Ever since the invention of Zero-Knowledge by Goldwasser, Micali, and Rackoff [1], Zero-Knowledge has become a central building block in cryptography with numerous applications, ranging from electronic cash to digital signatures. The properties of Zero-Knowledge range from the most simple (and not particularly useful in practice) requirements, such as honest-verifier zero-knowledge to the most ...

In 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras andΦ : A→ B is a linear map onto B that preserves the spectrum of elements, thenΦ is a Jordan isomorphism if either A or B is a C∗-al...

We show that an area preserving homeomorphism of the open annu lus which has at least one periodic point must in fact have in nitely many interior periodic points

This paper addresses the problem of finding an optimal correction of an inconsistent linear system, where only the nonzero coefficients of the constraint matrix are allowed to be perturbed for reconstructing a consistent system. Using the Frobenius norm as a measure of the distance to feasibility, a nonconvex minimization problem is formulated, whose objective function is a sum of fractional fu...

The zero-error capacity of a discrete classical channel was first defined by Shannon as the least upper bound of rates for which one transmits information with zero probability of error [C. Shannon, IRE Trans. Inform. Theory, IT-2(3):8–19, 1956]. Here, we define the quantum zero-error capacity, a new kind of classical capacity of a noisy quantum channel C represented by a trace-preserving map (...

Power consumption is one of the important issues in VLSI design. Reversible logic produces zero power; therefore, nowadays researchers attend to it in order to optimize power. In the digital systems, one of the methods of achieving to fault tolerance is parity preserving. This paper proposes a new parity preserving reversible gate, PPRG. The most significant aspect of the PPRG gate is that it c...

We construct both randomizable and strongly existentially unforgeable structure-preserving signatures for messages consisting of many group elements. To sign a message consisting of N = mn group elements we have a verification key size of m group elements and signatures contain n+2 elements. Verification of a signature requires evaluating n+1 pairing product equations. We also investigate the c...

In this paper, we verify the diameter of zero divisor graphs with respect to direct product. Keywords—Atomic lattice, complement of graph, diameter, direct product of lattices, 0-distributive lattice, girth, product of graphs, prime ideal, zero divisor graph.

In this paper we adopt the common cycle approach to economic lot scheduling problem and minimize the maximum aggregate inventory. We allow the occurrence of the idle times between any two consecutive products and consider limited capital for investment in inventory. We assume the setup times are negligible. To achieve the optimal investment in inventory we first find the idle times which minimi...