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.

We provide a simple and exact formula for the minimum Miller loop length in Ate _i pairing based on Brezing–Weng curves, in terms of the involved parameters, under a mild condition on the parameters. It will also be shown that almost all cryptographically useful/meaningful parameters satisfy the mild condition. Hence the simple and exact formula is valid for them. It will also turn out that the formula depends only on essentially two parameters, providing freedom to choose the other parameters to address the design issues other than minimizing the loop length.

We are motivated by Ramanujan’s recursion formula for sums of the product of two Eisenstein series (Berndt in Ramanujan’s Notebook, Part II, 1989, Entry 14, p.332) and its proof, and also by Besge-Liouville’s convolution identity for the ordinary divisor function σ k−1 (n)  (Williams in Number Theory in the Spirit of Liouville, vol. 76, 2011, Theorem 12.3). The objective of this paper is to introduce and prove convolution identities for the twisted divisor functions σ ∗ k−1 (n)  as well as for the twisted Eisenstein series S 2k+2,χ 0    and S 2k+2,χ 1    , S ∗ 2k+2   , S ∗ 2k+2,χ 0    , and S ∗ 2k+2,χ 1    . As applications based on our main results, we establish many interesting identities for pyramidal, triangular, Mersenne, and perfect numbers. Moreover, we show how our main results can be used to obtain arithmetical formulas for the number of representations of an integer n as the sums of s squares.

In this paper, we study the convolution sums involving restricted divisor functions, their generalizations, their relations to Bernoulli numbers, and some interesting applications.

This paper presents results of an all-sky searches for periodic gravitational waves in the frequency range $[50, 1190] \text{ Hz}$ and with frequency derivative ranges of $\sim[-2 \times 10^{-9}, 1.1 \times 10^{-10}] \text{ Hz}/s$ for the fifth LIGO science run (S5). The novelty of the search lies in the use of a non-coherent technique based on the Hough-transform to combine the information from coherent searches on timescales of about one day. Because these searches are very computationally intensive, they have been deployed on the Einstein@Home distributed computing project infrastructure. The search presented here is about a factor 3 more sensitive than the previous Einstein@Home search in early S5 LIGO data. The post-processing has left us with eight surviving candidates. We show that deeper follow-up studies rule each of them out. Hence, since no statistically significant gravitational wave signals have been detected, we report upper limits on the intrinsic gravitational wave amplitude $h_0$. For example, in the 0.5 Hz-wide band at 152.5 Hz, we can exclude the presence of signals with $h_0$ greater than $7.6 \times 10^{-25}$ with a 90% confidence level.

In this paper, we introduce an improved version of mapped weighted essentially non-oscillatory (WENO) schemes for solving Hamilton–Jacobi equations. To this end, we first discuss new smoothness indicators for WENO construction. Then the new smoothness indicators are combined with the mapping function developed by Henrick et al. (2005) [31]. The proposed scheme yields fifth-order accuracy in smooth regions and sharply resolve discontinuities in the derivatives. Numerical experiments are provided to demonstrate the performance of the proposed schemes on a variety of one-dimensional and two-dimensional problems.