Bit Length Research Articles

Is There a Shortage of Primes for Cryptography

Cryptographic algorithms often prescribe the use of primes whose length in bits is a power of 2. Recently, we proved that for m ＞ 1, there is no prime number with 2^m significant bits, exactly two of which are 0 bits. Here we generalize this theorem to impose many more restrictions on primes whose length in bits is a power of 2. No similar restrictions apply to primes of other lengths. We consider whether the restrictions on primes with length 2^m bits are so great that one should choose other lengths for primes to be used in cryptography.

Potential of Servo Pattern Printing on PMR Media With High-Density Servo Signal Pattern

Servo pattern printing (SPP) is recognized as a candidate for the future high resolution and high throughput servo track writing method. In terms of the application to perpendicular magnetic recording (PMR) media, there are two methods of SPP, "edge printing (EP)" and "bit printing (BP)," which use horizontal and vertical external field during printing process, respectively. Comparing between EP and BP, EP has higher potential for the PMR application, because of the properties of a dc-free signal, a higher signal-to-noise ratio (SNR) and smaller repeatable run out (RRO) from 8th to 19th order than a conventional head writing method. In the simulation, the less write-fringe of the recorded bits was confirmed as the benefits of EP. The most recent experiment demonstrated 55-nm bit length (BL) with adequate read back signal and EP is considered to have adaptability to the areal density beyond 48 Gbits/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (300 Gbpsi)

Tensor-product parity code for magnetic recording

In magnetic recording, a standard code architecture consists of an outer Reed-Solomon code in concatenation with an inner parity code. The inner parity code is used to detect and correct common error events. Generally, a parity code with short block length performs better, as multiple error events within one block and, consequently, miscorrection are less likely. In this paper, we study an inner code that offers the same system performance as a parity code with very short block length, even as short as the symbol length (in bits) of the outer Reed-Solomon code, but with higher code rate. This code is a tensor-product code, with a Bose-Chauduri-Hocquenghem (BCH) code and a short parity code as constituent codes. The decoder for this code is not much more complex than the optimal decoder of the baseline parity-coded channel; in fact, the only additional steps are Viterbi detection matched to the channel and decoding of the BCH code.

Multigigahertz range-Doppler correlative signal processing in optical memory crystals

Analog optical signal processing of complex radio-frequency signals for range-Doppler radar information is theoretically described and experimentally demonstrated using crystalline optical memory materials and off-the-shelf photonic components. A model of the range-Doppler processing capability of the memory material for the case of single-target detection is presented. Radarlike signals were emulated and processed by the memory material; they consisted of broadband (> 1 GHz), spread-spectrum, pseudorandom noise sequences of 512 bits in length, which were binary phase-shift keyed on a 1.9 GHz carrier and repeated at 100 kHz over 7.5 ms. Delay (range) resolution of 8 ns and Doppler resolution of 130 Hz over 100 kHz were demonstrated.

Three-Dimensional Optical Memory in a Photoacid-Induced Recording Medium

We report a photoacid-induced write-once read-many recording medium based on poly(methyl methacrylate) for three-dimensional (3D) optical memory. Three-layered recording was achieved using only an 800 nm-femtosecond oscillator with a 82-MHz-repetition rate without structural damage. Bits of arbitrary length used in the present modulation method of Compact Disc type memory can be recorded by photo-modification in the medium. The results suggest that the medium is an attractive candidate to solve the technical problems of 3D recording, in which micro-structural integrity of medium is altered.

Vulnerability of pixel-value differencing steganography to histogram analysis and modification for enhanced security

The pixel-value differencing (PVD) steganography can embed a large amount of secret bits into a still image with high imperceptibility as it makes use of the characteristics of human vision sensitivity. However, a loophole exists in the PVD method. Unusual steps in the histogram of pixel differences reveal the presence of a secret message. An analyst can even estimate the length of hidden bits from the histogram. To enhance security, a modified scheme is proposed which avoids occurrence of the above-mentioned steps in the pixel difference histogram while preserving the advantage of low visual distortion of the PVD. The histogram-based steganalysis is therefore defeated.

Dynamic random Weyl sampling for drastic reduction of randomness in Monte Carlo integration

To reduce randomness drastically in Monte Carlo (MC) integration, we propose a pairwise independent sampling, the dynamic random Weyl sampling (DRWS). DRWS is applicable even if the length of random bits to generate a sample may vary. The algorithm of DRWS is so simple that it works very fast, even though the pseudo-random generator, the source of randomness, might be slow. In particular, we can use a cryptographically secure pseudo-random generator for DRWS to obtain the most reliable numerical integration method for complicated functions.

High-performance compensation technique for the radix-4 CORDIC algorithm

Although the full radix-4 CORDIC algorithm is efficient compared to the standard radix-2 version, the scale-factor overhead causes its improvement to be limited. In this work, an algorithm and its associated architecture have been proposed for parallel compensation of the scale factor for the radix-4 CORDIC algorithm in the rotation mode. The proposed method, which makes no prior assumptions about the elementary angles of rotation, reduces the latency from n to (n/2)+3, where n is the precision length in bits, at the cost of a reasonable increase in hardware complexity. The architecture presented relates to the redundant signed-digit number system. The architecture has been modelled in VHDL and simulated to establish its functional validity.

Pseudo-spin-valve device performance for giant magnetoresistive random access memory applications

Write and read performance were characterized in current-in-plane pseudo-spin-valve (PSV) devices. The PSV stack evaluated in this work was Ta 5 nm/NiFe 6.5 nm/CoFe 1.5 nm/Cu 3.7 nm/CoFe 1.5 nm/NiFe 4.5 nm/Ta 20 nm. Minimum resistance (R/sub min/), storage layer switching fields in forward and reverse sweep directions (H/sub f/ and H/sub r/) for write, and resistance change (/spl Delta/R) for readback are reported as a function of temperature (25 to 100/spl deg/C) and bit width (500 to 900 nm). R/sub min/ and /spl Delta/R temperature coefficients are reported as a function of sense current (0.1 to 1 mA), I/sub s/. H/sub f/ and H/sub r/ temperature coefficients are reported as a function of I/sub s/ and applied hard-axis field (0 to 30 Oe), H/sub d/. The variation of R/sub min/ with temperature, normalized to R/sub min/ at 25/spl deg/C to account for bit width (BW), was approximately +1.4 m/spl Omega///spl deg/C//spl Omega/. The variation of /spl Delta/R with temperature, normalized to R/sub min/ at 25/spl deg/C, was approximately -60 /spl mu//spl Omega///spl deg/C//spl Omega/. The temperature dependences of R/sub min/ and /spl Delta/R were attributed to increased scattering as thermal energy increased. H/sub f/ and H/sub r/ show weak temperature dependence, between approximately 0 and -25 mOe//spl deg/C and 0 and +25 mOe//spl deg/C, respectively. The weak temperature dependence of H/sub f/ and H/sub r/ was ascribed to the weak temperature dependence of magnetization, anisotropy, and exchange over the measured range of temperatures.

Polarization properties of light emitted by a bent optical fiber probe and polarization contrast in scanning near-field optical microscopy

This article describes the polarization properties of light emitted by a bent optical fiber probe which is used for scanning near-field optical microscopy operated in atomic force mode (SNOM/AFM). SNOM/AFM can be applied to the observation of magnetic domains by imaging polarization contrast in transmission mode. A bent optical fiber probe with a subwavelength aperture is vibrated vertically as a cantilever for atomic force microscopy. Plane polarized light with an extinction ratio of better than 70:1 was emitted by the aperture by controlling the polarization state of incident light to the probe. A particular transverse polarization component of light transmitting a sample is selected by a polarization analyzer and detected. We obtained clear polarization contrast images of 0.7 μm length bits written with a conventional method using a focused laser beam on a bismuth-substituted dysprosium-iron-garnet film.

Polarization effect in scanning near-field optic/atomic-force microscopy (SNOM/AFM)

The polarization effect is reported using a bent optical fiber probe for a scanning near-field optic/atomic-force microscope (SNOM/AFM). We have demonstrated that the SNOM/AFM could be applied to the observation of magnetic domains by imaging polarization contrast in transmission mode. An optical fiber probe with a subwavelength aperture is bent and vibrated vertically as a cantilever for an atomic-force microscope (AFM) for atomic-force regulation. Plane polarized light with an extinction ratio of better than 70 : 1 was emitted by the aperture of the bent probe by controlling the polarization properties of incident light to the probe. By detecting a particular transverse polarization component of light transmitting a sample selected by a polarization analyzer, we obtained clear polarization contrast images of 0.7 μm length bits written on a bismuth-substituted dysprosium-iron-garnet film.

Memory efficient and high-speed search Huffman coding

Code compression is a key element in high-speed digital data transport. A major compression is performed by converting the fixed-length codes to variable-length codes through a (semi-)entropy coding scheme. Huffman coding is shown to be a very efficient coding scheme. To speed up the process of search for a symbol in a Huffman tree and to reduce the memory size we have proposed a tree clustering algorithm to avoid high sparsity of the tree. The method is shown to be extremely efficient in memory requirement, and fast in searching for the symbol. For an experimental video data with Huffman codes extended up to 13 bits in length, the entire memory space is shown to be 122 words, compared to 2/sup 13/=8192 words in a normal situation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

High speed pattern matching for a fast Huffman decoder

The fast Huffman decoding algorithm has been used in JPEG, MPEG and image data compression standards, etc. And code compression is a key element in high speed digital data transport. A major compression is performed by converting the fixed-length codes to variable-length codes through an entropy coding scheme. Huffman coding combined with run-length coding is shown to be a very efficient coding scheme. To speed up the process of search for a symbol in a Huffman tree and to reduce the memory size we have proposed a tree clustering and a pattern matching algorithm to avoid high sparsity of the tree. The method is shown to be very efficient in memory size and fast searching for the symbol. For an experimental video data with Huffman codes extended up to 16 bits in length, i.e. it is used for the standard JPEG, the result of experiments show that the proposed algorithm has a very high speed and performance. The design of the decoder is carried out using silicon-gate CMOS process. >

ON THE RECORDING CODE WHICH IMPROVES THE GROOVE PARAMETER

In order to increase the recording capacity the mark edge recording and (1, 7)RLL code are employed in the second generation ISO/IEC optical disk standard. However this recording method degrades groove parameter at ROM area because (1, 7)RLL code has long Tmax which causes recording pattern of combination of long pits and short spaces. New (2, 5)RLL code whose Tmax is small were developed. Because Tmax/Tmin gets close to unity, the information capacity of the code is small so that detection window width becomes narrow. Because narrow band signal to noise ratio is large and jitter is small in ROM area, the window margin of (2, 5)RLL code written in ROM area is same as that of (1, 7)RLL code written in MO area when both codes are recorded in the same recording density. The window width of (2, 5)RLL code is 0.4Tb and Tmin is 1.2Tb where Tb is one bit length of information bit.

Multipled block codes for all-optical transports

Multipled block codes (MBCs) for all-optical transport are investigated. Each block of the MBC comprises N subblocks, each n bits in length. A feature of the MBC family is that the clock component can be recovered through logical processing. First, coding efficiency is studied to show that choosing n=2N results in the maximum efficiency. Next, the jitter problem due to deviations in processing delays is investigated. Recovery of the clock component by the combined use of delay-and-multiply and delay-and-add logical processing is investigated. Numerical and simulation results show that the former causes no jitter when the pulse duty is chosen adequately, and only minor jitter is generated due to the latter. Applications of this type of line code to various systems such as trunk lines, cross connects, interconnects and local area networks (LANs) are discussed. Transmission frame processing suitable for photonic implementation is investigated. It is also shown that the applications of this type of line code to superbroadband cross connects, interconnects, and LANs are promising owing to simple clock recovery and frame processing capabilities.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Efficient VLSI digital logarithmic codecs

N bit digital words can be logarithmically encoded and compressed to a word length of (log/sub 2/n+m-1) bit maintaining a relative accuracy of m bit over (n-m) octaves of signal level. A bit-serial VLSI coder is reported, which requires little more than a log/sub 2/n counter and an output register and it has a latency of one wordlength. The bit-parallel coder can be built with less than n/sup 2/ transistors and has less than n/4 gate delays. The decoder has similar properties and it expands the logarithm to an antilogarithm with n bit of dynamic range. Using these codecs, digital multiplication, division, powers and roots are reduced to additions, subtractions and shifts, respectively.

Compaction of message patterns into succinct representations for multiprocessor interconnection networks

We describe a formalism for succinctly representing address sets and for representing message patterns for multiprocessor interconnection networks. In this formalism a mask is used to represent a set of equal length bit vectors. Such a set can be interpreted as either a set of processor addresses or a set of messages. First, we consider the problem of determining whether an arbitrary set of addresses or messages can be represented by a single mask. For this problem we present a linear time algorithm that constructs a mask representing the set if one exists. We then extend this algorithm so that it can be used to determine, in linear time, if a set of messages forms a bit permute-complement permutation. Finally, we consider the more general problem of determining if a set of masks, which represents a set of addresses or messages, can be merged into a single mask. We show this problem to be NP-hard. We also discuss the implications of this formalism with respect to the efficient manipulation and transmission of message patterns in multiprocessors.

An efficient method for representing and transmitting message patterns on multiprocessor interconnection networks

We describe a formalism for representing address sets and for representing message patterns for multiprocessor interconnection networks. In this formalism a descriptor called a mask is used to represent a set of equal length bit vectors. Such a set can be interpreted as a set of processor addresses, or as a set of messages. We focus on the implications that this formalism has for routing message patterns on bundled omega networks. Specifically, we show that when a message pattern is represented in this formalism, a number of properties of the message pattern can be determined in polynomial time. This includes such things as determining whether the message pattern contains congestion. In addition, we show that the formalism defines a subclass of message patterns for which the minimum round partitioning problem , which in general is NP-hard, is solvable in linear time. We show this result to be true for both broadcast and nonbroadcast bundled omega networks. This generalizes a known result for bit-permute-complement permutations to a more general class of message patterns and to a larger class of networks.

Optimal and suboptimal binary inputs for system identification

A heuristic random search technique for finding a near-optimum binary input sequence to a linear dynamical system is presented. The problem requires the optimization of a multimodal real function that depends on a string of binary integers. The algorithms combine a global random search procedure with a local (neighborhood) search which examines all sequences within a prescribed Hamming distance. The algorithm is applied to the determination of the sequence of air and oxygen breaths that are optimal for estimating lung parameter values. Simulation studies show that the algorithm finds an optimum input sequence 10 bits in length in 100% of the trials, and 20 bits in length in 97% of the trials. Near-optimum values are also located with strings 30 and 40 bits in length using approximately 1000 iterations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Exact Delay Analysis of Packet-Switching Concentrating Networks

We present an exact delay analysis for a packet-switching concentrating system consisting of an arbitrary number of active stations connected in tandem by unidirectional, asynchronous transmission lines, all with identical transmission rate. Packetized messages from exogenous sources enter the system at every station, are handled from station to station in a store-and-forward fashion, and exit at the downstream end; there are no intermediate departures. The service discipline at each station is either FCFS, fixed priority, or alternating priority, the transmission of a packet is not interrupted while in progress. We assume that the packets have identical length (in bits), that the sources are independent and that each source generates batch Poisson traffic. The FCFS case was solved by Kaplan [7] and Shalmon and Kaplan [19]. Here we analyze the priority disciplines. For the packets and messages from each source, we obtain the steady-state moment generating functions for their end-to-end waiting times. We offer simple formulas for the corresponding mean waiting times, and show that the Poisson approximation for departures is unreliable. The analysis for all three disciplines generalizes to the case where the line capacities are nonincreasing in the direction of the flow, and for the priority disciplines, it further generalizes to a concentrating tree network, and to an arrival process somewhat more general than batch Poisson.