A Rabin Cryptosystem-Based Lightweight Authentication Protocol and Session Key-Generation Scheme for IoT Deployment

Handling unpredictable attack vulnerabilities in self-proclaiming secure algorithms in WSNs is an issue. Vulnerabilities provide loop holes for adversary to barge in the privacy of the network. Attacks performed by the attacker can be active or passive. Adversary may listen to the sensitive information and exploit its confidentiality which is passive, or adversary may modify sensitive information being transferred over a WSN in case of active attacks. As Internet of things has basically three layers, middle-ware layer, Application layer, perceptron layer, most of the attacks are observed to happen at the perceptron layer in case of both wireless sensor network and RFID Tag implication Layer. Both are a major part of the perceptron layer that consist a small part of the IoT. Some of the major attack vulnerabilities are exploited by executing the attacks through certain flaws in the protocol that are difficult to identify and almost complex to identify in complicated bigger protocols. As most of the sensors are resource constrained in terms of memory, battery power, processing power, bandwidth and due to which implementation of complex cryptosystem to keep the data being transferred secure is a challenging phase. The three main objectives studied in this scenario are setting up the system, registering user and the sensors via multiple gateways. Generating a common key which can be used for a particular interaction session among user, gateway and the sensor network. In this paper, we address one or more of these objectives for some of the fundamental problems in authentication and mutual authentication phase of the WSN in IoT deployment. We prevent the leakage of sensitive information using the rabin cryptosystem to avoid attacks like Man-in-the-middle attack, sensor session key leakage, all session hi-jacking attack and sniffing attacks in which data is analyzed maliciously by the adversary. We also compare and prove the security of our protocol using proverif protocol verifier tool.

Dolbeault and J-Invariant Cohomologies on Almost Complex Manifolds

In this paper we relate the cohomology of J-invariant forms to the Dolbeault cohomology of an almost complex manifold. We find necessary and sufficient condition for the inclusion of the former into the latter to be true up to isomorphism. We also extend some results obtained by J. Cirici and S. O. Wilson about the computation of the left-invariant cohomology of nilmanifolds to the setting of solvmanifolds. Several examples are given.

Riemannian-polarized k-symplectic manifolds

In this paper, we give an analogue of the Hermitian structure in the almost complex case, on an [Formula: see text]-dimensional manifold endowed with an almost [Formula: see text]-complex metric. Also, we study the compatibility between Riemannian metric and polarized [Formula: see text]-symplectic structure. Also, we study some properties of an almost [Formula: see text]-complex structure. Moreover, we give an equivalence between almost [Formula: see text]-complex structures, [Formula: see text]-almost tangent structures and [Formula: see text]-almost cotangent structures.

On second non-HLC degree of closed symplecitc manifold

In this note, we show that for a closed almost-Kähler manifold [Formula: see text] with the almost complex structure [Formula: see text] satisfies [Formula: see text] the space of de Rham harmonic forms is contained in the space of symplectic-Bott–Chern harmonic forms. In particular, suppose that [Formula: see text] is four-dimensional, if the self-dual Betti number [Formula: see text], then we prove that the second non-HLC degree measures the gap between the de Rham and the symplectic-Bott–Chern harmonic forms.

On Kodaira dimension of almost complex 4-dimensional solvmanifolds without complex structures

The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, focusing on the case of compact [Formula: see text]-dimensional solvmanifolds without any integrable almost complex structure. According to the classification theory we consider: [Formula: see text], [Formula: see text] and [Formula: see text] with [Formula: see text]. For the first solvmanifold we introduce special families of almost complex structures, compute the corresponding Kodaira dimension and show that it is no longer a deformation invariant. Moreover, we prove Ricci flatness of the canonical connection for the almost Kähler structure. Regarding the other two manifolds we compute the Kodaira dimension for certain almost complex structures. Finally, we construct a natural hypercomplex structure providing a twistorial description.

TOTALLY REAL SURFACES IN $S^6$

The normal bundle $\bar \nu$ of a totally real surface $M$ in $S^6$ splits as $\bar\nu= JTM\oplus \bar\mu$ where $TM$ is the tangent bundle of $M$ and $\bar\mu$ is sub­bundle of $\bar\nu$ which is invariant under the almost complex structure $J$. We study the totally real surfaces M of constant Gaussian curvature K for which the second fundamental form $h(x, y) \in JTM$, and we show that $K = 1$ (that is, $M$ is totally geodesic).