scholarly journals Function Composition from Sine Function and Skew Tent Map and Its Application to Pseudorandom Number Generators

2021 ◽  
Vol 11 (13) ◽  
pp. 5769
Author(s):  
Leonardo Palacios-Luengas ◽  
Ricardo Marcelín-Jiménez ◽  
Enrique Rodriguez-Colina ◽  
Michael Pascoe-Chalke ◽  
Omar Jiménez-Ramírez ◽  
...  
Keyword(s):  
Linear Complexity ◽  
Initial Conditions ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Sine Function ◽  
Pseudorandom Sequences ◽  
Function Composition ◽  
Tent Map ◽  
Skew Tent Map ◽  
Key Space

In cryptography, the pseudorandom number sequences must have random appearance to be used in secure information systems. The skew tent map (STM) is an attractive map to produce pseudorandom sequences due to its easy implementation and the absence of stability islands when it is in chaotic behavior. Using the STM and sine function, we propose and analyze a function composition to propose a pseudorandom number generator (PRNG). In the analysis of the function composition, we use the bifurcation diagram and the Lyapunov exponent to perform a behavioral comparison against the STM. We show that the proposed function composition is more sensitive to initial conditions than the STM, and then it is a better option than the STM for cryptography applications. For the proposed function we determine and avoid the chaos annulling traps. The proposed PRNG can be configured to generate pseudorandom numbers of 8, 16 or 32 bits and it can be implemented on microcontrollers with different architectures. We evaluate the pseudorandomness of the proposed PRNG using the NIST SP 800-22 and TestU01 suites. Additionally, to evaluate its quality, we apply tests such as correlation coefficient, key sensitivity, statistical and entropy analysis, key space, linear complexity, and speed. Finally, we performed a comparison with similar PRNGs that produce pseudorandom sequences considering numbers of 8 and 32 bits. The results show that the proposed PRNG maintains its security regardless of the selected configuration. The proposed PRNG has five important features: easy implementation, configurable to produce number with 8, 16 or 32 bits, high processing speed, high linear complexity, and wide key space. These features are necessary for cryptographic systems.

scholarly journals A 1 Gbps Chaos-Based Stream Cipher Implemented in 0.18 μm CMOS Technology

Electronics ◽  
2019 ◽  
Vol 8 (6) ◽  
pp. 623 ◽  
Author(s):  
Miguel Garcia-Bosque ◽  
Guillermo Díez-Señorans ◽  
Adrián Pérez-Resa ◽  
Carlos Sánchez-Azqueta ◽  
Concepción Aldea ◽  
...  
Keyword(s):  
Stream Cipher ◽  
Complementary Metal Oxide Semiconductor ◽  
Cmos Technology ◽  
Oxide Semiconductor ◽  
Linear Feedback ◽  
Tent Map ◽  
Skew Tent Map ◽  
Key Space ◽  
Key Sensitivity ◽  
Randomness Tests

In this work, a novel chaos-based stream cipher based on a skew tent map is proposed and implemented in a 0.18 μm CMOS (Complementary Metal-Oxide-Semiconductor) technology. The proposed ciphering algorithm uses a linear feedback shift register that perturbs the orbits generated by the skew tent map after each iteration. This way, the randomness of the generated sequences is considerably improved. The implemented stream cipher was capable of achieving encryption speeds of 1 Gbps by using an approximate area of ~ 20 , 000 2-NAND equivalent gates, with a power consumption of 24.1 mW. To test the security of the proposed cipher, the generated keystreams were subjected to National Institute of Standards and Technology (NIST) randomness tests, proving that they were undistinguishable from truly random sequences. Finally, other security aspects such as the key sensitivity, key space size, and security against reconstruction attacks were studied, proving that the stream cipher is secure.

scholarly journals Simple method of selecting totalistic rules for pseudorandom number generator based on nonuniform cellular automaton

2021 ◽  
Author(s):  
Miroslaw Szaban
Keyword(s):  
Cellular Automaton ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Large Set ◽  
Number Generator ◽  
Pseudorandom Sequences ◽  
Simple Method ◽  
One Dimensional ◽  
Simple Selection ◽  
Selection Of

AbstractThis paper is devoted to selecting rules for one-dimensional (1D) totalistic cellular automaton (TCA). These rules are used for the generation of pseudorandom sequences, which could be useful in cryptography. The power of pseudorandom number generator (PRNG) based on nonuniform TCA can be improved using not only one rule but a large set of rules. For this purpose, each subset of rules should be analyzed with its assignation to cellular automaton (CA) cells should be analyzed. We examine each of the subsets of totalistic rules, consisting of rules with neighborhood radius equal to 1 and 2. The entropy of bitstreams generated by the nonuniform TCA points out the best set of rules appropriate for the TCA-based generator. The paper also presents the method of simple selection of CA rules based on a cryptographic criterion known as a balance. The proposed method selects a maximal size of the set of available CA rules for a given neighborhood radius and suitable for PRNG. The method guarantees to avoid conflicting assignments of rules resulting in the creation of unwanted stable bit sequences, and provides high-quality pseudorandom sequences. This technique is used to verify the subsets of rules selected experimentally. Verified rules are proposed for 1D TCA-based PRNG as a new subset of best nonuniform TCA rules. New picked, examined, and verified subset of rules could be used in TCA-based PRNG and provide cryptographically strong bit sequences and huge keyspace.

scholarly journals Beyond Statistical Analysis in Chaos-Based CSPRNG Design

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
John Prakash Arockiasamy ◽  
Lydia Elizabeth Benjamin ◽  
Rhymend Uthariaraj Vaidyanathan
Keyword(s):  
Statistical Analysis ◽  
Statistical Tests ◽  
Security Analysis ◽  
Statistical Testing ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Number Generator ◽  
Pseudorandom Sequences ◽  
Randomness Test ◽  
Modern Cryptography

The design of cryptographically secure pseudorandom number generator (CSPRNG) producing unpredictable pseudorandom sequences robustly and credibly has been a nontrivial task. Almost all the chaos-based CSPRNG design approaches invariably depend only on statistical analysis. Such schemes designed to be secure are being proven to be predictable and insecure day by day. This paper proposes a design and instantiation approach to chaos-based CSPRNG using proven generic constructions of modern cryptography. The proposed design approach with proper instantiation of such generic constructions eventually results in providing best of both worlds that is the provable security guarantees of modern cryptography and passing of necessary statistical tests as that of chaos-based schemes. Also, we introduce a new coupled map lattice based on logistic-sine map for the construction of CSPRNG. The proposed pseudorandom number generator is proven using rigorous security analysis as that of modern cryptography and tested using the standard statistical testing suites. It is observed that the generated sequences pass all stringent statistical tests such as NIST, Dieharder, ENT, and TestU01 randomness test suites.

scholarly journals High Throughput Pseudorandom Number Generator Based on Variable Argument Unified Hyperchaos

VLSI Design ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Kaiyu Wang ◽  
Qingxin Yan ◽  
Shihua Yu ◽  
Xianwei Qi ◽  
Yudi Zhou ◽  
...  
Keyword(s):  
High Throughput ◽  
Standard Test ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Hyperchaotic System ◽  
Number Generator ◽  
Maximum Throughput ◽  
Verilog Hdl ◽  
Pseudorandom Sequences ◽  
Different Chaotic Systems

This paper presents a new multioutput and high throughput pseudorandom number generator. The scheme is to make the homogenized Logistic chaotic sequence as unified hyperchaotic system parameter. So the unified hyperchaos can transfer in different chaotic systems and the output can be more complex with the changing of homogenized Logistic chaotic output. Through processing the unified hyperchaotic 4-way outputs, the output will be extended to 26 channels. In addition, the generated pseudorandom sequences have all passed NIST SP800-22 standard test and DIEHARD test. The system is designed in Verilog HDL and experimentally verified on a Xilinx Spartan 6 FPGA for a maximum throughput of 16.91 Gbits/s for the native chaotic output and 13.49 Gbits/s for the resulting pseudorandom number generators.

scholarly journals Encryption of pseudorandom number generator logic circuits

2021 ◽  
Vol 190 ◽  
pp. 370-376
Author(s):  
Mikhail Ivanov ◽  
Iliya Chugunkov ◽  
Bogdana Kliuchnikova ◽  
Evgenii Salikov
Keyword(s):  
Logic Circuits ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Number Generator

Pseudorandom Number Generators Based on Chaotic Dynamical Systems

2001 ◽  
Vol 08 (02) ◽  
pp. 137-146 ◽  
Author(s):  
Janusz Szczepański ◽  
Zbigniew Kotulski
Keyword(s):  
Dynamical Systems ◽  
Communication Systems ◽  
Initial Conditions ◽  
Pseudorandom Number ◽  
New Approach ◽  
Chaotic Dynamical Systems ◽  
Pseudorandom Number Generators ◽  
Transmission Of Information ◽  
Extreme Sensitivity ◽  
Contemporary Technology

Pseudorandom number generators are used in many areas of contemporary technology such as modern communication systems and engineering applications. In recent years a new approach to secure transmission of information based on the application of the theory of chaotic dynamical systems has been developed. In this paper we present a method of generating pseudorandom numbers applying discrete chaotic dynamical systems. The idea of construction of chaotic pseudorandom number generators (CPRNG) intrinsically exploits the property of extreme sensitivity of trajectories to small changes of initial conditions, since the generated bits are associated with trajectories in an appropriate way. To ensure good statistical properties of the CPRBG (which determine its quality) we assume that the dynamical systems used are also ergodic or preferably mixing. Finally, since chaotic systems often appear in realistic physical situations, we suggest a physical model of CPRNG.

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