BackgroundIncreasingly, hospitals and research institutes are developing technical solutions for sharing patient data in a privacy preserving manner. Two of these technical solutions are homomorphic encryption and distributed ledger technology. Homomorphic encryption allows computations to be performed on data without this data ever being decrypted. Therefore, homomorphic encryption represents a potential solution for conducting feasibility studies on cohorts of sensitive patient data stored in distributed locations. Distributed ledger technology provides a permanent record on all (...) transfers and processing of patient data, allowing data custodians to audit access. A significant portion of the current literature has examined how these technologies might comply with data protection and research ethics frameworks. In the Swiss context, these instruments include the Federal Act on Data Protection and the Human Research Act. There are also institutional frameworks that govern the processing of health related and genetic data at different universities and hospitals. Given Switzerland’s geographical proximity to European Union (EU) member states, the General Data Protection Regulation (GDPR) may impose additional obligations.MethodsTo conduct this assessment, we carried out a series of qualitative interviews with key stakeholders at Swiss hospitals and research institutions. These included legal and clinical data management staff, as well as clinical and research ethics experts. These interviews were carried out with two series of vignettes that focused on data discovery using homomorphic encryption and data erasure from a distributed ledger platform.ResultsFor our first set of vignettes, interviewees were prepared to allow data discovery requests if patients had provided general consent or ethics committee approval, depending on the types of data made available. Our interviewees highlighted the importance of protecting against the risk of reidentification given different types of data. For our second set, there was disagreement amongst interviewees on whether they would delete patient data locally, or delete data linked to a ledger with cryptographic hashes. Our interviewees were also willing to delete data locally or on the ledger, subject to local legislation.ConclusionOur findings can help guide the deployment of these technologies, as well as determine ethics and legal requirements for such technologies. (shrink)

With the development of mobile communication technology, location-based services are booming prosperously. Meanwhile privacy protection has become the main obstacle for the further development of LBS. The k-nearest neighbor search is one of the most common types of LBS. In this paper, we propose an efficient private circular query protocol with high accuracy rate and low computation and communication cost. We adopt the Moore curve to convert two-dimensional spatial data into one-dimensional sequence and encrypt the points of interest information with (...) the Brakerski-Gentry-Vaikuntanathan homomorphic encryption scheme for privacy-preserving. The proposed scheme performs the secret circular shift of the encrypted POIs information to hide the location of the user without a trusted third party. To reduce the computation and communication cost, we dynamically divide the table of the POIs information according to the value of k. Experiments show that the proposed scheme provides high accuracy query results while maintaining low computation and communication cost. (shrink)

The simulation hypothesis has recently excited renewed interest, especially in the physics and philosophy communities. However, the hypothesis specifically concerns {computers} that simulate physical universes, which means that to properly investigate it we need to couple computer science theory with physics. Here I do this by exploiting the physical Church-Turing thesis. This allows me to introduce a preliminary investigation of some of the computer science theoretic aspects of the simulation hypothesis. In particular, building on Kleene's second recursion theorem, I prove (...) that it is mathematically possible for us to be in a simulation that is being run on a computer \textit{by us}. In such a case, there would be two identical instances of us; the question of which of those is ``really us'' is meaningless. I also show how Rice's theorem provides some interesting impossibility results concerning simulation and self-simulation; briefly describe the philosophical implications of fully homomorphic encryption for (self-)simulation; briefly investigate the graphical structure of universes simulating universes simulating universes, among other issues. I end by describing some of the possible avenues for future research that this preliminary investigation reveals. (shrink)

Content-based image retrieval (CBIR) is a technique used to retrieve image from an image database. However, the CBIR process suffers from less accuracy to retrieve many images from an extensive image database and prove the privacy of images. The aim of this article is to address the issues of accuracy utilizing deep learning techniques such as the CNN method. Also, it provides the necessary privacy for images using fully homomorphic encryption methods by Cheon–Kim–Kim–Song (CKKS). The system has been (...) proposed, namely RCNN_CKKS, which includes two parts. The first part (offline processing) extracts automated high-level features based on a flatting layer in a convolutional neural network (CNN) and then stores these features in a new dataset. In the second part (online processing), the client sends the encrypted image to the server, which depends on the CNN model trained to extract features of the sent image. Next, the extracted features are compared with the stored features using a Hamming distance method to retrieve all similar images. Finally, the server encrypts all retrieved images and sends them to the client. Deep-learning results on plain images were 97.87% for classification and 98.94% for retriever images. At the same time, the NIST test was used to check the security of CKKS when applied to Canadian Institute for Advanced Research (CIFAR-10) dataset. Through these results, researchers conclude that deep learning is an effective method for image retrieval and that a CKKS method is appropriate for image privacy protection. (shrink)

In this essay we introduce a new tool for studying the patterns of sentential reference within the framework introduced in [2] and known as the language of paradox $\mathcal {L}_{\mathsf {P}}$ : strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms. In particular, we show that (i) strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms between $\mathcal {L}_{\mathsf {P}}$ constructions preserve paradoxicality, (ii) many (but not all) earlier results regarding the paradoxicality of $\mathcal {L}_{\mathsf {P}}$ constructions can be recast as special cases of our central result regarding (...) strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms, and (iii) that we can use strong $\mathcal {L}_{\mathsf { P}}$ -homomorphisms to provide a simple demonstration of the paradoxical nature of a well-known paradox that has not received much attention in this context: the McGee paradox. In addition, along the way we will highlight how strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms highlight novel connections between the graph-theoretic analyses of paradoxes mobilized in the $\mathcal {L}_{\mathsf {P}}$ framework and the methods and tools of category theory. (shrink)

The Snowden revelations in 2013 redrew the lines of debate surrounding surveillance, exposing the extent of state surveillance across multiple nations and triggering legislative reform in many. In the UK, this was in the form of the Investigatory Powers Act. As a contribution to understanding resistance to expanding state surveillance activities, this article reveals the intertwining of diverse interests and voices which speak in opposition to UK state surveillance. Through a computational topic modelling-based mixed methods analysis of the submissions made (...) to the draft Investigatory Powers Bill consultation, the article demonstrates the diversity and intersection of discourses within different actor groups, including civil society and the technology industry. We demonstrate that encryption is a key issue for these groups, and is additionally conflated with a human rights discourse. This serves to unite seemingly disparate interests by imbuing encryption with a responsibility for the protection of human rights, but also threatens to legitimate corporate interests and distract from their own data-driven activities of surveillance capitalism. (shrink)

We investigate the group of definable homomorphisms between two definable abelian groups A and B, in an o-minimal structure . We prove the existence of a “large”, definable subgroup of . If contains an infinite definable set of homomorphisms then some definable subgroup of B admits a definable multiplication, making it into a field. As we show, all of this can be carried out not only in the underlying structure but also in any structure definable in.

In nonstandard measure theory the standard part map is very useful to represent standard measures by Loeb measures. We give here a different method of representing measures using the concept of a σ -homomorphism. As an application a measure extension theorem is derived. Finally a nonstandard proof of a result of Pták is given showing that his assumption of nonmeasurable cardinality is redundant.

The composition series of Verma modules and homomorphisms between Verma modules in the case of a complex semisimple Lie algebra were studied by Verma and by Bernstein, Gelfand and Gelfand. The author studies homomorphisms between the Verma modules in characteristic p.

In this paper we define a suitable version of the notion of homomorphism for Kripke models of intuitionistic first-order logic and characterize theories that are preserved under images and also those that are preserved under inverse images of homomorphisms. Moreover, we define a notion of union of chain for Kripke models and define a class of formulas that is preserved in unions of chains. We also define similar classes of formulas and investigate their behavior in Kripke models. An application to (...) intuitionistic first-order arithmetic is also given. (shrink)

The article deals with the algorithm of encrypting graphic information using transformation matrixes. It presents the actions that can be done with the image. The article also gives algorithms for forming matrixes that are created with the use of random processes. Examples of matrixes and encryption results are shown. Calculations of the analysis of combinations and conclusions to them are carried out. The article shows the possibilities and advantages of this image encryption algorithm. The proposed algorithm will allow (...) to transmit encrypted information through open communication channels. The algorithm uses all possible actions that can be done with the image, namely: image resizing, adding redundant elements to the image, changing the location of the pixels, changing the brightness of the image pixels, inverting the image pixels, changing the colours of the images pixels. A randomized approach to matrix formation will make it impossible to use neural systems. The algorithm of the implementation of writing encryption code is rather simple. It is not possible to decrypt the image without a key as the number of possible combinations is extremely large. This algorithm can be used in the military, intelligence, information security. Encryption does not require significant computing or RAM resources. This algorithm can be implemented in WEB-technology and in mobile applications, it has no recursive functions and loop in loop. The algorithm hides the image size, which in turn adds extra protection. Redundant elements will not allow neural networks to compare pixels. Changing colors, changing brightness, inversion by random processes will not allow neural networks to find the decryption function. The article considers an image encryption algorithm that will give a possibility to generate a key. The key will be a set of two-dimensional arrays formed in a randomized manner. A randomized approach to matrix formation will make it impossible to use neural systems. The algorithm uses all possible actions that can be done with the image, namely: Image resizing. Adding redundant elements to the image. Changing the location of the pixels. Changing the brightness of the image pixels. Inverting the image pixels. Changing the colours of the images pixels. The pixel positioning matrix gives us! combinations. The pixel brightness change matrix gives us 8 *! combinations. The pixel inversion matrix gives us 8 *! combinations. The pixel colour change matrix gives us 6 *! Combinations. The total number of combinations N is equal to: It is not possible to decrypt the image without a key as the number of possible combinations is extremely large. The algorithm of the implementation of writing encryption code is rather simple. This algorithm can be used in the military, intelligence, information security. The advantage of this algorithm is the fact that the encrypted image can be transmitted through open chann. (shrink)

We survey various aspects of the problem of automatic continuity of homomorphisms between Polish groups.

We investigate homomorphisms of degree structures with various relations, functions and constants. Our main emphasis is on pseudolattices, i.e., partially ordered sets with a join operation and relations simulating the meet operation. We show that there are no finite quotients of the pseudolattice of degrees or of the pseudolattice of degrees 0′, but that many finite distributive lattices are pseudolattice quotients of the pseudolattice of computably enumerable degrees.

Topic of quantum chaos has begun to draw increasing attention in recent years. So, to ensure the security of digital image, an image encryption algorithm based on combining a hyperchaotic system and quantum 3D logistic map is proposed. This algorithm is applied in four stages. Initially, the key generator builds upon the foundation of mean for any row or column of the edges of the plain image. Its output value is used to yield initial conditions and parameters of the (...) proposed image encryption scheme. Next, it diffuses the plain image by the random sequences generated by 3D hyperchaotic system, and the diffusion process is realized by implementing XOR operation. Then, the diffused image and chaotic sequences are produced by the 3D quantum chaotic logistic map, expressed as a quantum superposition state using density matrix which is a representation of the state of a quantum system, and finally the resulting quantum image is then confused and diffused simultaneously by a unitary matrix generated by logistic chaos using XNOR operation to obtain the final cipher image. Because of the dependence on the plain image, the algorithm can frustrate the chosen-plaintext and known-plaintext attacks. Simulation results and theoretical analysis verify that the presented scheme has high safety performance, a good encryption effect, and a large key space. The method can effectively resist exhaustive, statistical, and differential attacks. Moreover, the encryption time of the proposed method is satisfactory, and the method can be efficiently used in practice for the secure transmission of image information. (shrink)

It is shown within Bishop's constructive mathematics that, under one extra, classically automatic, hypothesis, a continuous homomorphism from R onto a compact metric abelian group is periodic, but that the existence of the minimum value of the period is not derivable.

With the increasing volume of data transmission through insecure communication channels, big data security has become one of the important concerns in the cybersecurity domain. To address these concerns and keep data safe, a robust privacy-preserving cryptosystem is necessary. Such a solution relies on chaos encryption algorithms over standard cryptographic methods that possess multistage encryption levels, including high speed, high security, low compute overheads, and procedural power, among other characteristics. In this work, a secure image encryption scheme (...) is proposed using linear feedback shift register and chaos-based quantum chaotic map. The focus of the scheme is mainly dependent on the secret keys from the input of the algorithm. The threat landscape, the statistical test analysis, along critical comparisons with other schemes indicate that the presented algorithm is significantly secure and is resistant to a wide range of different attacks such as differential and statistical attacks. The proposed method has sufficiently higher sensitivity and security when compared to existing encryption algorithms. Several security parameters validated the security of proposed work such as correlation coefficient analyses among the neighboring pixels, entropy, the number of pixels change rate, unified average change intensity, mean square error, brute force, key sensitivity, and peak signal to noise ratio analyses. The randomness of the ciphers produced by the proposed technique is also passed through NIST-800-22. The results of NIST indicate that the ciphers are highly random and do not produce any type of periodicity or pattern. (shrink)

In the past decades, considerable attention has been paid to the chaos-based image encryption schemes owing to their characteristics such as extreme sensitivity to initial conditions and parameters, pseudo-randomness, and unpredictability. However, some schemes have been proven to be insecure due to using a single chaotic system. To increase the security, this work proposes a novel image encryption scheme based on the piecewise linear chaotic map and the standard map. To the best of our knowledge, it is the (...) first chaos-based image encryption scheme combining the PWLCM with the standard map, which adopts permutation-diffusion structure. Unlike the traditional scrambling way, a hierarchical diffusion strategy, which not only changes the pixel position but also modifies the value, is employed in the permutation phase. The operation model of row-by-row and column-by-column is further used to enhance the efficiency in the diffusion process. Consequently, a good trade-off efficiency and security can be achieved. Furthermore, the numerical simulations and performance analyses illustrate that the proposed encryption scheme can be used in practical application scenarios requiring lightweight security. (shrink)

The primary purpose of this paper is to analyze the relationship between the familiar non-Archimedean field of hyperreals from Abraham Robinson’s nonstandard analysis and Paolo Giordano’s ring extension of the real numbers containing nilpotents. There is an interesting nontrivial homomorphism from the limited hyperreals into the Giordano ring, whereas the only nontrivial homomorphism from the Giordano ring to the hyperreals is the standard part function, namely, the function that maps a value to its real part. We interpret this asymmetry to (...) mean that the nilpotent infinitesimal values of Giordano’s ring are “smaller” than the hyperreal infinitesimals. By viewing things from the “point of view” of the hyperreals, all nilpotents are zero, whereas by viewing things from the “point of view” of Giordano’s ring, nonnilpotent, nonzero infinitesimals register as nonzero infinitesimals. This suggests that Giordano’s infinitesimals are more fine-grained. (shrink)

In the paper A. I. Malcev's problem on the characterization of axioms for classes with strong homomorphisms is being solved.

In this paper, we propose a new and simple method for image encryption. It uses an external secret key of 128 bits long and an internal secret key. The novelties of the proposed encryption process are the methods used to extract an internal key to apply the zigzag process, affine transformation, and substitution-diffusion process. Initially, an original gray-scale image is converted into binary images. An internal secret key is extracted from binary images. The two keys are combined to (...) compute the substitution-diffusion keys. The zigzag process is firstly applied on each binary image. Using an external key, every zigzag binary image is reflected or rotated and a new gray-scale image is reconstructed. The new image is divided into many nonoverlapping subblocks, and each subblock uses its own key to take out a substitution-diffusion process. We tested our algorithms on many biomedical and nonmedical images. It is seen from evaluation metrics that the proposed image encryption scheme provides good statistical and diffusion properties and can resist many kinds of attacks. It is an efficient and secure scheme for real-time encryption and transmission of biomedical images in telemedicine. (shrink)

We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts (...) are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations. (shrink)

We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts (...) are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations. (shrink)

Semi-Post algebras have been introduced and investigated in [6]. This paper is devoted to semi-Post subalgebras and homomorphisms. Characterization of semi-Post subalgebras and homomorphisms, relationships between subalgebras and homomorphisms of semi-Post algebras and of generalized Post algebras are examined.

The paper presents an approach to encrypt the color images using bit-level permutation and alternate logistic map. The proposed method initially segregates the color image into red, green, and blue channels, transposes the segregated channels from the pixel-plane to bit-plane, and scrambles the bit-plane matrix using Arnold cat map (ACM). Finally, the red, blue, and green channels of the scrambled image are confused and diffused by applying alternate logistic map that uses a four-dimensional Lorenz system to generate a pseudorandom number (...) sequence for the three channels. The parameters of ACM are generated with the help of Logistic-Sine map and Logistic-Tent map. The intensity values of scrambled pixels are altered by Tent-Sine map. One-dimensional and two-dimensional logistic maps are used for alternate logistic map implementation. The performance and security parameters histogram, correlation distribution, correlation coefficient, entropy, number of pixel change rate, and unified averaged changed intensity are computed to show the potential of the proposed encryption technique. (shrink)

For given Boolean algebras$\mathbb {A}$and$\mathbb {B}$we endow the space$\mathcal {H}(\mathbb {A},\mathbb {B})$of all Boolean homomorphisms from$\mathbb {A}$to$\mathbb {B}$with various topologies and study convergence properties of sequences in$\mathcal {H}(\mathbb {A},\mathbb {B})$. We are in particular interested in the situation when$\mathbb {B}$is a measure algebra as in this case we obtain a natural tool for studying topological convergence properties of sequences of ultrafilters on$\mathbb {A}$in random extensions of the set-theoretical universe. This appears to have strong connections with Dow and Fremlin’s result stating (...) that there are Efimov spaces in the random model. We also investigate relations between topologies on$\mathcal {H}(\mathbb {A},\mathbb {B})$for a Boolean algebra$\mathbb {B}$carrying a strictly positive measure and convergence properties of sequences of measures on$\mathbb {A}$. (shrink)

Low-dimensional chaotic mappings are simple functions that have low computation cost and are easy to realize, but applying them in a cryptographic algorithm will lead to security vulnerabilities. To overcome this shortcoming, this paper proposes the coupled chaotic system, which coupled the piecewise and Henon mapping. Simulation results indicate that the novel mapping has better complexity and initial sensitivity and larger key space compared with the original mapping. Then, a new color image encryption algorithm is proposed based on the (...) new chaotic mapping. The algorithm has two processes: diffusion and confusion. In this scheme, the key is more than 2 216, and SSIM and PSNR are 0.009675 and 8.6767, respectively. The secret key is applied in the shuffling and diffusion. Security analysis indicates that the proposed scheme can resist cryptanalytic attacks. It has superior performance and has high security. (shrink)

The quotient ℝ/G of the additive group of the reals modulo a countable subgroup G does not admit nontrivial Baire measurable automorphisms.

Should all digital communication be accessible to government inspection? Is robust cryptography in the hands of the public a threat to our national security? With Dorothy Denning and Patrick Sullivan.

Should all digital communication be accessible to government inspection? Is robust cryptography in the hands of the public a threat to our national security? With Dorothy Denning and Patrick Sullivan.

It is known that a countable $\omega $ -categorical structure interprets all finite structures primitively positively if and only if its polymorphism clone maps to the clone of projections on a two-element set via a continuous clone homomorphism. We investigate the relationship between the existence of a clone homomorphism to the projection clone, and the existence of such a homomorphism which is continuous and thus meets the above criterion.

In this paper, we propose a method to design the pseudorandom number generator using three kinds of four-wing memristive hyperchaotic systems with different dimensions as multientropy sources. The principle of this method is to obtain pseudorandom numbers with good randomness by coupling XOR operation on the three kinds of FWMHSs with different dimensions. In order to prove its potential application in secure communication, the security of PRNG based on this scheme is analyzed from the perspective of cryptography. In addition, PRNG (...) has passed the NIST 800.22 and ENT test, which shows that PRNG has good statistical characteristics. Finally, an image encryption algorithm based on PRNG is adopted. In the encryption algorithm, the optimized Arnold matrix scrambling method and the diffusion processing based on XOR are used to obtain the final encrypted image. Through the evaluation of encryption performance, it is concluded that there is no direct relationship between the pristine image and encrypted image. The results show that the proposed image encryption scheme has good statistical output characteristics and security performance in line with cryptography. (shrink)

The lattices of the title generalize the concept of a De Morgan lattice. A representation in terms of ordered topological spaces is described. This topological duality is applied to describe homomorphisms, congruences, and subdirectly irreducible and free lattices in the category. In addition, certain equational subclasses are described in detail.

Personal data is highly vulnerable to security exploits, spurring moves to lock it down through encryption, to cryptographically ‘cloud’ it. But personal data is also highly valuable to corporations and states, triggering moves to unlock its insights by relocating it in the cloud. We characterise this twinned condition as ‘clouded data’. Clouded data constructs a political and technological notion of privacy that operates through the intersection of corporate power, computational resources and the ability to obfuscate, gain insights from and (...) valorise a dependency between public and private. First, we survey prominent clouded data approaches, suggesting their particular affordances produce distinctive versions of privacy. Next, we perform two notional code-based experiments using synthetic datasets. In the field of health, we submit a patient’s blood pressure to a notional cloud-based diagnostics service; in education, we construct a student survey that enables aggregate reporting without individual identification. We argue that these technical affordances legitimate new political claims to capture and commodify personal data. The final section broadens the discussion to consider the political force of clouded data and its reconstitution of traditional notions such as the public and the private. (shrink)

. What is a logic? Which properties are preserved by maps between logics? What is the right notion for equivalence of logics? In order to give satisfactory answers we generalize and further develop the topological approach of [4] and present the foundations of a general theory of abstract logics which is based on the abstract concept of a theory. Each abstract logic determines a topology on the set of theories. We develop a theory of logic maps and show in what (...) way they induce (continuous, open) functions on the corresponding topological spaces. We also establish connections to well-known notions such as translations of logics and the satisfaction axiom of institutions [5]. Logic homomorphisms are maps that behave in some sense like continuous functions and preserve more topological structure than logic maps in general. We introduce the notion of a logic isomorphism as a (not necessarily bijective) function on the sets of formulas that induces a homeomorphism between the respective topological spaces and gives rise to an equivalence relation on abstract logics. Therefore, we propose logic isomorphisms as an adequate and precise notion for equivalence of logics. Finally, we compare this concept with another recent proposal presented in [2]. (shrink)

This paper addresses the always online behavior of the data owner in proxy re- encryption schemes for re-encryption keys issuing. We extend and adapt multi-authority ciphertext policy attribute based encryption techniques to type-based proxy re-encryption to build our solution. As a result, user authentication and user authorization are moved to the cloud server which does not require further interaction with the data owner, data owner and data users identities are hidden from the cloud server, and re- (...) class='Hi'>encryption keys are only issued to legitimate users. An in depth analysis shows that our scheme is secure, flexible and efficient for mobile cloud computing. (shrink)