相关论文: Assessing security of some group based cryptosyste…
Consider two parties who want to compare their strings, e.g., genomes, but do not want to reveal them to each other. We present a system for privacy-preserving matching of strings, which differs from existing systems by providing a…
Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid…
Hash functions are a basic cryptographic primitive. Certain hash functions try to prove security against collision and preimage attacks by reductions to known hard problems. These hash functions usually have some additional properties that…
In this paper we study complexity of randomly generated instances of Dehn search problems in finitely presented groups. We use Crump-Mode-Jagers processes to show that most of the random instances are easy. Our analysis shows that for any…
We propose a cryptosystem based on matrices over group rings and claim that it is secure against adaptive chosen ciphertext attack.
This paper analyzes the security of a recent cryptosystem based on the ergodicity property of chaotic maps. It is shown how to obtain the secret key using a chosen-ciphertext attack. Some other design weaknesses are also shown.
We give a natural problem over input quantum oracles $U$ which cannot be solved with exponentially many black-box queries to $U$ and $U^\dagger$, but which can be solved with constant many queries to $U$ and $U^*$, or $U$ and…
Let G be a word-hyperbolic group with given finite generating set, for which various standard structures and constants have been pre-computed. A (non-practical) algorithm is described that, given as input two lists A and B, each composed of…
Baldi et \textit{al.} proposed a variant of McEliece's cryptosystem. The main idea is to replace its permutation matrix by adding to it a rank 1 matrix. The motivation for this change is twofold: it would allow the use of codes that were…
The article explores the creation of a cryptosystem using a halidon group ring of a dihedral group. Due to the non-abelian nature of the group, constructing the cryptosystem is more challenging compared to an abelian group. The logic used…
In recent years, a great amount of secure communications systems based on chaotic synchronization have been published. Most of the proposed schemes fail to explain a number of features of fundamental importance to all cryptosystems, such as…
Traditional social group analysis mostly uses interaction models, event models, or other methods to identify and distinguish groups. This type of method can divide social participants into different groups based on their geographic…
For the design and implementation of engineering systems, performing model-based analysis can disclose potential safety issues at an early stage. The analysis of hybrid system models is in general difficult due to the intrinsic complexity…
Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…
Recently the third named author defined a 2-parametric family of groups $G_n^k$ \cite{gnk}. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups $G_n^k$ and dynamical systems…
The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product semigroup $G\rtimes \mathrm{End}(G)$ for a finite semigroup $G$. Given $g\in G, \sigma\in…
The ability to hide information from unauthorized individuals has been a prevalent issue over the years. Countless algorithms such as DES, AES and SHA have been developed. These algorithms depend on varying key length and key management…
LWE-based cryptosystems are an attractive alternative to traditional ones in the post-quantum era. To minimize the storage cost of part of its public key - a $256 \times 640$ integer matrix, $\textbf{T}$ - a binary version of $\textbf{T}$…
We introduce the use of Fourier analysis on lattices as an integral part of a lattice based construction. The tools we develop provide an elegant description of certain Gaussian distributions around lattice points. Our results include two…
We present a new algorithm for the approximate near neighbor problem that combines classical ideas from group testing with locality-sensitive hashing (LSH). We reduce the near neighbor search problem to a group testing problem by…