaei , Ha T. Lam

Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols…

Group Theory · Mathematics 2016-09-07 Vladimir Shpilrain , Alexander Ushakov

The length-based approach is a heuristic for solving randomly generated equations in groups which possess a reasonably behaved length function. We describe several improvements of the previously suggested length-based algorithms, that make…

Cryptography and Security · Computer Science 2010-08-02 Dima Ruinskiy , Adi Shamir , Boaz Tsaban

Post-quantum cryptography (PQC) attempts to find cryptographic protocols resistant to attacks using for instance Shor's polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP).…

Cryptography and Security · Computer Science 2024-12-31 Pedro Hecht

Let $G_1$ be a cyclic multiplicative group of order $n$. It is known that the Diffie-Hellman problem is random self-reducible in $G_1$ with respect to a fixed generator $g$ if $\phi(n)$ is known. That is, given $g, g^x\in G_1$ and having…

Cryptography and Security · Computer Science 2007-05-23 Amitabh Saxena , Ben Soh

In this paper,we propose a modified Anshel-Anshel-Goldfeld(AAG) key exchange scheme. The hardness assumption underlying this modified construction is based on the membership problem for Mihailova subgroups of the braid group, a problem that…

Group Theory · Mathematics 2026-01-27 Hanling Lin , Yu Han

In discrete logarithm based cryptography, a method by Pohlig and Hellman allows solving the discrete logarithm problem efficiently if the group order is known and has no large prime factors. The consequence is that such groups are avoided.…

Cryptography and Security · Computer Science 2012-04-02 Felix Fontein

In this paper homomorphic cryptosystems are designed for the first time over any finite group. Applying Barrington's construction we produce for any boolean circuit of the logarithmic depth its encrypted simulation of a polynomial size over…

Cryptography and Security · Computer Science 2007-05-23 Dima Grigoriev , Ilia Ponomarenko

We describe a cryptographic protocol in which Wheeler's delayed choice experiment is used to generate the key distribution. The protocol, which uses photons polarized only along one axis, is secure against general attacks.

Quantum Physics · Physics 2009-10-28 M. Ardehali

We consider actions of a group or a semigroup on a set, which generalize the setup of discrete logarithm based cryptosystems. Such cryptographic group actions have gained increasing attention recently in the context of isogeny-based…

Cryptography and Security · Computer Science 2023-01-05 Oliver W. Gnilke , Jens Zumbrägel

We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption…

Cryptography and Security · Computer Science 2007-05-23 Ilia Toli

In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, we introduce a new $2$-cocycle $\alpha_{\lambda}$ to twist the dihedral group algebra. Using the ambient space…

Cryptography and Security · Computer Science 2021-12-16 Javier de la Cruz , Ricardo Villanueva-Polanco

In a previous paper we generalized the definition of a multilinear map to arbitrary groups and introduced two multiparty key-exchange protocols using nilpotent groups. In this paper we have a closer look at the protocols and will address…

Group Theory · Mathematics 2021-02-09 Delaram Kahrobaei , Antonio Tortora , Maria Tota

We introduce a new approach for cryptanalysis of key agreement protocols based on noncommutative groups. This approach uses functions that estimate the distance of a group element to a given subgroup. We test it against the…

Cryptography and Security · Computer Science 2010-11-05 Dima Ruinskiy , Adi Shamir , Boaz Tsaban

In this survey, we describe a general key exchange protocol based on semidirect product of (semi)groups (more specifically, on extensions of (semi)groups by automorphisms), and then focus on practical instances of this general idea. This…

Cryptography and Security · Computer Science 2016-04-21 Delaram Kahrobaei , Vladimir Shpilrain

We give a polynomial time attack on the McEliece public key cryptosystem based on subcodes of algebraic geometry (AG) codes. The proposed attack reposes on the distinguishability of such codes from random codes using the Schur product.…

Information Theory · Computer Science 2014-09-30 Alain Couvreur , Irene Márquez-Corbella , Ruud Pellikaan

This paper presents a novel methodology to test the security of the Diffie-Hellman public key exchange protocol. The security of many cryptographic schemes rely on the hardness of this problem. We are presenting a purely statistical test to…

Statistics Theory · Mathematics 2007-06-13 I. Florescu , A. Myasnikov , A. Mahalanobis

There are several public key establishment protocols as well as complete public key cryptosystems based on allegedly hard problems from combinatorial (semi)group theory known by now. Most of these problems are search problems, i.e., they…

Group Theory · Mathematics 2007-05-23 Vladimir Shpilrain , Gabriel Zapata