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

This paper shows a generic and simple conversion from weak asymmetric and symmetric encryption schemes into an asymmetric encryption scheme which is secure in a very strong sense- indistinguishability against adaptive chosen-ciphertext attacks in the random oracle model. In particular, this conversion can be applied efficiently to an asymmetric encryption scheme that provides a large enough coin space and, for every message, many enough variants of the encryption, like the ElGamal encryption scheme.

Secure integration of asymmetric and symmetric encryption schemes

Context The concept of citizen science (CS) is currently referred to by many actors inside and outside science and research. Several descriptions of this purportedly new approach of science are often heard in connection with large datasets and the possibilities of mobilizing crowds outside science to assists with observations and classifications. However, other accounts refer to CS as a way of democratizing science, aiding concerned communities in creating data to influence policy and as a way of promoting political decision processes involving environment and health. Objective In this study we analyse two datasets (N = 1935, N = 633) retrieved from the Web of Science (WoS) with the aim of giving a scientometric description of what the concept of CS entails. We account for its development over time, and what strands of research that has adopted CS and give an assessment of what scientific output has been achieved in CS-related projects. To attain this, scientometric methods have been combined with qualitative approaches to render more precise search terms. Results Results indicate that there are three main focal points of CS. The largest is composed of research on biology, conservation and ecology, and utilizes CS mainly as a methodology of collecting and classifying data. A second strand of research has emerged through geographic information research, where citizens participate in the collection of geographic data. Thirdly, there is a line of research relating to the social sciences and epidemiology, which studies and facilitates public participation in relation to environmental issues and health. In terms of scientific output, the largest body of articles are to be found in biology and conservation research. In absolute numbers, the amount of publications generated by CS is low (N = 1935), but over the past decade a new and very productive line of CS based on digital platforms has emerged for the collection and classification of data.

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What Is Citizen Science?--A Scientometric Meta-Analysis.

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Introduction To Cyclotomic Fields

Fog computing is a new paradigm that extends the Cloud platform model by providing computing resources on the edges of a network. It can be described as a cloud-like platform having similar data, computation, storage and application services, but is fundamentally different in that it is decentralized. In addition, Fog systems are capable of processing large amounts of data locally, operate on-premise, are fully portable, and can be installed on heterogeneous hardware. These features make the Fog platform highly suitable for time and location-sensitive applications. For example, Internet of Things (IoT) devices are required to quickly process a large amount of data. This wide range of functionality driven applications intensifies many security issues regarding data, virtualization, segregation, network, malware and monitoring. This paper surveys existing literature on Fog computing applications to identify common security gaps. Similar technologies like Edge computing, Cloudlets and Micro-data centres have also been included to provide a holistic review process. The majority of Fog applications are motivated by the desire for functionality and end-user requirements, while the security aspects are often ignored or considered as an afterthought. This paper also determines the impact of those security issues and possible solutions, providing future security-relevant directions to those responsible for designing, developing, and maintaining Fog systems.

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Fog computing security: a review of current applications and security solutions

We propose an efficient commutative group action suitable for non-interactive key exchange in a post-quantum setting. Our construction follows the layout of the Couveignes–Rostovtsev–Stolbunov cryptosystem, but we apply it to supersingular elliptic curves defined over a large prime field \(\mathbb F_p\), rather than to ordinary elliptic curves. The Diffie–Hellman scheme resulting from the group action allows for public-key validation at very little cost, runs reasonably fast in practice, and has public keys of only 64 bytes at a conjectured AES-128 security level, matching NIST’s post-quantum security category I.

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CSIDH: an efficient Post-Quantum Commutative Group Action

. We present an efficient key recovery attack on the Supersingular Isogeny Diffie–Hellman protocol (SIDH), based on a “glue-and-split” theorem due to Kani. Our attack exploits the existence of a small non-scalar endomorphism on the starting curve, and it also relies on the auxiliary torsion point information that Alice and Bob share during the protocol. Our Magma im-plementation breaks the instantiation SIKEp434 , which aims at security level 1 of the Post-Quantum Cryptography standardization process currently ran by NIST, in about one hour on a single core. This is a preliminary version of a longer article in preparation.

An efficient key recovery attack on SIDH (preliminary version)

We prove distribution estimates for primes in arithmetic progressions to large smooth squarefree moduli, with respect to congruence classes obeying Chinese remainder theorem conditions, obtaining an exponent of distribution 1/2 + 7/300.

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New equidistribution estimates of Zhang type

In this paper we present a p-adic algorithm to compute the zeta function of a nondegenerate curve over a finite field using Monsky-Washnitzer cohomology. The paper vastly generalizes previous work since in practice all known cases, e.g. hyperelliptic, superelliptic and Cab curves, can be transformed to fit the nondegenerate case. For curves with a fixed Newton polytope, the property of being nondegenerate is generic, so that the algorithm works for almost all curves with given Newton polytope. For a genus g curve over Fpn , the expected running time is e O(ng+ng), whereas the space complexity amounts to e O(ng), assuming p is fixed.

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Computing zeta functions of nondegenerate curves

We review previous work of (mainly) Koelman, Haase and Schicho, and Poonen and Rodriguez-Villegas on the dual operations of (i) taking the interior hull and (ii) moving out the edges of a two-dimensional lattice polygon. We show how the latter operation naturally gives rise to an algorithm for enumerating lattice polygons by their genus. We then report on an implementation of this algorithm, by means of which we produce the list of all lattice polygons (up to equivalence) whose genus is contained in {1,…,30}. In particular, we obtain the number of inequivalent lattice polygons for each of these genera. As a byproduct, we prove that the minimal possible genus for a lattice 15-gon is 45.

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Wouter Castryck

Papers

CSIDH: an efficient Post-Quantum Commutative Group Action

An efficient key recovery attack on SIDH (preliminary version)

New equidistribution estimates of Zhang type

Computing zeta functions of nondegenerate curves

Moving Out the Edges of a Lattice Polygon