Impossibility of Three Pass Protocol using Public Abelian Groups

Key transport protocols are designed to transfer a secret key from an initiating principal to other entities in a network. The three-pass protocol is a key transport protocol developed by Adi Shamir in 1980 where Alice wants to transport a secret message to Bob over an insecure channel, and they do not have any pre-shared secret information. In this paper, we prove the impossibility of secret key transportation from a principal to another entity in a network by using the three pass protocol over public Abelian groups. If it were possible to employ public Abelian groups to implement the three-pass protocol, we could use it in post-quantum cryptography for transporting keys providing information theoretic security without relying on any computationally difficult problem

Extremal Aging For Trap Models

In the seminal work [5], Ben Arous and \v{C}ern\'y give a general characterization of aging for trap models in terms of $\alpha$-stable subordinators with $\alpha \in (0,1)$. Some of the important examples that fall into this universality class are Random Hopping Time (RHT) dynamics of Random Energy Model (REM) and $p$-spin models observed on exponential time scales. In this paper, we explain a different aging mechanism in terms of {\it extremal processes} that can be seen as the extension of $\alpha$-stable aging to the case $\alpha=0$. We apply this mechanism to the RHT dynamics of the REM for a wide range of temperature and time scales. The other examples that exhibit extremal aging include the Sherrington Kirkpatrick (SK) model and $p$-spin models [6, 9], and biased random walk on critical Galton-Watson trees conditioned to survive [11]

Uneven key pre-distribution scheme for multi-phase wireless sensor networks

In multi-phase Wireless Sensor Networks (WSNs), sensor nodes are redeployed periodically to replace nodes whose batteries are depleted. In order to keep the network resilient against node capture attacks across different deployment epochs, called generations, it is necessary to refresh the key pools from which cryptographic keys are distributed. In this paper, we propose Uneven Key Pre-distribution (UKP) scheme that uses multiple different key pools at each generation. Our UKP scheme provides self healing that improves the resiliency of the network at a higher level as compared to an existing scheme in the literature. Moreover, our scheme provides perfect local and global connectivity. We conduct our simulations in mobile environment to see how our scheme performs under more realistic scenarios

Uniqueness of planar tangent maps in the modified Ericksen model

We prove the uniqueness of homogeneous blow-up limits of maps minimizing the modified Ericksen energy for nematic liquid crystals in a planar domain. The proof is based on the Weiss monotonicity formula, and a blow-up argument, originally due to Allard and Almgren \cite{AA} for minimal surfaces, and L. Simon \cite{SL} for energy-minimizing maps into analytic targets, which exploits the integrability of certain Jacobi fields.Comment: 17 page

Barzakh : for string quartet

Repository copy includes the score of 16 pages, including 1 page of performance instruction, in a pdf format from the original, edited in Sibelius 8.2.0.Barzakh means separation in Arabic. Moreover, in the Islamic eschatology, it is a barrier between the physical and spiritual worlds. In this piece, I am using this idea as an inspiration to my creation so that a disrupting sound and its developments are separating the sound worlds and opening new dimensions for new musical spaces. The piece is composed for string quartet and its duration is approximately 9 minutes