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

With the rapid development of computer software and hardware technologies, more and more healthcare data are becoming readily available from clinical institutions, patients, insurance companies, and pharmaceutical industries, among others. This access provides an unprecedented opportunity for data science technologies to derive data-driven insights and improve the quality of care delivery. Healthcare data, however, are usually fragmented and private making it difficult to generate robust results across populations. For example, different hospitals own the electronic health records (EHR) of different patient populations and these records are difficult to share across hospitals because of their sensitive nature. This creates a big barrier for developing effective analytical approaches that are generalizable, which need diverse, "big data." Federated learning, a mechanism of training a shared global model with a central server while keeping all the sensitive data in local institutions where the data belong, provides great promise to connect the fragmented healthcare data sources with privacy-preservation. The goal of this survey is to provide a review for federated learning technologies, particularly within the biomedical space. In particular, we summarize the general solutions to the statistical challenges, system challenges, and privacy issues in federated learning, and point out the implications and potentials in healthcare.

/pdf/federated-learning-for-healthcare-informatics-10ealruc85.pdf

Federated Learning for Healthcare Informatics

Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. The users or service providers with the key have exclusive rights on the data. Especially with popular cloud services, control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encryption (HE), a special kind of encryption scheme, can address these concerns as it allows any third party to operate on the encrypted data without decrypting it in advance. Although this extremely useful feature of the HE scheme has been known for over 30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE) scheme, which allows any computable function to perform on the encrypted data, was introduced by Craig Gentry in 2009. Even though this was a major achievement, different implementations so far demonstrated that FHE still needs to be improved significantly to be practical on every platform. Therefore, this survey focuses on HE and FHE schemes. First, we present the basics of HE and the details of the well-known Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which are important pillars for achieving FHE. Then, the main FHE families, which have become the base for the other follow-up FHE schemes, are presented. Furthermore, the implementations and recent improvements in Gentry-type FHE schemes are also surveyed. Finally, further research directions are discussed. This survey is intended to give a clear knowledge and foundation to researchers and practitioners interested in knowing, applying, and extending the state-of-the-art HE, PHE, SWHE, and FHE systems.

https://dl.acm.org/doi/pdf/10.1145/3214303

A Survey on Homomorphic Encryption Schemes: Theory and Implementation

Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encryption (HE), a special kind of encryption scheme, can address these concerns as it allows any third party to operate on the encrypted data without decrypting it in advance. Although this extremely useful feature of the HE scheme has been known for over 30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE) scheme, which allows any computable function to perform on the encrypted data, was introduced by Craig Gentry in 2009. Even though this was a major achievement, different implementations so far demonstrated that FHE still needs to be improved significantly to be practical on every platform. First, we present the basics of HE and the details of the well-known Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which are important pillars of achieving FHE. Then, the main FHE families, which have become the base for the other follow-up FHE schemes are presented. Furthermore, the implementations and recent improvements in Gentry-type FHE schemes are also surveyed. Finally, further research directions are discussed. This survey is intended to give a clear knowledge and foundation to researchers and practitioners interested in knowing, applying, as well as extending the state of the art HE, PHE, SWHE, and FHE systems.

Steganography, the art of hiding of information in apparently innocuous objects or images, is a field with a rich heritage, and an area of rapid current development. This clear, self-contained guide shows you how to understand the building blocks of covert communication in digital media files and how to apply the techniques in practice, including those of steganalysis, the detection of steganography. Assuming only a basic knowledge in calculus and statistics, the book blends the various strands of steganography, including information theory, coding, signal estimation and detection, and statistical signal processing. Experiments on real media files demonstrate the performance of the techniques in real life, and most techniques are supplied with pseudo-code, making it easy to implement the algorithms. The book is ideal for students taking courses on steganography and information hiding, and is also a useful reference for engineers and practitioners working in media security and information assurance.

http://www.gbv.de/dms/ilmenau/toc/608077828.PDF

Steganography in Digital Media: Principles, Algorithms, and Applications

Processing encrypted signals requires special properties of the underlying encryption scheme. A possible choice is the use of homomorphic encryption. In this paper, we propose a selection of the most important available solutions, discussing their properties and limitations.

/pdf/a-survey-of-homomorphic-encryption-for-nonspecialists-3h2jygsf38.pdf

A Survey of Homomorphic Encryption for Nonspecialists

The use of syndrome coding in steganographic schemes tends to reduce distortion during embedding. The more complete model comes from the wet papers [FGLS05] which allow to lock positions that cannot be modified. Recently, BCH codes have been investigated, and seem to be good candidates in this context [SW06]. Here, we show that Reed-Solomon codes are twice better with respect to the number of locked positions and that, in fact, they are optimal. We propose two methods for managing these codes in this context: the first one is based on a naive decoding process through Lagrange interpolation; the second one, more efficient, is based on list decoding techniques and provides an adaptive trade-off between the number of locked positions and the embedding efficiency.

How can Reed-Solomon codes improve steganographic schemes

The use of syndrome coding in steganographic schemes tends to reduce distortion during embedding. The more complete model comes from the wet papers (J. Fridrich et al., 2005) and allow to lock positions which cannot be modified. Recently, binary BCH codes have been investigated and seem to be good candidates in this context (D. Schonfeld and A. Winkler, 2006). Here, we show that Reed-Solomon codes are twice better with respect to the number of locked positions; in fact, they are optimal. First, a simple and efficient scheme based on Lagrange interpolation is provided to achieve the optimal number of locked positions. We also consider a new and more general problem, mixing wet papers (locked positions) and simple syndrome coding (low number of changes) in order to face not only passive but also active wardens. Using list decoding techniques, we propose an efficient algorithm that enables an adaptive tradeoff between the number of locked positions and the number of changes.

/pdf/how-reed-solomon-codes-can-improve-steganographic-schemes-2kuygnpbju.pdf

How Reed-Solomon codes can improve steganographic schemes

How can reed-Solomon codes improve steganographic schemes?

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A Survey of Homomorphic Encryption for Nonspecialists

How can Reed-Solomon codes improve steganographic schemes

How Reed-Solomon codes can improve steganographic schemes

How can reed-Solomon codes improve steganographic schemes?