Lower Bounds on OBDD Proofs with Several Orders

This article is motivated by seeking lower bounds on OBDD(∧, w, r) refutations, namely, OBDD refutations that allow weakening and arbitrary reorderings. We first work with 1 - NBP ∧ refutations based on read-once nondeterministic branching programs. These generalize OBDD(∧, r) refutations. There are polynomial size 1 - NBP(∧) refutations of the pigeonhole principle, hence 1-NBP(∧) is strictly stronger than OBDD}(∧, r). There are also formulas that have polynomial size tree-like resolution refutations but require exponential size 1-NBP(∧) refutations. As a corollary, OBDD}(∧, r) does not simulate tree-like resolution, answering a previously open question. The system 1-NBP(∧, ∃) uses projection inferences instead of weakening. 1-NBP(∧, ∃ k is the system restricted to projection on at most k distinct variables. We construct explicit constant degree graphs G n on n vertices and an ε > 0, such that 1-NBP(∧, ∃ ε n ) refutations of the Tseitin formula for G n require exponential size. Second, we study the proof system OBDD}(∧, w, r ℓ ), which allows ℓ different variable orders in a refutation. We prove an exponential lower bound on the complexity of tree-like OBDD(∧, w, r ℓ ) refutations for ℓ = ε log n , where n is the number of variables and ε > 0 is a constant. The lower bound is based on multiparty communication complexity.

On the number of factorizations of $ t $ mod $ N $ and the probability distribution of Diffie-Hellman secret keys for many users

<p style='text-indent:20px;'>We study the number <inline-formula><tex-math id="M3">\begin{document}$ R_n(t,N) $\end{document}</tex-math></inline-formula> of tuplets <inline-formula><tex-math id="M4">\begin{document}$ (x_1,\ldots, x_n) $\end{document}</tex-math></inline-formula> of congruence classes modulo <inline-formula><tex-math id="M5">\begin{document}$ N $\end{document}</tex-math></inline-formula> such that</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} x_1\cdots x_n \equiv t \pmod{N}. \end{equation*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>As a result, we derive a recurrence for <inline-formula><tex-math id="M6">\begin{document}$ R_n(t,N) $\end{document}</tex-math></inline-formula> and prove some multiplicative properties of <inline-formula><tex-math id="M7">\begin{document}$ R_n(t,N) $\end{document}</tex-math></inline-formula>. Furthermore, we apply the result to study the probability distribution of Diffie-Hellman keys used in multiparty communication. We show that this probability distribution is not uniform.</p>

A SAT-Based Planning Approach for Finding Logical Attacks on Cryptographic Protocols

Cryptographic protocols form the backbone of digital society. They are concurrent multiparty communication protocols that use cryptography to achieve security goals such as confidentiality, authenticity, integrity, etc., in the presence of adversaries. Unfortunately, protocol verification still represents a critical task and a major cost to engineer attack-free security protocols. Model checking and SAT-based techniques proved quite effective in this context. This article proposes an efficient automatic model checking approach that exemplifies a security property violation. In this approach, a protocol verification is abstracted as a compact planning problem, which is efficiently solved by a state-of-the-art SAT solver. The experiments performed on some real-world cryptographic protocols succeeded in detecting new logical attacks, violating some security properties. Those attacks encompass both “type flaw” and “replay” attacks, which are difficult to tackle with the existing planning-based approaches.

Dynamic Scheduling and Communication System to Manage Last Mile Handovers

Last mile handover is the most problematic phase in the delivery process, while real-time communication and dynamic scheduling are major problem areas associated with attended last mile handovers. These problem areas need to be addressed holistically to facilitate efficient last mile handovers. The aim of this paper is to report the design and functionalities of a decision-support system which holistically addresses these problem areas. The functionalities of decision-support system which addresses dynamic scheduling and real-time communication problem areas are discussed using case studies. We conclude that a holistic decision-support system with multiparty communication among the stakeholders facilitates improving customer satisfaction, business opportunities and reducing operational costs for logistics companies.

Effect of noise on joint remote preparation of multi-qubit state

Quantum noise severely affects the security and reliability of quantum communication system. In this paper, we study the effect of quantum noise on quantum multiparty communication protocols. Taking a two-qubit joint remote state preparation (JRSP) scheme as an example, we point out that there are some calculation mistakes in a former JRSP scheme [X.W. Guan, X.B. Chen, L.C. Wang and Y.X. Yang, Int. J. Theor. Phys. 53(4) (2014) 2236.]. The revised output states and fidelities in two types of noise are presented, respectively. More importantly, we present a more general form for describing the effect of noise on multi-qubit system, which is fit for the case where different types of noise act on the system consecutively. The process of the JRSP scheme in two types of noise is discussed, respectively. It is shown that the noisy effect in the general case is much stronger than the former one for the most part. Our study will be helpful for analyzing the effect of quantum noise on quantum multiparty communication system.