We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

A novel colour image encryption algorithm based on chaos

This paper proposes a novel confusion and diffusion method for image encryption. One innovation is to confuse the pixels by transforming the nucleotide into its base pair for random times, the other is to generate the new keys according to the plain image and the common keys, which can make the initial conditions of the chaotic maps change automatically in every encryption process. For any size of the original grayscale image, after being permuted the rows and columns respectively by the arrays generated by piecewise linear chaotic map (PWLCM), each pixel of the original image is encoded into four nucleotides by the deoxyribonucleic acid (DNA) coding, then each nucleotide is transformed into its base pair for random time(s) using the complementary rule, the times is generated by Chebyshev maps. Experiment results and security analysis show that the scheme can not only achieve good encryption result, but also the key space is large enough to resist against common attacks.

Image encryption using DNA complementary rule and chaotic maps

A symmetric image encryption algorithm based on mixed linear–nonlinear coupled map lattice

Color image encryption using spatial bit-level permutation and high-dimension chaotic system

Image encryption is somehow different from text encryption due to some inherent features of image such as bulk data capacity and high correlation among pixels, which are generally difficult to handle by conventional methods. The desirable cryptographic properties of the chaotic maps such as sensitivity to initial conditions and random-like behavior have attracted the attention of cryptographers to develop new encryption algorithms. Therefore, recent researches of image encryption algorithms have been increasingly based on chaotic systems, though the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper proposes a Coupled Nonlinear Chaotic Map, called CNCM, and a novel chaos-based image encryption algorithm to encrypt color images by using CNCM. The chaotic cryptography technique which used in this paper is a symmetric key cryptography with a stream cipher structure. In order to increase the security of the proposed algorithm, 240 bit-long secret key is used to generate the initial conditions and parameters of the chaotic map by making some algebraic transformations to the key. These transformations as well as the nonlinearity and coupling structure of the CNCM have enhanced the cryptosystem security. For getting higher security and higher complexity, the current paper employs the image size and color components to cryptosystem, thereby significantly increasing the resistance to known/chosen-plaintext attacks. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.

Color image encryption based on Coupled Nonlinear Chaotic Map

There is an increasing trend in the automotive industry towards integrating trusted third-party apps with In-Vehicle-Infotainment systems (IVI) via smartphones. This integration is typically facilitated by a pair of apps, one that executes on the smartphone and the other executes on the IVI which is connected to the Vehicle's Controller Area Network (CAN) bus. Throughout the evolution of these IVI and App platforms, there has been little public analysis of the security of these protocols and the frameworks that implement these apps on the IVI. This raises the question: to what extent are these apps, protocols and underlining IVI implementations vulnerable to an attacker who might gain control of a driver's smartphone?

In this paper, we focus on gaining insights into this question by performing a comprehensive security analysis on an IVI system that is included in at least one 2015 model vehicle from a major automotive manufacturer. This IVI system included vestigial support for the MirrorLink protocol which is intentionally disabled but can be enabled by updating a single configuration value after applying a publicly available firmware update that is securely signed by the manufacturer. Based on our analysis, we document and demonstrate insecurities in the MirrorLink protocol and IVI implementation that could potentially enable an attacker with control of a driver's smartphone to send malicious messages on the vehicle's internal network.

/pdf/a-security-analysis-of-an-in-vehicle-infotainment-and-app-1wvjmh6vte.pdf

A security analysis of an in vehicle infotainment and app platform

We explore a new security model for secure computation on large datasets. We assume that two servers have been employed to compute on private data that was collected from many users, and, in order to improve the efficiency of their computation, we establish a new tradeoff with privacy. Specifically, instead of claiming that the servers learn nothing about the input values, we claim that what they do learn from the computation preserves the differential privacy of the input. Leveraging this relaxation of the security model allows us to build a protocol that leaks some information in the form of access patterns to memory, while also providing a formal bound on what is learned from the leakage. We then demonstrate that this leakage is useful in a broad class of computations. We show that computations such as histograms, PageRank and matrix factorization, which can be performed in common graph-parallel frameworks such as MapReduce or Pregel, benefit from our relaxation. We implement a protocol for securely executing graph-parallel computations, and evaluate the performance on the three examples just mentioned above. We demonstrate marked improvement over prior implementations for these computations.

https://dl.acm.org/doi/pdf/10.1145/3243734.3243851

Secure Computation with Differentially Private Access Patterns

Image encryption is somehow different from text encryption due to some inherent features of image such as bulk data capacity and high correlation among pixels, which are generally difficult to handle by traditional methods. The exceptionally desirable properties of the chaotic maps such as sensitivity to initial conditions and random-like behavior have attracted the attention of cryptographers to develop new encryption algorithms. This paper proposes a new symmetric image cipher based on the widely used confusion-diffusion architecture which utilizes the chaotic 2D Standard map and 1D Logistic map. It is specifically designed for the color images, which are 3D arrays of data streams. We prefer chaotic Standard map to Baker and Cat maps since the key space of the chaotic Standard map is large enough as compared to the Baker and Cat maps, which makes the brute-force attack infeasible. The initial conditions and system parameters of the chaotic maps constitute the secret key of the algorithm. To further enhance the security, the control parameters used in the confusion stage and the keystream employed for diffusion stage are distinct in different rounds and related to the plain-image. These control parameters are generated by a Tent map. For getting higher security and higher complexity, the current scheme employs two kinds of diffusion processes namely the horizontal and vertical diffusions which are completed by mixing the properties of horizontally and vertically adjacent pixels using a Logistic map, respectively. The results of several experiments, including the most important ones like key space analysis, key sensitivity test, statistical analysis, and visual test by histograms of encrypted images, the correlation coefficients of adjacent pixels, and differential analysis, demonstrate the satisfactory security and efficiency of the proposed image encryption scheme for real-time image encryption and transmission.

Color image cryptosystem using chaotic maps

/pdf/differentially-private-access-patterns-in-secure-computation-3pqs3a7qcp.pdf

Sahar Mazloom

Papers

Color image encryption based on Coupled Nonlinear Chaotic Map

A security analysis of an in vehicle infotainment and app platform

Secure Computation with Differentially Private Access Patterns

Color image cryptosystem using chaotic maps

Differentially Private Access Patterns in Secure Computation.