On unbalanced Feistel networks with contracting MDS diffusion

Though unbalanced Feistel networks (UFN) are widely considered as an alternative to balanced Feistel networks (BFN) and substitution?Cpermutation networks (SPN) in symmetric cryptography, little has been known yet about their resistance against differential and linear cryptanalysis. In this work, we tackle the problem at the example of d-branch SP-type UFNs with contracting MDS diffusion (dCUFN-SP). Under some restrictions on the contracting MDS matrices over multiple rounds, we prove lower bounds on the number of differentially active S-boxes for dCUFN-SP with ${d\in\{3,4\}}$ and on the number of linearly active S-boxes for dCUFN-SP with d ?? 3. As opposed to SPNs and BFNs, the number of differentially active S-boxes for such constructions does not directly translate to an upper bound on the probability of differential trails. So we provide a thorough analysis of single-round differentials that yields an upper bound on the probability of a differential trail. It is also shown that the efficiency level of dCUFN-SP is comparable to that of BFNs and SPNs with respect to differential and linear cryptanalysis.     

Generalized steiner problem in outerplanar networks

The generalized Steiner problem (GSP) is concerned with the determination of a minimum cost subnetwork of a given network where some (not necessarily all) vertices satisfy certain pairwise (vertex or edge) connectivity requirements.The GSP has applications to the design of water and electricity supply networks, communication networks and other large-scale systems where connectivity requirements ensure the communication between the selected vertices when some vertices and/or edges can become inoperational due to scheduled maintenance, error, or overload.The GSP is known to beNP-complete. In this paper we show that if the subnetwork is required to be biconnected or respectively edge-biconnected, and the underlying network is outerplanar, the GSP can be solved in linear time.     

Generalized PageRank on directed configuration networks

This paper studies the distribution of a family of rankings, which includes Google's PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges in distribution to a finite random variable that can be written as a linear combination of i.i.d. copies of the attracting endogenous solution to a stochastic fixed‐point equation of the form where is a real‐valued vector with , and the are i.i.d. copies of , independent of . Moreover, we provide precise asymptotics for the limit , which when the in‐degree distribution in the directed configuration model has a power law imply a power law distribution for with the same exponent. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 237–274, 2017     

Generalized steiner problem in series-parallel networks

The generalized Steiner problem (GSP) is concerned with the determination of a minimum cost subnetwork of a given network where some (not necessarily all) vertices satisfy certain pairwise (vertex or edge) connectivity requirements. The GSP has applications to the design of water and electricity supply networks, communication networks and other large-scale systems where connectivity requirements ensure the communication between the selected vertices when some vertices and/or edges can become inoperational due to scheduled maintenance, error, or overload. The GSP is known to be NP-complete. In this paper we show that if the subnetwork is required to be respectively biconnected and edge-biconnected, and the underlying network is series-parallel, both problems can be solved in linear time.     

Generalized synchronization between two different complex networks

In this paper, generalized synchronization (GS) between two coupled complex networks is theoretically and numerically studied, where the node vectors in different networks are not the same, and the numbers of nodes of both networks are not necessarily equal. First, a sufficient criterion for GS, one kind of outer synchronizations, of two coupled networks is established based on the auxiliary system method and the Lyapunov stability theory. Numerical examples are also included which coincide with the theoretical analysis.     

Towards the optimality of Feistel ciphers with substitution-permutation functions

We explore the optimality of balanced Feistel ciphers with SP-type F-functions with respect to their resistance against differential and linear cryptanalysis. Instantiations of Feistel ciphers with the wide class of (SP) \(^u\) and (SP) \(^u\) S F-functions are considered: one F-function can contain an arbitrary number of S-box layers interleaved with linear diffusion. For the matrices with maximum diffusion, it is proven that SPS and SPSP F-functions are optimal in terms of the proportion of active S-boxes in all S-boxes—a common efficiency metric for substitution-permutation ciphers. Interestingly, one SP-layer in the F-function is not enough to attain optimality whereas taking more than two S-box layers does not increase the efficiency either.     

Generalized outer synchronization between non-dissipatively coupled complex networks with different-dimensional nodes

This paper investigates the generalized outer synchronization (GOS) between two non-dissipatively coupled complex dynamical networks (CDNs) with different time-varying coupling delays. Our drive-response networks also possess nonlinear inner coupling functions and time-varying outer coupling configuration matrices. Besides, in our network models, the nodes in the same network are nonidentical and the nodes in different networks have different state dimensions. Asymptotic generalized outer synchronization (AGOS) and exponential generalized outer synchronization (EGOS) are defined for our CDNs. Our main objective in this paper is to design AGOS and EGOS controllers for our drive-response networks via the open-plus-closed-loop control technique. Distinguished from most existing literatures, it is the partial intrinsic dynamics of each node in response network that is restricted by the QUAD condition, which is easy to be satisfied. Representative simulation examples are given to verify the effectiveness and feasibility of our GOS theoretical results in this paper.     

SAND: an AND-RX Feistel lightweight block cipher supporting S-box-based security evaluations

Designs, Codes and Cryptography - We revisit designing AND-RX block ciphers, that is, the designs assembled with the most fundamental binary operations—AND, Rotation and XOR operations and do...     

Generalized outer synchronization between complex dynamical networks with time delay and noise perturbation

In this paper, the generalized outer synchronization between two different delay-coupled complex dynamical networks with noise perturbation is investigated. With a nonlinear control scheme, the sufficient condition for almost sure generalized outer synchronization is developed based on the LaSalle-type invariance principle for stochastic differential equations. Numerical examples are examined to illustrate the effectiveness of the analytical results. The theoretic result is also applied to investigate the outer synchronization between two delay-coupled Hindmarsh–Rose neuronal networks with noise perturbation.     

Generalized loopy 2U: A new algorithm for approximate inference in credal networks

Credal networks generalize Bayesian networks by relaxing the requirement of precision of probabilities. Credal networks are considerably more expressive than Bayesian networks, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal networks. The algorithm is based on an important representation result we prove for general credal networks: that any credal network can be equivalently reformulated as a credal network with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal network is then updated by L2U, a loopy approximate algorithm for binary credal networks. Overall, we generalize L2U to non-binary credal networks, obtaining a scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences with respect to other state-of-the-art algorithms is evaluated by extensive numerical tests.     

Construction of $${\text {MDS}}$$ MDS matrices from generalized Feistel structures

Designs, Codes and Cryptography - This paper investigates the construction of $${\text {MDS}}$$ matrices with generalized Feistel structures ( $${\text {GFS}}$$ ). The approach developed by this...     

Control parameters in Boolean networks and cellular automata revisited from a logical and a sociological point of view

The use of “control parameters” as applied to describe the dynamics of complex mathematical systems within models of real social systems is discussed. Whereas single control parameters cannot sufficiently characterize the dynamics of such systems it is suggested that domains of values of certain sets of parameters are appropriately denoting necessary conditions for highly disordered dynamics of social systems. Various of those control parameters permit a straightforward interpretation in terms of properties of social rules and structures. © 1999 John Wiley & Sons, Inc.     

Napoleon revisited

Napoleon's Theorem can be neatly proved using a tessellation of the plane. The theorem can be generalized by using three similar triangles (instead of the three equilateral triangles) erected in different ways on the three sides of the triangle. Various interesting special cases occur.Dedicated to H. S. M. Coxeter on the occasion of his 80th birthday.     

Paracompactness revisited

New proofs of the characterization of paracompact frames as those frames which admit a complete uniformity, and of the existence of the paracompact regular reflection, based on the Samuel type completion, is presented.     

Prosthaphaeresis revisited

The trigonometric identities for the product of two sines and the product of two cosines were first published in 1588. The discovery of the two equations, however, clearly predates that publication. Credit for priority was debated at the end of the last century and tentatively assigned to Paul Wittich of Breslau. But at least some of the conclusions reached at that time were not completely sound, even with respect to the evidence then available; and in the meantime, new evidence has come to light. Reevaluation of the issue now suggests a very questionable role for Wittich in the discovery of either equation. The first one was certainly discovered by Johannes Werner in about 1510, and probably resurrected from his papers by Wittich, while the second one appears to have been discovered from a knowledge of the first by Joost Bürgi in about 1585. But if Wittich loses one aspect of his priority in this reevaluation, he gains in another aspect. For it is now clear that Wittich had developed the method of prosthaphaeresis—the idea of using a product formula to simplify calculations—well before he arrived on Hven in 1580.     

Forcing revisited

The purpose of this paper is to propose and explore a general framework within which a wide variety of model construction techniques from contemporary set theory can be subsumed. Taking our inspiration from presheaf constructions in category theory and Boolean ultrapowers, we will show that generic extensions, ultrapowers, extenders and generic ultrapowers can be construed as examples of a single model construction technique. In particular, we will show that Łoś's theorem can be construed as a specific case of Cohen's truth lemma, and we isolate the weakest conditions a filter must satisfy in order for the truth lemma to work.     

Transitivity revisited

A survey is given of research on transitivity.The debate about the assumption of transitivity turns upon the interpretation of certain real world experiences