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

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

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

Bread and Empire: The Workings of Grain Provisioning in Istanbul During the Eighteenth Century

Provisioning of the Imperial capital Istanbul had been one of the major concerns of the Ottoman rulers from the classical age to the dawn of the modern era. Grain occupied a particularly important place in the provisioning policies of the Ottoman state due to the fact that the Ottoman sultans considered the steady supply of "people's bread" in the capital city as one of the ways to promote and reproduce their image of sovereignty in the general public opinion. This consideration remained unchanged throughout the eighteenth century during which time the Ottoman economy faltered vis-à-vis the European centered world-economy and the Ottoman polity began to gradually withdraw from the economic realm. In the face of mounting fiscal burdens, the Ottoman state limited its provisioning policies to the raw materials needed by the military industries and to the basic foods consumed by the populace. In this context, the traditional protectionist attitude of the state towards the craft guilds of the imperial capital was abandoned, leaving these organizations at the mercy of circumstances not to say the market principle. The only institutions that were insulated from the changing policy of the state were the grain-related crafts, i.e. bakers' guild. This paper argues with reference to a series of published documents that the Ottoman state continued, if not hardened, its provisioning policies of grain to the imperial capital during the eighteenth century and thereafter.Istanbul, Ottoman state, grain provision, food supply

A Model of Dynamic Liquidity Contracts

The main goal of this paper is to analyze the nature of long-term liquidity contracts that arise between lenders and borrowers in the absence of perfect enforceability and when both parties are financially constrained. We study an infinite horizon dynamic contracting model between a borrower and a lender with the following features: The borrower, is credit-constrained, faces a stochastic project arrival process every period, can choose to renege each period, and can save through the lender. Projects are indivisible. The lender is resource- constrained, and can commit to the terms of the contract as long as it is ex-ante individually rational to do so. We show that: (i) Enforcement problems and endogenous resource constraints can severely curtail the possibility of financing projects, (ii) the economy exhibits investment cycles, (iii) credit is rationed if either the lender has too little capital or the borrower has too little financial collateral. This paper’s technical contribution is to show the existence and characterization of financial contracts that are solutions to a non- convex dynamic programming problem.Credit Rationing, Investment Cycles, Limited Enforceability, Liquidity Provision, Resource Constraints

Aging in the GREM-like trap model

The GREM-like trap model is a continuous time Markov jump process on the leaves of a finite volume $L$-level tree whose transition rates depend on a trapping landscape built on the vertices of the whole tree. We prove that the natural two-time correlation function of the dynamics ages in the infinite volume limit and identify the limiting function. Moreover, we take the limit $L\to\infty$ of the two-time correlation function of the infinite volume $L$-level tree. The aging behavior of the dynamics is characterized by a collection of clock processes, one for each level of the tree. We show that for any $L$, the joint law of the clock processes converges. Furthermore, any such limit can be expressed through Neveu's continuous state branching process. Hence, the latter contains all the information needed to describe aging in the GREM-like trap model both for finite and infinite levels.Comment: 30 pages, 1 figur