Related papers: Discrete Logarithms in Generalized Jacobians

We show that a linear decomposition attack based on the decomposition method introduced by the author works by finding the exchanged secret keys in all main protocols using semidirect products of (semi)grops proposed by Kahrobaei,…

We describe a provably quasi-polynomial algorithm to compute discrete logarithms in the multiplicative groups of finite fields of small characteristic, that is finite fields whose characteristic is logarithmic in the order. We partially…

We construct new families of elliptic curves over \(\FF_{p^2}\) with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as Gallant-Lambert-Vanstone (GLV) and…

Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. Remaining instances are built over finite fields of large characteristic and…

We analyze the security and reliability of a recently proposed class of public-key cryptosystems against attacks by unauthorized parties who have acquired partial knowledge of one or more of the private key components and/or of the…

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…

A directly public verifiable signcryption scheme is introduced in this paper that provides the security attributes of message confidentiality, authentication, integrity, non-repudiation, unforgeability, and forward secrecy of message…

Consider an ordinary differential equation which has a Lax pair representation A'(x)= [A(x),B(x)], where A(x) is a matrix polynomial with a fixed regular leading coefficient and the matrix B(x) depends only onA(x). Such an equation can be…

We consider a generalization of the dining philosophers problem to arbitrary connection topologies. We focus on symmetric, fully distributed systems, and we address the problem of guaranteeing progress and lockout-freedom, even in presence…

In this paper, we propose a blind signature scheme and three practical educed schemes based on elliptic curve discrete logarithm problem. The proposed schemes impart the GOST signature structure and utilize the inherent advantage of…

We address a cryptanalysis of two protocols based on the supposed difficulty of discrete logarithm problem on (semi) groups of matrices over a group ring. We can find the secret key and break entirely the protocols.

We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly…

A simply laced Dynkin diagram gives rise to a family of curves over $\mathbb{Q}$ and a coregular representation, using deformations of simple singularities and Vinberg theory respectively. Thorne has conjectured and partially proven a…

In this work, we present a generalization of the recently proposed quantum Tanner codes by Leverrier and Z\'emor, which contains a construction of asymptotically good quantum LDPC codes. Quantum Tanner codes have so far been constructed…

This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models. - In the classical generic group model (GGM), we find simple alternative proofs for the…

Since 1870s, scientists have been taking deep insight into Lie groups and Lie algebras. With the development of Lie theory, Lie groups have got profound significance in many branches of mathematics and physics. In Lie theory, exponential…

A study is presented of fully discretized lattice equations associated with the KdV hierarchy. Loop group methods give a systematic way of constructing discretizations of the equations in the hierarchy. The lattice KdV system of Nijhoff et…

We give an exposition of the hidden subgroup problem for dihedral groups from the point of view of the standard hidden subgroup quantum algorithm for finite groups. In particular, we recall the obstructions for strong Fourier sampling to…

Public-key cryptosystems are suggested based on invariants of groups. We give also an overview of the known cryptosystems which involve groups.

We construct (generalized) logarithmic derivatives for general n-dimensional local fields K of mixed characteristics (0,p) in which p is not necessarily a prime element with residue field k such that [k:k^p]=p^{n-1}. For the construction of…