This study proposes a novel procedural modeling method using convolution sums of divisor functions to model a variety of natural trees in a virtual ecosystem efficiently. The basic structure of the modeling method defines the growth grammar, including the branch propagation, a growth pattern of branches and leaves, and a process of growth deformation for various tree generation. Here, the proposed procedural method for trees is to utilize convolution sums of divisor functions as a novel approach. The structure of convolution sums has branch propagation of a uniform pattern, which is controllable, so that it is efficient for real­time virtual ecosystem construction. Furthermore, it can process changes of environment factors or growth deformation for various and unique tree generation simply through the properties of divisor functions. Finally, an experiment is performed in order to evaluate our proposed modeling method whether it can generate natural and various tree models, and a real­time virtual ecosystem of a large area where a variety of trees are presented using the modeling method can be constructed efficiently.Copyright © 2013 John Wiley & Sons, Ltd

Using p-adic integral, many new convolution identities involving Bernoulli, Euler and Genocchi numbers are given.

MSC:11B68, 11S80.

Because wireless sensor network (WSN), which is composed of a large number of low­cost and resource­constrained devices, communicates on the basis of wireless protocols such as IEEE 802.15.4, ZigBee, and DASH­7, it is easily vulnerable to eavesping, illegal modification, privacy infringement and denial­of­service attacks. These attacks destroy the data integrity, confidentiality, and authentication of the basic WSN security requirements and then the reliability and security of the WSN­based applications are deteriorated. There have been many research efforts to make secure WSN environments. Among these efforts, TinyECC is one of outstanding works. It provides several security protocols such as Elliptic Curve Diffie–Hellman, Elliptic Curve Digital Signature Algorithm, and Elliptic Curve Integrated Encryption Scheme, based on the Elliptic Curve Cryptography (ECC). TinyECC is basically a well­written TinyOS­based code and is optimized to resource­constrained environments. The Barrett reduction, hybrid multiplication, and several optimization techniques are also used for high performance even with low­energy consumption. However, the hybrid multiplication technique used in TinyECC is known to be not suitable for 16­bit processor, MSP430, which is a familiar processor for sensor node. This is due to the fact that the MSP 430 processor does not provide enough number of registers for hybrid multiplication techniques. Because the multiplication operation over the finite field is a major operation of the ECC, it causes a high latency of multiplication operations and eventually degrades the performance of the ECC operation. In this paper, we propose a novel multiplication operation based on the cached operands and reordered partial products. The proposed method shows that the latency of the polynomial multiplication, which is the core operation of the ECC, is 6% smaller than previously known results. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we propose the first strong designated verifier signature scheme with a tight security reduction to the LRSW assumption in the standard model.

Jiang et al. proposed an authentication scheme for Vehicle-to-Infrastructure communications using a Binary Authentication Tree. The scheme can effectively eliminate the performance bottleneck when verifying a mass of signatures within a rigorously required interval and filtering bogus messages. In this paper, we show that Jiang et al.'s scheme is insecure against forgery attacks, replay attacks and Sybil attacks. To overcome the weaknesses, we reconstruct a conditional privacy-preserving authentication scheme, called sf CPP-BAT, for Vehicle-to-Infrastructure communications based on secure identity-based signature, aggregate signature schemes and the Binary Authentication Tree.