Browsing by Subject "Information security"

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Open Access
An unrestricted Arnold’s cat map transformation
(Springer New York LLC, 2024-02-06) Turan, Mehmet; Gökçay, Erhan; Tora, Hakan
The Arnold's Cat Map (ACM) is one of the chaotic transformations, which is utilized by numerous scrambling and encryption algorithms in Information Security. Traditionally, the ACM is used in image scrambling whereby repeated application of the ACM matrix, any image can be scrambled. The transformation obtained by the ACM matrix is periodic; therefore, the original image can be reconstructed using the scrambled image whenever the elements of the matrix, hence the key, is known. The transformation matrices in all the chaotic maps employing ACM has limitations on the choice of the free parameters which generally require the area-preserving property of the matrix used in transformation, that is, the determinant of the transformation matrix to be +/- 1.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm 1.$$\end{document} This reduces the number of possible set of keys which leads to discovering the ACM matrix in encryption algorithms using the brute-force method. Additionally, the period obtained is small which also causes the faster discovery of the original image by repeated application of the matrix. These two parameters are important in a brute-force attack to find out the original image from a scrambled one. The objective of the present study is to increase the key space of the ACM matrix, hence increase the security of the scrambling process and make a brute-force attack more difficult. It is proved mathematically that area-preserving property of the traditional matrix is not required for the matrix to be used in scrambling process. Removing the restriction enlarges the maximum possible key space and, in many cases, increases the period as well. Additionally, it is supplied experimentally that, in scrambling images, the new ACM matrix is equivalent or better compared to the traditional one with longer periods. Consequently, the encryption techniques with ACM become more robust compared to the traditional ones. The new ACM matrix is compatible with all algorithms that utilized the original matrix. In this novel contribution, we proved that the traditional enforcement of the determinant of the ACM matrix to be one is redundant and can be removed.
Open Access
Privacy-preserving protocols for aggregate location queries via homomorphic encryption and multiparty computation
(2019-07) Eryonucu, Cihan
Two main goals of the businesses are to serve their customers better and in the meantime, increase their pro t. One of the ways that businesses can improve their services is using location information of their customers (e.g., positioning their facilities with an objective to minimize the average distance of their customers to their closest facilities). However, without the customer's location data, it is impossible for businesses to achieve such goals. Luckily, in today's world, large amounts of location data is collected by service providers such as telecommunication operators or mobile apps such as Swarm. Service providers are willing to share their data with businesses, doing this will violate the privacy of their customers. Here, we propose two new privacy-preserving schemes for businesses to utilize location data of their customers that is collected by location-based service providers (LBSPs). We utilize lattice based homomorphic encryption and multiparty computation for our new schemes and then we compare them with our existing scheme which is based on partial homomorphic encryption. In our protocols, we hide customer lists of businesses from LBSPs, locations of the customers from the businesses, and query result from LBSPs. In such a setting, we let the businesses send location-based queries to the LBSPs. In addition, we make the query result only available to the businesses and hide them from the LBSPs. We evaluate our proposed schemes to show that they are practical. We then compare our three protocols, discussing each one's advantages and disadvantages and give use cases for all protocols. Our proposed schemes allow data sharing in a private manner and create the foundation for the future complex queries.