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With the proliferation of mobile technology and IT development, people can use social network services at any place and anytime. Among many social network mining problems, identifying cohesive subgraphs attract many attentions from…
We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of…
Cryptographic access control has been studied for over 30 years and is now a mature research topic. When symmetric cryptographic primitives are used, each protected resource is encrypted and only authorized users should have access to the…
Thin spanning trees lie at the intersection of graph theory, approximation algorithms, and combinatorial optimization. They are central to the long-standing \emph{thin tree conjecture}, which asks whether every $k$-edge-connected graph…
Recent oracle separations [Kretschmer, TQC'21, Kretschmer et. al., STOC'23] have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if the polynomial hierarchy collapses. We…
The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian…
We address univariate root isolation when the polynomial's coefficients are in a multiple field extension. We consider a polynomial $F \in L[Y]$, where $L$ is a multiple algebraic extension of $\mathbb{Q}$. We provide aggregate bounds for…
Recently, an image encryption algorithm using block-based scrambling and image filtering has been proposed by Hua et al. In this paper, we analyze the security problems of the encryption algorithm in detail and break the encryption by a…
The subset cover problem for $k \geq 1$ hash functions, which can be seen as an extension of the collision problem, was introduced in 2002 by Reyzin and Reyzin to analyse the security of their hash-function based signature scheme HORS. The…
Since the braid group was discovered by E. Artin, the question of its conjugacy problem has been solved by Garside and Birman, Ko and Lee. However, the solutions given thus far are difficult to compute with a computer, since the number of…
For a fixed property (graph class) ${\Pi}$, given a graph G and an integer k, the ${\Pi}$-deletion problem consists in deciding if we can turn $G$ into a graph with the property ${\Pi}$ by deleting at most $k$ edges. The ${\Pi}$-deletion…
It is known for many algorithmic problems that if a tree decomposition of width $t$ is given in the input, then the problem can be solved with exponential dependence on $t$. A line of research by Lokshtanov, Marx, and Saurabh [SODA 2011]…
Given a cryptographic group action, we show that the Group Action Inverse Problem (GAIP) and other related problems cannot be NP-hard unless the Polynomial Hierarchy collapses. We show this via random self-reductions and the design of…
We present TRAIL: an algorithm that uses a novel consensus procedure to tolerate failed or malicious shards within a blockchain-based cryptocurrency. Our algorithm takes a new approach of selecting validator shards for each transaction from…
Blockchain systems and cryptocurrencies have exploded in popularity over the past decade, and with this growing user base, the number of cryptocurrency scams has also surged. Given the graphical structure of blockchain networks and the…
Isolating the real roots of univariate polynomials is a fundamental problem in symbolic computation and it is arguably one of the most important problems in computational mathematics. The problem has a long history decorated with numerous…
We consider in this paper the information-theoretic secure key distribution problem over main and wire-tap noise channels with a public discussion in presence of an active adversary. In contrast to the solution proposed by ourselves for a…
We describe the most efficient solutions to the word problem of Artin's braid group known so far, i.e., in other words, the most efficient solutions to the braid isotopy problem, including the Dynnikov method, which could be especially…
Lo and Ko in [1] have developed some attacks on the cryptosystem called AlphaEta [2], claiming that these attacks undermine the security of AlphaEta for both direct encryption and key generation. In this paper, we show that their arguments…
We introduce a computational problem of distinguishing between the output of an ideal coarse-grained boson sampler and the output of a true random number generator, as a resource for cryptographic schemes, which are secure against…