DIEHARD Test Suites Research Articles

A High-Performance FPGA PRNG Based on Multiple Deep-Dynamic Transformations.

Pseudo-random number generators (PRNGs) are important cornerstones of many fields, such as statistical analysis and cryptography, and the need for PRNGs for information security (in fields such as blockchain, big data, and artificial intelligence) is becoming increasingly prominent, resulting in a steadily growing demand for high-speed, high-quality random number generators. To meet this demand, the multiple deep-dynamic transformation (MDDT) algorithm is innovatively developed. This algorithm is incorporated into the skewed tent map, endowing it with more complex dynamical properties. The improved one-dimensional discrete chaotic mapping method is effectively realized on a field-programmable gate array (FPGA), specifically the Xilinx xc7k325tffg900-2 model. The proposed pseudo-random number generator (PRNG) successfully passes all evaluations of the National Institute of Standards and Technology (NIST) SP800-22, diehard, and TestU01 test suites. Additional experimental results show that the PRNG, possessing high novelty performance, operates efficiently at a clock frequency of 150 MHz, achieving a maximum throughput of 14.4 Gbps. This performance not only surpasses that of most related studies but also makes it exceptionally suitable for embedded applications.

Implementation of TRNG with SHA-3 for hardware security

Random Number Generators (RNGs) are the solution for cryptographic applications to enhance hardware security. These RNGs ought to have three specific properties unpredictability, aperiodic, and good statistical criteria. This brief presents a True Random Number Generator (TRNG) based on Ring oscillators' jitter with MLFSR. The MLFSR is augmented with a set of prime primitive polynomials, Boolean, and non-linear functions to attain a non-linear, unpredictable, and extended sequence period. Paper mainly focused on achieving high randomness by integrated the TRNG with a new promising crypto engine Keccak as a post-processing block; leads to extensively more security in data transfer, encryption keys, data authenticity of ICs, and IoT based applications. The RNG design is coded in Verilog HDL and implemented on the FPGA Zed board. Hashing is performed with a throughput of 2.4Gbps at 100 MHz either with RNG data or SHA data. Evaluated the randomness of the generated non-deterministic bitstreams (10 Mb) using the NIST 800–22 & Diehard test suite and successfully passed.

IESCA: An efficient image encryption scheme using 2-D cellular automata

In the present era of Information Technology (IT), transfer of multimedia data is happening at a rapid pace. In many Internet-of-Things (IoT) based applications, sensor devices are sending information in the form of images. However, if the IoT applications are used in the information sensitive sectors like defense, healthcare, etc., the images must be encrypted before sending to the gateway fog nodes. Again, traditional encryption algorithms will not work in such scenarios due to the resource constraint nature of IoT devices. Here, Cellular Automata (CA) plays an important role. In this paper, a new secure and efficient image encryption technique is proposed using 2-D Moore Cellular Automata (MCA), called as IESCA which is lossless and easy to implement in hardware. Cellular Automata can generate random and chaotic sequence much faster than the existing chaotic sequence generators. It uses local transformations based on one bit state values of each of its neighbors. It makes CA implementation very easy and less resource consuming. Moreover, considering Moore convention has increased the key space more than the existing CA based image ciphering techniques. The randomness of the cipher images are evaluated using DIEHARD and NIST statistical test suites. Additionally, several security and performance analyses of the IESCA have proved its robustness and resistance against security attacks. Experimental results of the IESCA show its efficiency when compared to the existing encryption techniques. The proposed scheme has achieved 2.76% improvement in terms of execution time when compared with the state-of-the-arts. Moreover, the proposed scheme has achieved 5.02% improvement in terms of NPCR and 7.69% improvement in terms of UACI values when compared with the existing schemes.

IEVCA: An efficient image encryption technique for IoT applications using 2-D Von-Neumann cellular automata

Present era is marked by exponential growth in transfer of multimedia data through internet. Most of the Internet-of-Things(IoT) applications send images to cloud storages through internet. However, in sensitive applications such as healthcare, defense, etc., these images should be encrypted before transmission through insecure public channels to gateway fog nodes. Conventional encryption algorithms cannot be used there due to the resource constraint characters of IoT devices. Here, Cellular Automata (CA) based encryption algorithms can be used because of their inherent simplicity in implementation in hardware, without affecting the capability of generating highly random sequences. In this paper, a lightweight, robust and secure image encryption technique has been proposed using 2-D Von-Neumann Cellular Automata (VCA), called IEVCA, which is lossless, correlation immune and has all the essential properties of a good image cipher. Additionally, the proposed technique passes all the randomness tests of DIEHARD and NIST statistical test suites. Moreover, several security and performance analyses of the IEVCA proved its efficiency and resistance against security attacks. Experimental results of the IEVCA show its better performance when compared to the existing encryption techniques.

A hybrid algorithm for robust image steganography

In this work, a novel hybrid algorithm has been developed for achieving imperceptible and robust image steganography for secure data communication. The novelty of the work lies in the careful manipulation of higher frequency coefficient of Discrete Cosine Transform (DCT) to maintain the perceptual quality of the image followed by embedding secret bits in the controlled DCT coefficients using random locations identified by deterministic Coupled Chaotic Map (CCM). The randomness of the CCM map is confirmed by National Institute of Standards and Technology, DIEHARD, ENT and TestU01 test suites. The experimental results demonstrate that the proposed technique has excellent stego-image quality keeping zero Bit Error Rate at maximum embedding capacity (EC). The proposed method has capability to withstand against malicious users as well as outperforms existing steganography techniques in terms of EC, and Peak Signal to Noise Ratio. The security of the proposed technique is subsequently examined by the key length, key sensitivity parameter and histogram analysis.

Design of a Hybrid Programmable 2-D Cellular Automata Based Pseudo Random Number Generator

This paper proposes a hybrid programmable two-dimensional Cellular Automata (CA) based pseudo-random number generator which includes a newly designed rule set. The properties and evolution of one and two dimensional CA are revisited. The various metrics for evaluating CA as a Pseudo-Random Number Generator (PRNG) are discussed. It is proved that the randomness is high irrespective of the initial seed by applying this newly designed rule set. The PRNG is tested against a popular statistical test called Diehard test suite and the results show that the PRNG is highly random. The chaotic measures like entropy, hamming distance and cycle length have been measured

IECA: an efficient IoT friendly image encryption technique using programmable cellular automata

Digital images play a vital role in multimedia communications in the modern era. With the advent of internet-of-things (IoT) applications, multimedia transfers are happening at a rapid pace. However, providing security to these data is essential if the data is sensitive. It is a challenging task in case of IoT applications due to the limitations of the sensors in terms of memory and computational efficiency. Therefore, conventional ciphers cannot be applied in the IoT devices. However, cellular automata (CA) can be used in this resource-constrained environment for providing security to the IoT devices, as it is inherently capable of creating complex patterns and pseudo-random sequences. It is also easy to implement in hardware. In this work, an IoT friendly programmable cellular automata (PCA) based block cipher called IECA is proposed. Further, randomness in the generated cipher-image has been tested using various statistical testings present in NIST test suite and DIEHARD test suite. The test results show that IECA generates high degree of randomness in the produced cipher-image. In addition to this, correlation, entropy and differential analysis of the proposed scheme justifies the robustness against different types of attacks. Experimental results show the efficiency of IECA as compared to the existing block ciphers.

A blind and robust color images watermarking method based on block transform and secured by modified 3-dimensional Hénon map

This paper proposes a blind and robust color image watermarking method based on a new three-dimensional Henon chaotic map and uses integer wavelet transform, discrete wavelet transform and contourlet transform in embedding and extracting processes. In the presented approach, color images are divided into $$4\times 4$$ main nonoverlapping parts, and one of the transforms is applied to these parts. Then the low–low sub-band of transform is selected. The suggested map is used to find $$2\times 2$$ blocks in the embedding process. The bits of watermark are embedded in the parts of images to increase the robustness of the proposed watermarking scheme. To improve the quality of the final watermark, the suggested technique uses a correction process in the extracting process. In this paper, the bifurcation diagram, Lyapunov exponent, cobweb plot and trajectory diagram are used to show the chaotic behavior of the proposed map. Based on DIEHARD, ENT and NIST test suites, the suggested map can be used as a pseudo-random number generator. The simulation results show that the proposed watermarking algorithm is robust against most image processing attacks like salt & pepper, cropping, low-pass filter, wiener filter, blurring, etc. The comparison results between the suggested watermarking scheme, and some similar methods show that the presented technique has good performance, imperceptibility, acceptable robustness and outperforms most related methods.

Feistel-inspired scrambling improves the quality of linear congruential generators

Abstract Generating pseudorandom numbers is a prerequisite for many areas including Monte Carlo simulation and randomized algorithms. The performance of pseudorandom number generators (PRNGs) depends on the quality of the generated random sequences. They must be generated quickly and have good statistical properties. Several statistical test suites have been developed to evaluate a single stream of random numbers such as those from the TestU01 library, the DIEHARD test suite, the tests from the SPRNG package, and a set of tests designed to evaluate bit sequences developed at NIST. This paper presents a new pseudorandom number generation scheme that produces pseudorandom sequences with good statistical properties via a scrambling procedure motivated by cryptographic transformations. We will specifically apply this to a popular set of PRNGs called the Linear Congruential generators (LGCs). The scrambling technique is based on a simplified version of a Feistel network. The proposed method seeks to improve the quality of the LCGs output stream. We show that this Feistel-inspired scrambling technique breaks up the regularities that are known to exist in LCGs. The Feistel-inspired scrambling technique is modular, and can be applied to any 64-bit PRNG, and so we believe that it can serve as an inexpensive model for a scrambler that can be used with most PRNGs via post-processing.

Analysis of Elementary Cellular Automata Chaotic Rules Behavior

We present detailed and in depth analysis of Elementary Cellular Automata (ECA) with periodic cylindrical configuration. The focus is to determine whether Cellular Automata (CA) is suitable for the generation of pseudo random number sequences (PRNs) of cryptographic strength. Additionally, we identify the rules that are most suitable for such applications. It is found that only two sub-clusters of the chaotic rule space are actually capable of producing viable PRNs. Furthermore, these two sub-clusters consist of two majorly non-linear rules. Each sub-cluster of rules is derived from a cluster leader rule by reflection or negation or the combined two transformations. It is shown that the members of each subcluster share the same dynamical behavior. Results of testing the ECA running under these rules for comprehensively large number of lattice lengths using the Diehard Test suite have shown that apart from some anomaly, the whole output sequence can be potentially utilized for cryptographic strength pseudo random sequence generation with sufficiently large number of p-values pass rates.

AN IMPROVED VIRTUAL 3D CA PRNG BASED ON MOORE NEIGHBORHOOD METHOD

The security of most of the cryptosystems depend on the secret key generator. However, implementation for hardwares, of this key generator is inefficient because secret key generators depend on mathematical problem to generate the high randomness quality. Cellular automata (CA) pseudorandom number generator (PRNG) is more efficiently implemented rather than mathematical problem based PRNGs because a structure of CA PRNG is highly regular and simpler than the other PRNGs. In this paper, a virtual three-dimension (3D) CA PRNG based on the Moore neighborhood structure is proposed. The proposed PRNG uses new methods which are the rule numbering function that provides a high-quality randomness and cell position function that diminishes correlations between global states. In order to evaluate the quality of randomness, the ENT and DIEHARD test suites are used. The results of these tests show that the quality of randomness is superior to previous PRNGs.

PSEUDO RANDOM NUMBER GENERATOR BASED ON SYNCHRONIZED CHAOTIC MAPS

In this paper, a hierarchy of coupled maps in synchronized state is introduced. Then some discussions about the individual properties of these chaotic maps are presented, from a dynamical systems viewpoint. Also, one of these chaotic map is used as a Nonlinear Pseudo Random Generator (NPRNG). This paper addresses the chaotic features of this map which are useful for generating nonlinear pseudo random numbers. Results of the analysis and extensive tests such as the NIST, DIEHARD and ENT test suites indicate that the NPRNG exhibits good statistical randomness properties.

LAYERED CELLULAR AUTOMATA FOR PSEUDORANDOM NUMBER GENERATION

The proposed Layered Cellular Automata (L-LCA), which comprises of a main CA with L additional layers of memory registers, has simple local interconnections and high operating speed. The time-varying L-LCA transformation at each clock can be reduced to a single transformation in the set {Af | f = 1, 2, …, 2n -1} formed by the transformation matrix A of a maximum length Cellular Automata (CA), and the entire transformation sequence for a single period can be obtained. The analysis for the period characteristics of state sequences is simplified by analyzing representative transformation sequences determined by the phase difference between the initial states for each layer. The L-LCA model can be extended by adding more layers of memory or through the use of a larger main CA based on widely available maximum length CA. Several L-LCA (L = 1, 2, 3, 4) with 10- to 48-bit main CA are subjected to the DIEHARD test suite and better results are obtained over other CA designs reported in the literature. The experiments are repeated using the well-known nonlinear functions f30 and f45 in place of the linear function f204 used in the L-LCA. Linear complexity is significantly increased when f30 or f45 is used.

High performance physical random number generator

A field programmable gate array (FPGA) -based implementation of a physical random number generator (PRNG) is presented. The PRNG uses an alternating step generator construction to decorrelate an oscillator-phase-noise-based physical random source. The resulting design can be implemented completely in digital technology, requires no external components, is very small in area, achieves very high throughput and has good statistical properties. The PRNG was implemented on an FPGA device and tested using the NIST, Diehard and TestU01 random number test suites.

A feedback strategy to improve the entropy of a chaos-based random bit generator

In this paper, the guidelines to design a true random bit generator (TRBG) circuit with a predefined minimum entropy are discussed. The approach is proposed for a TRBG based on a one-dimensional piecewise-linear chaotic map; it does not require bit throughput reduction, and it is suitable for the development of integrated TRBG circuits. In particular, the proposed design strategy is based on a feedback control procedure that allows to dynamically change the system parameters for the correction of the circuit nonidealities (e.g., the circuit offsets). The correction algorithm does not require a direct measurement of the system nonidealities or of the effective value of the map parameters, but only a dynamic estimation of these quantities based on the observation of the TRBG output. The design approach is validated by a hardware prototype implemented on a field-programmable analog array. The results of the NIST FIPS 140-2 test suite, the DIEHARD test suite, and the Coron's Universal test, applied to the TRBG output sequences before and after a simple post processing without throughput reduction, are reported and discussed.

Random number generators and causality

We advance a prescription to randomize physical or algorithmic Random Number Generators (RNG's) that do not pass Marsaglia's DIEHARD test suite and discuss a special physical quantifier, based on an intensive statistical complexity measure, that is able to adequately assess the improvements produced thereby. Eight RNG's are evaluated and the associated results are compared to those obtained by recourse to Marsaglia's DIEHARD test suite. Our quantifier, which is evaluated using causality arguments, can forecast whether a given RNG will pass the above mentioned test.

True Random Bit Generation From a Double-Scroll Attractor

In this paper, a novel true random bit generator (TRBG) based on a double-scroll attractor is proposed. The double-scroll attractor is obtained from a simple model which is qualitatively similar to Chua's circuit. In order to face the challenge of using the proposed TRBG in cryptography, the proposed TRBG is subjected to statistical tests which are the well-known Federal Information Processing Standards-140-1 and Diehard test suite in the area of cryptography. The proposed TRBG successfully passes all these tests and can be implemented in integrated circuits.

Evolvable characteristic-based pseudo random number generation

We have recently succeeded in developing genetic algorithm (GA)-based random number generators (RNG) by encoding generators in genomes that manifest themselves as combinations of basic mathematical operators and randomized seeds/parameters. The combination of operators and parameters are “optimized” by selecting the “most fit” algorithm as measured by our GA's objective function (a metrized version of the Federal Information Protection Standard 140-1 (FIPS) statistical tests). Moreover, offline testing (with Marsaglia's Diehard test suite) shows that our characteristic-based RNGs perform well.

A FAMILY OF CONTROLLABLE CELLULAR AUTOMATA FOR PSEUDORANDOM NUMBER GENERATION

In this paper, we present a family of novel Pseudorandom Number Generators (PRNGs) based on Controllable Cellular Automata (CCA) CCA0, CCA1, CCA2 (NCA), CCA3 (BCA), CCA4 (asymmetric NCA), CCA5, CCA6 and CCA7 PRNGs. The ENT and DIEHARD test suites are used to evaluate the randomness of these CCA PRNGs. The results show that their randomness is better than that of conventional CA and PCA PRNGs while they do not lose the structure simplicity of 1D CA. Moreover, their randomness can be comparable to that of 2D CA PRNGs. Furthermore, we integrate six different types of CCA PRNGs to form CCA PRNG groups to see if the randomness quality of such groups could exceed that of any individual CCA PRNG. Genetic Algorithm (GA) is used to evolve the configuration of the CCA PRNG groups. Randomness test results on the evolved CCA PRNG groups show that the randomness of the evolved groups is further improved as compared with any individual CCA PRNG.