This paper proposes a two-level continuum transportation system approach to modeling a dynamic taxi traffic assignment (DTTA) problem in a dense network with real-time traffic information provision and three types of vehicles, including private cars, occupied taxis, and vacant taxis. The proposed approach treats the dense network as a continuum in the first level, in which private car and occupied taxi drivers are free to choose their paths in a two-dimensional continuous space. The proposed approach also divides the modeling region into many identical squares to form a cell-based network in the second level, in which the cells are classified into two categories: target cell with an acceptable expected rate of return (EROR) to vacant taxi drivers and non-target cell with an unacceptable EROR. The EROR associated with a cell is the ratio of the cumulative expected profit of a taxi driver who successfully picks up a customer during the customer search that starts from that cell to the sum of expected search time for this customer and expected occupied travel time to serve this customer. Based on the cell-based network, we develop a cell-based intervening opportunity model to capture the fact that vacant taxi drivers can meet a customer on the way to their destination zones and estimate the EROR. Each vacant taxi driver has a mixed strategy to determine his/her customer-search direction according to the EROR: Each vacant taxi driver in a target cell selects its neighbor cells with maximum EROR, and each vacant taxi driver in a non-target cell selects the travel time-based shortest path to his/her target cell. Meanwhile, each private car driver chooses the path that minimizes his/her own generalized travel cost, and each occupied taxi driver chooses the path that minimizes his/her customer's generalized in-vehicle travel cost. In our model, traffic density in the system is governed by the conservation law (CL), and the flow directions of different vehicles are determined by the path-choice strategies of their drivers, which are captured by Hamilton–Jacobi (HJ) equations. Both the proposed CL and HJ equations can be solved by the Lax–Friedrichs scheme, which forms the backbone of the developed solution algorithm. Finally, numerical examples and a case study are used to demonstrate the properties of the model, the performance of the solution algorithm, and the value of using our methodology for estimating network performance.

We show that Multivariate Public Key Cryptosystems (MPKCs) over fields of small odd prime characteristic, say 31, can be highly efficient. Indeed, at the same design security of 2^{80} under the best known attacks, odd-char MPKC is generally faster than prior MPKCs over \GF{2^k}, which are in turn faster than "traditional'' alternatives. This seemingly counter-intuitive feat is accomplished by exploiting the comparative over-abundance of small integer arithmetic resources in commodity hardware, here embodied by SSE2 or more advanced special multimedia instructions on modern x86-compatible CPUs. We explain our implementation techniques and design choices in implementing our chosen MPKC instances modulo small a odd prime. The same techniques are also applicable in modern FPGAs which often contains a large number of multipliers.

Key Exchange (KE) from RLWE (Ring-Learning with Errors) is a potential alternative to Diffie-Hellman (DH) in a post quantum setting. Key leakage with RLWE key exchange protocols in the context of key reuse has already been pointed out in previous work. The initial attack described by Fluhrer is designed in such a way that it only works on Peikert’s KE protocol and its variants that derives the shared secret from the most significant bits of the approximately equal keys computed by both parties. It does not work on Ding’s key exchange that uses the least significant bits to derive a shared key. The Signal leakage attack relies on changes in the signal sent by the responder reusing his key, in a sequence of key exchange sessions initiated by an attacker with a malformed key. A possible defense against this attack would be to require the initiator of a key exchange to send the signal, which is the one pass case of the KE protocol. In this work, we describe a new attack on Ding’s one pass case without relying on the signal function output but using only the information of whether the final key of both parties agree. We also use LLL reduction to create the adversary’s keys in such a way that the party being compromised cannot identify the attack in trivial ways. This completes the series of attacks on RLWE key exchange with key reuse for all variants in both cases of the initiator and responder sending the signal. Moreover, we show that the previous Signal leakage attack can be made more efficient with fewer queries and how it can be extended to Peikert’s key exchange, which was used in the BCNS implementation and integrated with TLS and a variant used in the New Hope implementation.

Consider an unstable quantum system that has been found undecayed at an instant s and denote by R(t,s) the rate of its regeneration into an original (undecayed) state at a later instant t+s. It is proved that the reduced evolution is a semigroup, i.e., there is no regeneration at all, provided R(t,s)1/2 can be estimated by a sufficiently regular function that is nondecreasing in s and has zero derivative with respect to t at t=0 for every s. This generalizes the theorem of Misra and Sinha [Helv. Phys. Acta 45, 619 (1972)] in a different direction than in a recent paper by Nishioka [J. Math. Phys. 29, 1860 (1988)].

A BDDC (Balancing Domain Decomposition by Constraints) algorithm is developed and analyzed for a staggered discontinuous Galerkin (DG) finite element approximation of second order scalar elliptic problems. On a quite irregular subdomain partition, an optimal condition number bound is proved for two-dimensional problems. In addition, a sub-optimal but scalable condition number bound is obtained for three-dimensional problems. These bounds are shown to be independent of coefficient jumps in the subdomain partition. Numerical results are also included to show the performance of the algorithm.