Power analysis of a chaos-based Random Number Generator for cryptographic security

This paper and its companion (Part II) are devoted to the analysis of the application of a chaotic piecewise-linear one-dimensional (PL1D) map as random number generator (RNG). Piecewise linearity of the map enables us to mathematically find parameter values for which a generating partition is Markov and the RNG behaves as a Markov information source, and then to mathematically analyze the information generation process and the RNG. In the companion paper we discuss practical aspects of our chaos-based RNGs.

A side channel analysis is major threat in secure communication device. Here our object is very clear to protect the sensitive information by adding DNA cryptography with chaotic countermeasure method. To overcome the side channel issues. Due to the side-channel attack can retrieve easily sensitive information from crypto embedded devices. So that the reason we need to protect the sensitive information (encryption key) in crypto embedded devices by applying the random number generation method. Mostly the random number generation used in medical data transmission, information security, and all sensitive areas. So in the research work, we apply a random generation by using the chaotic circuit. And also the paper concentrate to realize the chaotic circuit in hardware using FPGA with partially reconfigurable. And also based on Lorenz’s chaotic circuit used to protect sensitive information. Simulation and Synthesis verification done by using the VIVADO tool. Security analysis is done by hierarchical UACI, NPCR, and correlation.KeywordsSide channel attackFPGAChaotic

Chapter 3 - Random Number Generation

The cryptographic security provided by various techniques of random number generator (RNG) construction is one of the developing research areas today. Among various types of RNG, the true random bit generator (TRBG) can be considered as the most unpredictable and most secure because its randomness seed is generated from chaotic sources. This paper proposes a design of TRBG model based on double-scroll attractors circuits with GST memristor. After implementation and simulation of the chaotic circuit with GST memristor emulator, the chaotic behavior of the output voltage and inductor current were received. Moreover, their dependence on the input voltage revealed the close to double-scroll form. The randomness generated from the proposed circuit was tested by analysis of the Fast Fourier Transform (FFT) and Lyapunov exponents of the output voltage.

This paper presents the FPGA (Field Programmable Gate Array) implementation and the coupling analysis of a metastability-based random number generator (RNG). The metastability is acquired through exploiting transient effect ring oscillators (TEROs) and the random bit generation is accomplished through irregular sampling of regular waveform method. As the proposed RNG is made up of only digital logic gates, it is prototyped on a Xilinx ZedBoard Zynq-7000 evaluation platform. It is demonstrated that the RNG output bitstream satisfies NIST 800-22 statistical tests of randomness without any need for post-processing and the proposed RNG can provide high data throughput. Furthermore, the proposed RNG uses less number of components compared to previously reported TERO based RNGs, thus enabling lower power consumption and smaller footprint. Additionally, the proposed RNG is subjected to correlation based cryptanalysis study. In classical ring oscillator (RO) based RNGs, the ring oscillators are required to be placed at a distance from each other to avoid locking phenomenon that may occur due to coupling between adjacent ROs. This study demonstrates that unlike classical RO based RNGs, the proposed RNG is insensitive to locking phenomenon and TERO structures are not required to be placed way from each other. Therefore, the proposed method lead to a more compact RNG design compared to classical RO based RNGs.

There is a wide range of problems devoted to the possibility of traversing the maze by finite automatons. They can differ as the type of maze (it can be any graph, even infinite), and the automata themselves or their number. In particular, a finite state machine can have a memory (store) or a random bit generator. In the future, we will assume that the robot — is a finite automaton with a random bit generator, unless otherwise stated. In addition, in this system, there can be stones-an object that the finite state machine can carry over the graph, and flags-an object whose presence the finite state machine can only observe. This topic is of interest due to the fact that some of these problems are closely related to problems from probability theory and computational complexity. This paper continues to address some of the open questions posed in Ajans’s thesis: traversal by a robot with a random bit generator of integer spaces in the presence of a stone and a subspace of [4] flags. Such problems help to develop the mathematical apparatus in this area, in addition, in this work we investigate the almost unexplored behavior of a robot with a random number generator. It is extremely important to transfer combinatorial methods developed by A. M. Raigorodsky in the problems of this topic. This work is devoted to the maze traversal by a finite automaton with a random bit generator. This problem is part of the actively developing theme of traversing the maze by various finite automata or their teams, which is closely related to problems from the theory of complexity of calculations and probability theory. In this work it is shown what dimensions a robot with a generator of random bits, and you can get around stone integer space with flag subspace. In this paper, we will study the behavior of a finite automaton with a random bit generator on integer spaces. In particular, it is proved that the robot bypasses Z 2 and cannot bypass Z 3 ; the c ++ robot bypasses Z 4 and cannot bypass Z 5 ; a robot with a stone and a flag bypasses Z 6 and cannot bypass Z 7 ; a robot with a stone and a flag plane bypasses Z 8 and cannot bypass Z 9 .

Much scientific work has focused on the generation of random numbers as well as the distribution of said random numbers for use as a cryptographic key. However, emphasis is often placed on one of the two to the exclusion of the other, but both are often simultaneously important. Here we present a simple hybrid free-space link scheme for both the generation and secure distribution of (pseudo-)random numbers between two remote parties, drawing the randomness from the stochastic nature of atmospheric turbulence. The atmosphere is simulated using digital micro-mirror devices for efficient, all-digital control. After outlining one potential algorithm for extracting random numbers based on finding the centre-of-mass (COM) of turbulent beam intensity profiles, the statistics of our experimental COM measurements is studied and found to agree well with the literature. After implementing the scheme in the laboratory, Alice and Bob are able to establish a string of correlated random bits with an 84% fidelity. Finally, we make a simple modification to the original setup in an attempt to thwart the hacking attempts of an eavesdropper, Eve, who has access to the free-space portion of the link. We find that the fidelity between Eve’s key and that of Alice/Bob is 54%, only slightly above the theoretical minimum. Atmospheric turbulence could hence be leveraged as an added security measure, rather than being seen as a drawback.

Random bit generation (RBG) with chaotic semiconductor lasers has been extensively studied because of its potential applications in secure communications and high-speed numerical simulations. Researchers in this field have mainly focused on the improvement of the generation rate and the compactness of the random bit generators. In this paper, we experimentally demonstrate the existence of two regimes of fast RBG using a single chaotic laser subjected to delayed optical feedback: the first one is based on the extraction of all min-entropy contained in each random sample, and the second one is to demonstrate a possibility of increasing the generation rate by extracting 55 bits from each variable.

A semiconductor laser with distributed feedback from a fiber Bragg grating (FBG) is investigated for random bit generation (RBG). The feedback perturbs the laser to emit chaotically with the intensity being sampled periodically. The samples are then converted into random bits by a simple postprocessing of self-differencing and selecting bits. Unlike a conventional mirror that provides localized feedback, the FBG provides distributed feedback which effectively suppresses the information of the round-trip feedback delay time. Randomness is ensured even when the sampling period is commensurate with the feedback delay between the laser and the grating. Consequently, in RBG, the FBG feedback enables continuous tuning of the output bit rate, reduces the minimum sampling period, and increases the number of bits selected per sample. RBG is experimentally investigated at a sampling period continuously tunable from over 16 ns down to 50 ps, while the feedback delay is fixed at 7.7 ns. By selecting 5 least-significant bits per sample, output bit rates from 0.3 to 100 Gbps are achieved with randomness examined by the National Institute of Standards and Technology test suite.

This paper reports the experimental investigation of two different approaches to random bit generation based on the chaotic dynamics of a semiconductor laser with optical feedback. By computing high-order finite differences of the chaotic laser intensity time series, we obtain time series with symmetric statistical distributions that are more conducive to ultrafast random bit generation. The first approach is guided by information-theoretic considerations and could potentially reach random bit generation rates as high as 160 Gb/s by extracting 4 bits per sample. The second approach is based on pragmatic considerations and could lead to rates of 2.2 Tb/s by extracting 55 bits per sample. The randomness of the bit sequences obtained from the two approaches is tested against three standard randomness tests (ENT, Diehard, and NIST tests), as well as by calculating the statistical bias and the serial correlation coefficients on longer sequences of random bits than those used in the standard tests.

Today, cryptographic security depends primarily on having strong keys and keeping them secret. The keys should be produced by a reliable and robust to external manipulations generators of random numbers. To hamper different attacks, the generators should be implemented in the same chip as a cryptographic system using random numbers. It forces a designer to create a random number generator purely digitally. Unfortunately, the obtained sequences are biased and do not pass many statistical tests. Therefore an output of the random number generator has to be subjected to a transformation called post-processing. In this paper the hash function SHA-256 as post-processing of bits produced by a combined random bit generator using jitter observed in ring oscillators (ROs) is proposed. All components – the random number generator and the SHA-256, are implemented in a single Field Programmable Gate Array (FPGA). We expect that the proposed solution, implemented in the same FPGA together with a cryptographic system, is more attack-resistant owing to many sources of randomness with significantly different nominal frequencies.

A new approach for high-speed physical random bit generation (RBG) based on broadband random optoelectronic oscillator (OEO) is proposed and experimentally demonstrated. In this scheme, a broadband random OEO based on Rayleigh scattering (RS) is employed as the entropy source of RBG. Compared with other broadband random OEOs which require an additional pump source, the optical signal output from the laser in the proposed scheme can realize excited Brillouin scattering as well as acting as an optical carrier. Benefiting from the introduction of randomly distributed feedback by RS, which breaks the limitation of the fixed loop length of the conventional chaotic OEO, the signals generated by the proposed broadband random OEO have random characteristics. Meanwhile, the generated signals exhibit wide and flat frequency spectrum characteristics due to the avoidance of semiconductor chaotic laser relaxation oscillations. The experimental results show the proposed RBG technique can generate physical random bits with a rate of up to 500 Gb/s which can fully pass the NIST test.

The problem of random number generation from an uncorrelated random source (of unknown probability distribution) dates back to von Neumann's 1951 work. Elias (1972) generalized von Neumann's scheme and showed how to achieve optimal efficiency in unbiased random bits generation. Hence, a natural question is what if the sources are correlated? Both Elias and Samuelson proposed methods for generating unbiased random bits in the case of correlated sources (of unknown probability distribution), specifically, they considered finite Markov chains. However, their proposed methods are not efficient or have implementation difficulties. Blum (1986) devised an algorithm for efficiently generating random bits from degree-2 finite Markov chains in expected linear time, however, his beautiful method is still far from optimality on information-efficiency. In this paper, we generalize Blum's algorithm to arbitrary degree finite Markov chains and combine it with Elias's method for efficient generation of unbiased bits. As a result, we provide the first known algorithm that generates unbiased random bits from an arbitrary finite Markov chain, operates in expected linear time and achieves the information-theoretic upper bound on efficiency.

In this paper, we propose a new HW (hardware)-based truly random bit sequence generation method and show its experimental results. The method can be used in a personal computer and ensures the randomness of the obtained bit sequence. We can generate a HW-based truly random bit sequence at high speed based on the realtime clock deviation which is unpredictable. Also, the random bit sequences generated by this method have passed ldquoA Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22)rdquo with appropriate parameters. The proposed random bit sequence generation method can be used in many cryptographic applications.

The additional information (side effects) in Elliptic Curve Cryptography (ECC) hardware can be used to attack cryptographic systems. Additional information related to time, power consumption and electromagnetic radiation. Side channel attacks have been done with SPA (Simple Power Analysis), DPA (Differential Power Analysis), SEMA (Simple Electromagnetic Analysis) and DEMA (Differential Electromagnetic Analysis). Some scalar multiplication algorithm can be used to countermeasure SPA attack on elliptic curve cryptography. In this study, conducted experiments side-channel attacks ECC hardware implementations use binary algorithms by observing power consumption of ECC processor on FPGA. Experimental of side-channel attack is conducted to guess the secret key for data encryption and decryption by looking at the physical differences on hardware side effects. In this study, side-channel attack experimental is successful 100% get the key by analyzing of power consumption ECC processor.