A SURVEY OF LIMITED NONDETERMINISM IN COMPUTATIONAL COMPLEXITY THEORY

Nondeterminism is typically used as an inherent part of the computational models used incomputational complexity. However, much work has been done looking at nondeterminism asa separate resource added to deterministic machines. This survey examines several differentapproaches to limiting the amount of nondeterminism, including Kintala and Fischer\u27s βhierarchy, and Cai and Chen\u27s guess-and-check model

On implemented graph based generator of cryptographically strong pseudorandom sequences of multivariate nature

Classical Multivariate Cryptography (MP) is searching for special families of functions of kind ^nF=T_1FTT_2 on the vector space V= (F_q)^n where F is a quadratic or cubical polynomial map of the space to itself, T_1 and T^2 are affine transformations and T is the piece of information such that the knowledge of the triple T_1, T_2, T allows the computation of reimage x of given nF(x) in polynomial time O(n^ᾳ). Traditionally F is given by the list of coefficients C(^nF) of its monomial terms ordered lexicographically. We consider the Inverse Problem of MP of finding T_1, T_2, T for F given in its standard form. The solution of inverse problem is harder than finding the procedure to compute the reimage of ^nF in time O(n^ᾳ). For general quadratic or cubic maps nF this is NP hard problem. In the case of special family some arguments on its inclusion to class NP has to be given

Oblivious Transfer from weakly Random Self-Reducible Public-Key Cryptosystem

In this work, we define a new notion of weakly Random-Self-Reducibile cryptosystems and show how it can be used to implement secure Oblivious Transfer. We also show that two recent (Post-quantum) cryptosystems (based on Learning with errors and Approximate Integer GCD) can be considered as weakly Random-Self-Reducible

Efficient design of WIMAX/802.16 mesh networks

Broadband wireless networks are becoming increasingly popular due to their fast and inexpensive deployment and their capabilities of providing flexible and ubiquitous Internet access. While the majority of existing broadband wireless networks are still exclusively limited to single hop access, it is the ability of these networks to forward data frames over multi-hop wireless routes which enabled them to easily extend the network coverage area. Unfortunately, achieving good multi- hop throughput has been challenging due to several factors, such as lossy wireless links caused by interference from concurrent transmissions, and intra-path interference caused by transmissions on successive hops along a single path. A wireless mesh network WMN consists of a number of stationary wireless mesh routers, forming a wireless backbone. The wireless mesh routers serve as access points (APs) for wireless mobile devices, and some of them also act as gateways to the Internet via high speed wireless links. Several technologies are currently being considered for mesh (multi-hop) networks, including, IEEE 802.11 (both single channel and multi-channel), IEEE 802.16/WiMAX, and next generation cellular networks (LTE). In this work, we focus on the IEEE 802.16. To maximize the network performance of mesh networks (e.g., throughput), it is essential to consider a cross-layer design, exploiting the dependency between protocol layers such as the routing network layer and the scheduling resource allocation MAC layer. Therefore this PhD thesis considers a cross-layer design approach for designing efficient wireless mesh networks; we first develop mathematical models (link-based and path-based) for the problem of joint routing tree construction and link scheduling in WiMAX-based mesh networks with the objective of minimizing the schedule length to satisfy a set of uplink and downlink demands. This is achieved by maximizing the number of concurrent active transmissions in the network by efficiently reusing the spectrum spatially. Second, we exploit the broadcasts nature of the wireless medium and enhance our design models by incorporating opportunistic network coding into the joint routing tree construction and link scheduling problem. Identifying coding-aware routing structures and utilizing the broadcasting feature of the wireless medium play an important role in realizing the achievable gain of network coding. Last, the uprising mobile WiMAX (802.16e amendment) has introduced more difficulties and challenges into the network design problem; thus, ensuring larger connection lifetime and better routing stability become of greater interest for the joint routing and scheduling problem. This is addressed by augmenting the previously designed models. Throughout this thesis, we assume centralized scheduling at the base station (BS) and we develop, for the joint problems, integer linear programming (ILP) models which require the enumeration of all feasible solutions to reach the optimal solution. Given their complexities, we rely on optimization decomposition methods using column generation for solving each model in an efficient way