This paper proposes a (t,n)–threshold verifiable secret sharing scheme with changeable parameters based on a trapdoor one-way function. This scheme consists of a generation phase, a distribution phase, an encoding phase and a reconstruction phase. The generation and distribution phases are, respectively, based on Shamir’s and Feldman’s approaches, while the encoding phase is based on a novel trapdoor one-way function. In the reconstruction phase, the shares and reconstructed secret are validated using a cryptographic hash function. In comparison with existing schemes, the proposed scheme leaks no direct information about the secret from public information. Furthermore, unlike some existing schemes, the generation and distribution phases of the proposed scheme are both independent of the secret. This feature leads to a number of advantages over existing approaches such as the dealer’s ability to perform the following modifications without updating the shares (i) modify the secret and (ii) adjust the threshold parameters of the scheme. Furthermore, each participant receives a single share, and designated participants can be given the privilege of choosing their own shares for reconstructing a secret S. Moreover, the proposed scheme possesses a high level of security which is inherited from the schemes of Shamir and Feldman, in addition to the trapdoor one-way function and the employed cryptographic hash function.

Abstract The idea of employing chaotic maps in building encryption schemes has attracted the attention of many researchers since the late 1980s. In 1998, M.S. Baptista proposed an elegant encryption scheme based on a one–dimensional chaotic map. Many variants of this scheme have been proposed. Baptista's scheme and some of its variants have been subjected to cryptanalytic attacks such as the one‐time pad attack and the entropy attack. We propose a variant of Baptista's encryption scheme based on two coupled one–dimensional chaotic maps, which also employs mixing, that is, every character in the ciphertext depends on all preceding plaintext characters. Our proposed scheme overcomes the aforementioned attacks. Empirical results show that this idea improves the performance of the scheme. Baptista's approach generates a ciphertext, which is generally larger than the plaintext, but the distribution of the ciphertext symbols allows compression. Simulation results verify that our proposed scheme accommodates better compression rates than the original scheme. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a robust blind frequency domain watermarking scheme based on chaotic maps. The proposed scheme embeds a black and white watermark logo in the midband components of a host image according to a discrete wavelet transform. Each watermark bit is embedded into a small submatrix of selected second level subbands of an image resulting from iterated applications of a two-dimensional discrete wavelet transform. This scheme embeds two copies of the watermark using two different methods, in two different subbands of the image. At the cost of embedding capacity, this results in improving the security and robustness of the watermarking scheme. Experimental results demonstrate that the suggested scheme provides imperceptibility and robustness against image processing attacks such as JPEG compression, low-pass filtering, median filtering, Gaussian noise, scaling, rotating, cropping, histogram equalization, and gamma correction. Experimental results also show superior robustness of the suggested scheme over existing algorithms with a similar approach. Copyright © 2013 John Wiley & Sons, Ltd.

SUMMARY In this paper, we suggest a cryptographic protocol for symmetric key exchange based on a set of m commutative square singular matrices of dimension n×n. The suggested scheme provides a concurrent technique for users of symmetric‐key cipher systems to securely exchange their private keys over public channels. This protocol is shown to possess a high level of security based on the algorithm's parameters. We also present a scheme for generating pseudorandom numbers from a single chaotic map for use in various applications, in particular, the suggested key exchange protocol.Copyright © 2011 John Wiley & Sons, Ltd.

The unit distance graph $\mathcal{R}$ is the graph with vertex set $\mathbb{R}^2$ in which two vertices (points in the plane) are adjacent if and only if they are at Euclidean distance 1. We prove that the circular chromatic number of $\mathcal{R}$ is at least 4, thus improving the known lower bound of $32/9$ obtained from the fractional chromatic number of $\mathcal{R}$.