Nonlinear Block Cipher Primitive Using True Random Numbers

Abstract

The protection of confidential information is a worldwide challenge and block encryption algorithms are the most reliable option by which data security is accomplished. The famous information theorist, Claude Shannon has given two desirable characteristics that should exist in a strong cipher which are confusion and diffusion in his fundamental research on "Communication Theory of Secrecy Systems”. Block ciphers strictly follow the confusion and diffusion principle in an iterative manner to generate the ciphertext. The confusion property is used to, make the complex relation between the simple statistics of the ciphertext and the simple description of the key. The diffusion property dissipates the statistical structure of the plaintext that causes redundancy in the ciphertext. The confusion property prevents the cryptanalyst to predict the key from the ciphertext and makes the relationship between the ciphertext and key as complex as possible. Block cipher strength against various attacks relies on its confusion property which is gained through the nonlinear primitive. Responsibility to create a randomized relation among ciphertext and the key as undetectable as possible is also on the nonlinear primitive. In the literature, algebraic structures and chaos-based techniques are extensively used to design the nonlinear primitive of the block cipher. Although both these techniques have favorable characteristics for the design of nonlinear primitive, however researchers have also pointed out various weaknesses and potential attacks which include interpolation attacks, gröbner basis attacks, linear and differential attacks, XL attacks, XSL attacks, SAT solver, dynamical degradation, discontinuity in chaotic sequences, small number of control parameters, finite precision effect and short quantity of randomness. On the other side, randomness is a fundamental feature of nature and an indubitably valuable resource for cryptography. Researchers endorsed the true random numbers for cryptography due to the fact that true random numbers are irreversible, unpredictable, and unreproducible, even if their internal structure and output history are known to the adversaries. Instead of chaotic and algebraic approaches, in this research we proposed three different novel techniques for the construction of nonlinear block cipher primitive by utilizing the nondeterministic strength of nature. The first technique constructs S-boxes using difference-based 2D Maps and true random numbers, generated from the entropy source of schizophrenic patient's EEG. To the best of our knowledge, this nature of research is performed for the first time, in which psychiatric disorder is utilized for the design of any block cipher primitive. The second technique constructs S-boxes using a knight's tour chain and true random numbers, generated from the entropy source of underwater acoustics waves. According to our knowledge, this nature of research is also performed for the first time, in which natural randomness of underwater acoustic waves is used for the construction of nonlinear block cipher primitive. The third technique constructs Sboxes using random walk and true random numbers, generated from the entropy source of lightning strikes. Similarly, this nature of research is also performed for the first time, in which natural randomness of lightning strikes is utilized for the generation of nonlinear block cipher primitive. The biggest advantage of this research is that, the existing attacks and weaknesses of algebraic and chaos-based techniques are not applicable and irrelevant to our proposed techniques, due to the fact that my proposed techniques are purely dependent on true random numbers. The proposed techniques satisfy all standard evaluation tests of nonlinear block cipher primitive construction and true random numbers generation. For the comparative analysis, the proposed S-boxes are compared with more than sixty-five state-of-the-art S-boxes (2020 to 2022) and the results show that the strength of our proposed S-boxes is equal to or better than state-of-the-art S-boxes. More than seven million true random bits have been analyzed using the NIST randomness test suite, and the results showed that my proposed physical and psychological entropy sources are outstanding resources for true random number generation. Also in this research, a Systematic Literature Review (SLR) was conducted to study which metaheuristic optimization technique is most endorsed in the current decade for the optimization of Sboxes. Based on the SLR recommendation, a technique is also presented for the optimization of TRNG based S-boxes using a Genetic Algorithm. This research opens up new avenues in cryptographic primitive design through the fusion of computing, natural science, neuroscience, and mathematics.