In this letter, we give a trace representation of binary Jacobi sequences with period pq over an extension field of the odd prime field Fr. Our method is based on the use of a pqth root of unity over the extension field, and the representation of the Jacobi sequences by corresponding indicator functions and quadratic characters of two primes p and q.

Boneh et al. proposed the new idea of pairing-based cryptography by using the composite order group instead of prime order group. Recently, many cryptographic schemes using pairings of composite order group were proposed. Miller's algorithm is used to compute pairings, and the time of computing the pairings depends on the cost of calculating the Miller loop. As a method of speeding up calculations of the pairings of prime order, the number of iterations of the Miller loop can be reduced by choosing a prime order of low Hamming weight. However, it is difficult to choose a particular composite order that can speed up the pairings of composite order. Kobayashi et al. proposed an efficient algorithm for computing Miller's algorithm by using a window method, called Window Miller's algorithm. We can compute scalar multiplication of points on elliptic curves by using a window hybrid binary-ternary form (w-HBTF). In this paper, we propose a Miller's algorithm that uses w-HBTF to compute Tate pairing efficiently. This algorithm needs a precomputation both of the points on an elliptic curve and rational functions. The proposed algorithm was implemented in Java on a PC and compared with Window Miller's Algorithm in terms of the time and memory needed to make their precomputed tables. We used the supersingular elliptic curve y2=x3+x with embedding degree 2 and a composite order of size of 2048-bit. We denote w as window width. The proposed algorithm with w=6=2·3 was about 12.9% faster than Window Miller's Algorithm with w=2 although the memory size of these algorithms is the same. Moreover, the proposed algorithm with w=162=2·34 was about 12.2% faster than Window Miller's algorithm with w=7.

The unique characteristic of Ternary ripple-carry addition enables us to optimize Ternary Full Adder for this specific application. Carbon nanotube field effect transistors are used in this paper to design new Ternary Half and Full Adders, which are essential components of Ternary ripple-carry adder. The novel designs take the sum of input variables as a single input signal, and generate outputs in a way which is far more efficient than the previously presented similar structures. The new ripple-carry adder operates rapidly, with high performance, and low-transistor-count.

In holographic data storage, information is recorded within the volume of a holographic medium. Typically, the data is presented as an array of pixels with modulation in amplitude and/or phase. In the 4-f orientation, the Fourier domain representation of the data array is produced optically, and this image is recorded. If the Fourier image contains large peaks, the recording material can saturate, which leads to errors in the read-out data array. In this paper, we present a coding process that produces sparse ternary data arrays. Ternary modulation is used because it inherently provides Fourier domain smoothing and allows more data to be stored per array in comparison to binary modulation. Sparse arrays contain fewer on-pixels than dense arrays, and thus contain less power overall, which reduces the severity of peaks in the Fourier domain. The coding process first converts binary data to a sequence of ternary symbols via a high-rate block code, and then uses guided scrambling to produce a set of candidate codewords, from which the most sparse is selected to complete the encoding process. Our analysis of the guided scrambling division and selection processes demonstrates that, with primitive scrambling polynomials, a sparsity greater than 1/3 is guaranteed for all encoded arrays, and that the probability of this worst-case sparsity decreases with increasing block size.

Pseudo-random sequences with high linear complexity play important roles in many domains. We give linear complexity of generalized cyclotomic quaternary sequences with period pq over Z4 via the weights of its Fourier spectral sequence. The results show that such sequences have high linear complexity.

In this Letter, a new face recognition approach based on curvelets and local ternary patterns (LTP) is proposed. First, we observe that the curvelet transform is a new anisotropic multi-resolution transform and can efficiently represent edge discontinuities in face images, and that the LTP operator is one of the best texture descriptors in terms of characterizing face image details. This motivated us to decompose the image using the curvelet transform, and extract the features in different frequency bands. As revealed by curvelet transform properties, the highest frequency band information represents the noisy information, so we directly drop it from feature selection. The lowest frequency band mainly contains coarse image information, and thus we deal with it more precisely to extract features as the face's details using LTP. The remaining frequency bands mainly represent edge information, and we normalize them for achieving explicit structure information. Then, all the extracted features are put together as the elementary feature set. With these features, we can reduce the features' dimension using PCA, and then use the sparse sensing technique for face recognition. Experiments on the Yale database, the extended Yale B database, and the CMU PIE database show the effectiveness of the proposed methods.

This letter presents three methods for producing 8-QAM+ sequences. The first method transforms a ternary complementary sequence set (CSS) with even number of sub-sequences into an 8-QAM+ periodic CSS with both of the period and the number of sub-sequences unaltered. The second method results in an 8-QAM+ aperiodic CSS with confining neither the period nor the number of sub-sequences. The third method produces 8-QAM+ periodic sequences having ideal autocorrelation property on the real part of the autocorrelation function. The proposed sequences can be potentially applied to suppression of multiple access interference or synchronization in a communication system.

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms compared with the linear block codes. The objective of this letter is to present a new family of ternary cyclic codes with parameters [3m-1,3m-1-2m,4], where m is an odd integer. The proposed cyclic codes are optimal in the sense that their parameters meet the Sphere Packing bound.

In this paper, one new class of quaternary generalized cyclotomic sequences with the period 2pq over F4 is established. The linear complexity of proposed sequences with the period 2pq is determined. The results show that such sequences have high linear complexity.

In this paper, a simple yet efficient texture representation is proposed for texture classification by exploring the joint statistics of local quantized patterns (jsLQP). In order to combine information of different domains, the Gaussian derivative filters are first employed to obtain the multi-scale gradient responses. Then, three feature maps are generated by encoding the local quantized binary and ternary patterns in the image space and the gradient space. Finally, these feature maps are hybridly encoded, and their joint histogram is used as the final texture representation. Extensive experiments demonstrate that the proposed method outperforms state-of-the-art LBP based and even learning based methods for texture classification.

In this letter, constructions of sequences with perfect odd autocorrelation and sequence sets with zero odd correlation zone (ZOCZ) over the 8-QAM+ constellation are presented. Based on odd perfect ternary sequences, odd perfect sequences and ZOCZ sequence sets over the 8-QAM+ constellation are constructed by using shift vectors and mappings. These odd perfect sequences and ZOCZ sequence sets over 8-QAM+ constellation can be used in communication systems to achieve high transmission data rate (TDR) and low interference.

In this paper, for an odd prime p, new quaternary sequences of even period 2p with ideal autocorrelation property are constructed using the binary Legendre sequences of period p. For the new quaternary sequences, two properties which are considered as the major characteristics of pseudo-random sequences are derived. Firstly, the autocorrelation distribution of the proposed quaternary sequences is derived and it is shown that the autocorrelation values of the proposed quaternary sequences are optimal. For both p≡1 mod 4 and p≡3 mod 4, we can construct optimal quaternary sequences while only for p≡3 mod 4, the binary Legendre sequences can satisfy ideal autocorrelation property. Secondly, the linear complexity of the proposed quaternary sequences is also derived by counting non-zero coefficients of the discrete Fourier transform over the finite field Fq which is the splitting field of x2p-1. It is shown that the linear complexity of the quaternary sequences is larger than or equal to p or (3p+1)/2 for p≡1 mod 4 or p≡3 mod 4, respectively.

A unified construction for transforming binary sequences of balance or unbalance into quaternary sequences is presented. On the one hand, when optimal and balanced binary sequences with even period are employed, our construction is exactly the same Jang, et al.'s and Chung, et al.'s ones, which result in balanced quaternary sequences with optimal autocorrelation magnitude. On the other hand, when ideal and balanced binary sequences with odd period N are made use of, our construction produces new balanced quaternary sequences with optimal autocorrelation value (OAV), in which there are N distinct sequences in terms of cyclic shift equivalence, and includes Tang, et al.'s and Jang, et al.'s ones as special cases. In addition, when binary sequences without period 2n-1 or balance are employed, the transformation of Jang, et al.'s method is invalid, however, the proposed construction works very good. As a consequence, this unified construction allows us to construct optimal and balanced quaternary sequences from ideal/optimal balanced binary sequences with arbitrary period.

The linear complexity of quaternary sequences plays an important role in cryptology. In this paper, the minimal polynomial of a class of quaternary sequences with low autocorrelation constructed by generalized cyclotomic sequences pairs is determined, and the linear complexity of the sequences is also obtained.

The three-bit balanced ternary quantum voltage generator was designed and tested. This voltage generator is based on zero-crossing Shapiro steps (ZCSSs) in asymmetric two-junction SQUID. ZCSSs were observed on the current-voltage curves, and maximum and minimum current of ZCSSs were almost same, respectively for the three bits. 27-step quantum voltages from -13Φ0f to +13 Φ0f were observed by combinations of inputs of bit1, bit2 and bit3.

This letter presents a framework, including two constructions, for yielding several types of sequences with optimal autocorrelation properties. Only by simply choosing proper coefficients in constructions and optimal known sequences, two constructions transform the chosen sequences into optimally required ones with two or four times periods as long as the original sequences', respectively. These two constructions result in binary and quaternary sequences with optimal autocorrelation values (OAVs), perfect QPSK+ sequences, and multilevel perfect sequences, depending on choices of the known sequences employed. In addition, Construction 2 is a generalization of Construction B in [5] so that the number of distinct sequences from the former is larger than the one from the latter.

In contemporary communications, Golay, periodic and Z- complementary sequence sets play a very important role, since such sequence sets possess impulse-like or zero correlation zone (ZCZ) autocorrelation. On the other hand, the advantages of the signals over the quadrature amplitude modulation (QAM) constellation are more and more prominent. Hence, the design of such sequence sets over the QAM constellation has turned into one of the all-important issues in communications. Therefore, the construction methods of such sequence sets over the 16-QAM constellation are investigated, in this letter, and our goals are arrived at by the known quaternary Golay, periodic and Z- complementary sequence sets. Finally, many examples illuminate the validity of the proposed methods.

In this correspondence, we devise a new method for constructing a ternary column sequence set of length 3m+1-1 form ternary sequences of period 3m-1 with ideal autocorrelation, and the ternary LCZ sequence set of period 3n-1 is constructed by using the column sequence set when (m+1)|n. In addition, the method is popularized to the p-ary LCZ sequence. The resultant LCZ sequence sets in this paper are optimal with respect to the Tang-Fan-Matsufuji bound.

Ternary content addressable memory (TCAM) is becoming very popular for designing high-throughput forwarding engines on routers. However, TCAM has potential problems in terms of hardware and power costs, which limits its ability to deploy large amounts of capacity in IP routers. In this paper, we propose new hardware architecture for fast forwarding engines, called fast prefix search RAM-based hardware (FPS-RAM). We designed FPS-RAM hardware with the intent of maintaining the same search performance and physical user interface as TCAM because our objective is to replace the TCAM in the market. Our RAM-based hardware architecture is completely different from that of TCAM and has dramatically reduced the costs and power consumption to 62% and 52%, respectively. We implemented FPS-RAM on an FPGA to examine its lookup operation.

The present paper introduces a novel construction of ternary sequences having a zero-correlation zone. The cross-correlation function and the side-lobe of the auto-correlation function of the proposed sequence set is zero for the phase shifts within the zero-correlation zone. The proposed sequence set consists of more than one subset having the same member size. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a wider zero-correlation zone than that of the correlation function of sequences of the same subset (intra-subset correlation function). The wide inter-subset zero-correlation enables performance improvement during application of the proposed sequence set. The proposed sequence set has a zero-correlation zone for periodic, aperiodic, and odd correlation functions.