A Random Number Generator Using Ring Oscillators and SHA-256 as Post-Processing

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 Robust Chaos-Based True Random Number Generator Embedded in Reconfigurable Switched-Capacitor Hardware

This paper presents a new chaos-based True Random Number Generator (TRNG) with a decreased voltage supply sensitivity. Contrary to the traditionally used sources of randomness it uses a well-defined deterministic switched-capacitor circuit that exhibits chaos. The whole design is embedded into a commercially available mixed-signal Cypress PSoC reconfigurable device without any external components. The proposed design is optimized for a reduction of influence of the supply voltage to the quality of the generated random bit stream. The influence of circuit non-idealities is significantly reduced by the proposed XOR corrector and optimized circuit topology. The ultimate output bit rate of the proposed TRNG is 60 kbit/s and the quality of generated bit-streams is confirmed by passing standard FIPS and correlation statistical tests performed in the full range of PSoC device supply voltages

Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems

Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, the quantization is inevitable for any digital devices, which causes dynamical degradation. To cope with this problem, many methods were proposed, such as perturbing chaotic states and cascading multiple chaotic systems. This paper aims at developing a novel methodology to design the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite precision. The proposed system is based on the chaos generation strategy controlled by random sequences. It is proven to satisfy the Devaney's definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The application of HDDCS in image encryption is demonstrated via FPGA platform. As each operation of HDDCS is executed in the same fixed precision, no quantization loss occurs. Therefore, it provides a perfect solution to the dynamical degradation of digital chaos.Comment: 12 page

Producing Random Bits with Delay-Line Based Ring Oscillators

One of the sources of randomness for a random bit generator (RBG) is jitter present in rectangular signals produced by ring oscillators (ROs). This paper presents a novel approach for the design of delays used in these oscillators. We suggest using delay elements made on carry4 primitives instead of series of inverters or latches considered in the literature. It enables the construction of many high frequency ring oscillators with different nominal frequencies in the same field programmable gate array (FPGA). To assess the unpredictability of bits produced by RO-based RBG, the restarts mechanism, proposed in earlier papers, was used. The output sequences pass all NIST 800-22 statistical tests for smaller number of ring oscillators than the constructions described in the literature. Due to the number of ROs with different nominal frequencies and the method of construction of carry4 primitives, it is expected that the proposed RBG is more robust to cryptographic attacks than RBGs using inverters or latches as delay element

Random Number Generation Based on Oscillatory Metastability in Ring Circuits

Random number generator designs are discussed, which utilize oscillatory metastability, induced by switching between two stable states of ring-connected digital gates. For a short time after the switch-over the circuits behave quite randomly, influenced by the circuit noise. We provide simple programs, which simulate the fundamental behavior of our circuits. We also present a mathematical model and theoretical explanations of the underlying physical phenomena, the random phase drift and pulse decay. These also illuminate the principles of other recently published random number generators. The feasibility of the designs was confirmed by FPGA prototypes. These random number generators are small, fast and built of standard logic gates. The simplest example contains just one XOR gate as the source of randomness

Метод та програмні засоби генерації випадкових чисел для систем захисту інформації

Дипломний проект присвячено вдосконаленню технологій отримання випадкових величин за допомогою вимірювання фізично випадкових флуктуацій швидкості обер¬тання жорстких магнітних дисків. Розроблені програмні засоби вимірювання цих флуктуацій, проведене експериментальне дослідження розподілу отриманих випадкових величин. Запропоновано метод одержання випадкових чисел з використанням спеціального форматування жорсткого диску. Розроблені та протестовані програмні засоби для практичної реалізації цього методу отримання дійсно реальних чисел.The diploma project is devoted to the improvement of technologies for obtaining random values by measuring physically random fluctuations in the speed of rotation of hard magnetic disks. Software tools for measuring these fluctuations were developed, and an experimental study of the distribution of the obtained random variables was conducted. A method of obtaining random numbers using special hard disk formatting has been presented. Developed and tested software tools for practical implementation of this method of obtaining really real numbers