The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.

[서평]「Applied Cryptography」

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the “bible of computer algebra”, gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany oneor two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.

Modern computer algebra

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms.

/pdf/a-comprehensive-survey-on-particle-swarm-optimization-1d380v5xx1.pdf

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Neuromorphic computing has come to refer to a variety of brain-inspired computers, devices, and models that contrast the pervasive von Neumann computer architecture This biologically inspired approach has created highly connected synthetic neurons and synapses that can be used to model neuroscience theories as well as solve challenging machine learning problems The promise of the technology is to create a brain-like ability to learn and adapt, but the technical challenges are significant, starting with an accurate neuroscience model of how the brain works, to finding materials and engineering breakthroughs to build devices to support these models, to creating a programming framework so the systems can learn, to creating applications with brain-like capabilities In this work, we provide a comprehensive survey of the research and motivations for neuromorphic computing over its history We begin with a 35-year review of the motivations and drivers of neuromorphic computing, then look at the major research areas of the field, which we define as neuro-inspired models, algorithms and learning approaches, hardware and devices, supporting systems, and finally applications We conclude with a broad discussion on the major research topics that need to be addressed in the coming years to see the promise of neuromorphic computing fulfilled The goals of this work are to provide an exhaustive review of the research conducted in neuromorphic computing since the inception of the term, and to motivate further work by illuminating gaps in the field where new research is needed

A Survey of Neuromorphic Computing and Neural Networks in Hardware.

In this chapter we will present the basic concepts of term rewriting that are needed in this book. More details on term rewriting, its applications, and related subjects can be found in the textbook of Baader and Nipkow [BN98]. Readers versed in German are also referred to the textbooks of Avenhaus [Ave95], Bundgen [Bun98], and Drosten [Dro89]. Moreover, there are several survey articles [HO80, DJ90, Klo92, Pla93] that can also be consulted.

Term Rewriting Systems

Systolic arrays provide a large amount of parallelism. However, their applicability is restricted to a small set of computational problems due to their lack of flexibility. This limitation can be circumvented by using reconfigurable systolic arrays, where the node interconnections and operations can be redefined even at run time. In this context, several alternative systolic architectures can be explored and powerful tools are needed to model and evaluate them. We show how well-known rewriting-logic environments could be used to quickly model and simulate complex application specific digital systems speeding-up its subsequent prototyping. We show how to use rewriting-logic to model and evaluate reconfigurable systolic architectures which are applied to the efficient treatment of several dynamic programming methods for resolving well-known problems such as global and local sequence alignment (Smith-Waterman algorithm), approximate string matching and computation of the longest common subsequence. A VHDL description of the conceived architecture was implemented from the rewriting-logic based abstract models and synthesized over an FPGA of the APEX family.

http://www.fpl.uni-kl.de/staff/hartenstein/SBCCI_04-RH-Ayala.pdf

Modeling and prototyping dynamically reconfigurable systems for efficient computation of dynamic programming methods by rewriting-logic

Nominal unification is an extension of first-order unification that takes into account the \(\alpha \)-equivalence relation generated by binding operators, following the nominal approach. We propose a sound and complete procedure for nominal unification with commutative operators, or nominal C-unification for short, which has been formalised in Coq. The procedure transforms nominal C-unification problems into simpler (finite families) of fixed point constraints, whose solutions can be generated by algebraic techniques on combinatorics of permutations.

Nominal C-Unification

We propose a new axiomatisation of the alpha-equivalence relation for nominal terms, based on a primitive notion of fixed-point constraint. We show that the standard freshness relation between atoms and terms can be derived from the more primitive notion of permutation fixed-point, and use this result to prove the correctness of the new alpha-equivalence axiomatisation. This gives rise to a new notion of nominal unification, where solutions for unification problems are pairs of a fixed-point context and a substitution. Although it may seem less natural than the standard notion of nominal unifier based on freshness constraints, the notion of unifier based on fixed-point constraints behaves better when equational theories are considered: for example, nominal unification remains finitary in the presence of commutativity, whereas it becomes infinitary when unifiers are expressed using freshness contexts.

/pdf/fixed-point-constraints-for-nominal-equational-unification-dhu0m546g2.pdf

Fixed-Point Constraints for Nominal Equational Unification

This paper presents a low cost architecture for the solution of linear equations based on the Gaussian Elimination Method using a reconfigurable system based on FPGA. This architecture can handle single data precision that follows the IEEE 754 floating point standard. The implementation takes advantage of both the internal memory and the DSP blocks (available in the Virtex-5 FPGA). The architectural approach is composed of four modules and one specific unit (namely, Change Row Module, Pivo Module, FB Module, Normalization Module and finally the Gaussian Elimination Controller Unit). This structure can be combined with other smaller arithmetic units in order to maintain the accuracy of the results without the need to internally normalize and de-normalize the floatingpoint data. Also, a special Memory Access Unit was implemented in order to deal with the writing/reading operations to/from the internal RAM. The resource consumption of the implementation (specially the internal RAM memory blocks that are used) points out several improvements when compared to previous work of the authors and other more elaborated architectures whose implementations are significantly more complex and, thus, unsuitable for low cost applications.

A fast and low cost architecture developed in FPGAs for solving systems of linear equations

Nominal systems are an alternative approach for the treatment of variables in computational systems. In the nominal approach variable bindings are represented using techniques that are close to first-order logical techniques, instead of using a higher-order metalanguage. Functional nominal computation can be modelled through nominal rewriting, in which α-equivalence, nominal matching and nominal unification play an important role. Nominal unification was initially studied by Urban, Pitts and Gabbay and then formalised by Urban in the proof assistant Isabelle/HOL and by Kumar and Norrish in HOL4. In this work, we present a new specification of nominal unification in the language of PVS and a formalisation of its completeness. This formalisation is based on a natural notion of nominal α-equivalence, avoiding in this way the use of the intermediate auxiliary weak α-relation considered in previous formalisations. Also, in our specification, instead of applying simplification rules to unification and freshness constraints, we recursively build solutions for the original problem through a straightforward functional specification, obtaining a formalisation that is closer to algorithmic implementations. This is possible by the independence of freshness contexts guaranteed by a series of technical lemmas.

https://kclpure.kcl.ac.uk/portal/files/54129606/LSFA2015paper15_camready.pdf

Mauricio Ayala-Rincón

Papers

Modeling and prototyping dynamically reconfigurable systems for efficient computation of dynamic programming methods by rewriting-logic

Nominal C-Unification

Fixed-Point Constraints for Nominal Equational Unification

A fast and low cost architecture developed in FPGAs for solving systems of linear equations

Completeness in PVS of a Nominal Unification Algorithm