相关论文: On Security Properties of All-or-nothing Transform…
We give simple necessary and sufficient conditions for the inclusion-exclusion identity to hold for an infinite countable number of sets. In terms of a random variable, whose range are nonnegative integers, this condition is equivalent to…
We prove that for any infinite countable amenable group $G$, any $\epsilon > 0$ and any finite subset $K\subset G$, there exists a tiling (partition of $G$ into finite "tiles" using only finitely many "shapes"), where all the tiles are $(K;…
Oblivious transfer is a fundamental cryptographic primitive which is useful for secure multiparty computation. There are several variants of oblivious transfer. We consider 1 out of 2 oblivious transfer, where a sender sends two bits of…
The collection of all topologies on a set X forms a complete lattice with respect to the inclusion order, which have been investigated by many researchers. Sobriety is one of the core and extensively studied properties in non-Hausdorff…
Algorithmic decidability is established for two order-theoretic properties of downward closed subsets defined by finitely many obstructions in two infinite posets. The properties under consideration are: (a) being atomic, i.e. not being…
Security against eavesdropping is one of the key concerns in the design of any communication system. Many common considerations of the security of a wireless communication channel rely on comparing the signal level measured by Bob (the…
Relativistic protocols have been proposed to overcome some impossibility results in classical and quantum cryptography. In such a setting, one takes the location of honest players into account, and uses the fact that information cannot…
We use Bowen's definition of topological entropy and Ahlfors five islands theorem, as well as the theory of polynomial-like mappings, to show that the topological entropy of any entire transcendental function is infinity. In addition the…
Critical infrastructure systems - for which high reliability and availability are paramount - must operate securely. Attack trees (ATs) are hierarchical diagrams that offer a flexible modelling language used to assess how systems can be…
We generalize several results of the classical theory of Thermodynamic Formalism by considering a compact metric space $M$ as the state space. We analyze the shift acting on $M^\mathbb{N}$ and consider a general a-priori probability for…
A set of integers is $S$-recognizable in an abstract numeration system $S$ if the language made up of the representations of its elements is accepted by a finite automaton. For abstract numeration systems built over bounded languages with…
The S-transform is shown to satisfy a specific twisted multiplicativity property for free random variables in a B-valued Banach noncommutative probability space, for an arbitrary unital complex Banach algebra B. Also, a new proof of the…
We present a new idea to design perfectly secure information exchange protocol, based on so called Deep Randomness, which means randomness relying on hidden probability distribution. Such idea drives us to introduce a new axiom in…
More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…
Current safety alignment methods encode safe behavior implicitly within model parameters, creating a fundamental opacity: we cannot easily inspect why a model refuses a request, nor intervene when its safety judgments fail. We propose Safe…
Recently, Defant and Propp [2020] defined the degree of noninvertibility of a function $f\colon X\to Y$ between two finite nonempty sets by $\text{deg}(f)=\frac{1}{|X|}\sum_{x\in X}|f^{-1}(f(x))|$. We obtain an exact formula for the…
In this work, a tensor completion problem is studied, which aims to perfectly recover the tensor from partial observations. The existing theoretical guarantee requires the involved transform to be orthogonal, which hinders its applications.…
In this paper we give sufficient conditions guaranteeing the validity of the well-known minimax theorem for the lower Snell envelope with respect to a family of absolutely continuous probability measures. Such minimax results play an…
Some theories on data flow security are based on order-theoretical concepts, most commonly on lattice concepts. This paper presents a correspondence between security concepts and partial order concepts, by which the former become an…
We study cryptography based on operator theory, and propose quantum no-key (QNK) protocols from the perspective of operator theory, then present a framework of QNK protocols. The framework is expressed in two forms: trace-preserving quantum…