Generalised Mersenne Numbers Revisited

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attractive choice for modular multiplication implementation. However, the issue of residue multiplication efficiency seems to have been overlooked. Asymptotically, using a cyclic rather than a linear convolution, residue multiplication modulo a Mersenne number is twice as fast as integer multiplication; this property does not hold for prime GMNs, unless they are of Mersenne's form. In this work we exploit an alternative generalisation of Mersenne numbers for which an analogue of the above property --- and hence the same efficiency ratio --- holds, even at bitlengths for which schoolbook multiplication is optimal, while also maintaining very efficient reduction. Moreover, our proposed primes are abundant at any bitlength, whereas GMNs are extremely rare. Our multiplication and reduction algorithms can also be easily parallelised, making our arithmetic particularly suitable for hardware implementation. Furthermore, the field representation we propose also naturally protects against side-channel attacks, including timing attacks, simple power analysis and differential power analysis, which is essential in many cryptographic scenarios, in constrast to GMNs.Comment: 32 pages. Accepted to Mathematics of Computatio

Cutting tool tracking and recognition based on infrared and visual imaging systems using principal component analysis (PCA) and discrete wavelet transform (DWT) combined with neural networks

The implementation of computerised condition monitoring systems for the detection cutting tools’ correct installation and fault diagnosis is of a high importance in modern manufacturing industries. The primary function of a condition monitoring system is to check the existence of the tool before starting any machining process and ensure its health during operation. The aim of this study is to assess the detection of the existence of the tool in the spindle and its health (i.e. normal or broken) using infrared and vision systems as a non-contact methodology. The application of Principal Component Analysis (PCA) and Discrete Wavelet Transform (DWT) combined with neural networks are investigated using both types of data in order to establish an effective and reliable novel software program for tool tracking and health recognition. Infrared and visual cameras are used to locate and track the cutting tool during the machining process using a suitable analysis and image processing algorithms. The capabilities of PCA and Discrete Wavelet Transform (DWT) combined with neural networks are investigated in recognising the tool’s condition by comparing the characteristics of the tool to those of known conditions in the training set. The experimental results have shown high performance when using the infrared data in comparison to visual images for the selected image and signal processing algorithms

Randomized cache placement for eliminating conflicts

Applications with regular patterns of memory access can experience high levels of cache conflict misses. In shared-memory multiprocessors conflict misses can be increased significantly by the data transpositions required for parallelization. Techniques such as blocking which are introduced within a single thread to improve locality, can result in yet more conflict misses. The tension between minimizing cache conflicts and the other transformations needed for efficient parallelization leads to complex optimization problems for parallelizing compilers. This paper shows how the introduction of a pseudorandom element into the cache index function can effectively eliminate repetitive conflict misses and produce a cache where miss ratio depends solely on working set behavior. We examine the impact of pseudorandom cache indexing on processor cycle times and present practical solutions to some of the major implementation issues for this type of cache. Our conclusions are supported by simulations of a superscalar out-of-order processor executing the SPEC95 benchmarks, as well as from cache simulations of individual loop kernels to illustrate specific effects. We present measurements of instructions committed per cycle (IPC) when comparing the performance of different cache architectures on whole-program benchmarks such as the SPEC95 suite.Peer ReviewedPostprint (published version

High-Performance Hardware and Software Implementations of the Cyclic Redundancy Check Computation

The Cyclic Redundancy Check (CRC) is an error detection code used in many digital transmission and storage systems. The two major research areas surrounding CRCs concern developing computation approaches and studying error detection properties. This thesis aims to explore the various aspects of the CRC computation, with the primary objective being to propose novel computation approaches which outperform the existing ones. The work begins with a thorough examination of the formulations found throughout the literature. Then, their subsequent realizations as hardware architectures and software algorithms are investigated. During this investigation, some improvements are presented including optimizations of the state-space trans­ formed and primitive architectures. Afterward, novel formulations are derived and the most significant contribution consists of a matrix decomposition that gives rise to a high-performance software algorithm. Simulation and implementation results are gathered for both hardware and software deployments of the investigated computa­ tion approaches. The theoretical results obtained by simulations are validated with implementation experiments. The proposed algorithm is shown to outperform the existing comparable low-memory algorithm in terms of time complexity

A versatile Montgomery multiplier architecture with characteristic three support

We present a novel unified core design which is extended to realize Montgomery multiplication in the fields GF(2n), GF(3m), and GF(p). Our unified design supports RSA and elliptic curve schemes, as well as the identity-based encryption which requires a pairing computation on an elliptic curve. The architecture is pipelined and is highly scalable. The unified core utilizes the redundant signed digit representation to reduce the critical path delay. While the carry-save representation used in classical unified architectures is only good for addition and multiplication operations, the redundant signed digit representation also facilitates efficient computation of comparison and subtraction operations besides addition and multiplication. Thus, there is no need for a transformation between the redundant and the non-redundant representations of field elements, which would be required in the classical unified architectures to realize the subtraction and comparison operations. We also quantify the benefits of the unified architectures in terms of area and critical path delay. We provide detailed implementation results. The metric shows that the new unified architecture provides an improvement over a hypothetical non-unified architecture of at least 24.88%, while the improvement over a classical unified architecture is at least 32.07%