True-Randomness and Pseudo-Randomness in Ring Oscillator-Based True Random Number Generators

The paper deals with true random number generators employing oscillator rings, namely, with the one proposed by Sunar et al. in 2007 and enhanced by Wold and Tan in 2009. Our mathematical analysis shows that both architectures behave identically when composed of the same number of rings and ideal logic components. However, the reduction of the number of rings, as proposed by Wold and Tan, would inevitably cause the loss of entropy. Unfortunately, this entropy insufficiency is masked by the pseudo-randomness caused by XOR-ing clock signals having different frequencies. Our simulation model shows that the generator, using more than 18 ideal jitter-free rings having slightly different frequencies and producing only pseudo-randomness, will let the statistical tests pass. We conclude that a smaller number of rings reduce the security if the entropy reduction is not taken into account in post-processing. Moreover, the designer cannot avoid that some of rings will have the same frequency, which will cause another loss of entropy. In order to confirm this, we show how the attacker can reach a state where over 25% of the rings are locked and thus completely dependent. This effect can have disastrous consequences on the system security.

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Time-Adaptive Statistical Test for Random Number Generators

Entropy ◽

10.3390/e22060630 ◽

2020 ◽

Vol 22 (6) ◽

pp. 630 ◽

Cited By ~ 1

Author(s):

Boris Ryabko

Keyword(s):

Random Number ◽

Statistical Tests ◽

Asymptotic Properties ◽

Test Sequence ◽

P Value ◽

Specific Test ◽

Random Number Generators ◽

P Values ◽

Small Deviations ◽

The One

The problem of constructing effective statistical tests for random number generators (RNG) is considered. Currently, there are hundreds of RNG statistical tests that are often combined into so-called batteries, each containing from a dozen to more than one hundred tests. When a battery test is used, it is applied to a sequence generated by the RNG, and the calculation time is determined by the length of the sequence and the number of tests. Generally speaking, the longer is the sequence, the smaller are the deviations from randomness that can be found by a specific test. Thus, when a battery is applied, on the one hand, the “better” are the tests in the battery, the more chances there are to reject a “bad” RNG. On the other hand, the larger is the battery, the less time it can spend on each test and, therefore, the shorter is the test sequence. In turn, this reduces the ability to find small deviations from randomness. To reduce this trade-off, we propose an adaptive way to use batteries (and other sets) of tests, which requires less time but, in a certain sense, preserves the power of the original battery. We call this method time-adaptive battery of tests. The suggested method is based on the theorem which describes asymptotic properties of the so-called p-values of tests. Namely, the theorem claims that, if the RNG can be modeled by a stationary ergodic source, the value − l o g π ( x 1 x 2 … x n ) / n goes to 1 − h when n grows, where x 1 x 2 … is the sequence, π ( ) is the p-value of the most powerful test, and h is the limit Shannon entropy of the source.

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A New Statistical Test for PRNG Based on the Attendance’s Law

Journal of Advances in Mathematics and Computer Science ◽

10.9734/jamcs/2021/v36i130328 ◽

2021 ◽

pp. 37-46

Author(s):

Babacar Alasane Ndaw ◽

Ousmane Ndiaye ◽

Mamadou Sanghar´e ◽

Cheikh Thi´ecoumba Gueye

Keyword(s):

Random Number ◽

Statistical Tests ◽

Random Number Generator ◽

Deterministic Algorithm ◽

Statistical Test ◽

The Other ◽

Cryptographic Primitives ◽

Random Number Generators ◽

Other Hand ◽

The One

One family of the cryptographic primitives is random Number Generators (RNG) which have several applications in cryptography such that password generation, nonce generation, Initialisation vector for Stream Cipher, keystream. Recently they are also used to randomise encryption and signature schemes. A pseudo-random number generator (PRNG) or a pseudo-random bit generator (PRBG) is a deterministic algorithm that produces numbers whose distribution is on the one hand indistinguishable from uniform ie. that the probabilities of appearance of the different symbols are equal and that these appearances are all independent. On the other hand, the next output of a PRNG must be unpredictable from all its previous outputs. Indeed, A set of statistical tests for randomness has been proposed in the literature and by NIST to evaluate the security of random(pseudo) bit or block. Unfortunately there are non-random binary streams that pass these standardized tests. In this pap er, as outcome, we intro duce on the one hand a new statistical test in a static contextcalled attendance’s law and on the other hand a distinguisher based on this new attendance’s law.

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An overview of hybrid random number generators

Scientific Bulletin of Naval Academy ◽

10.21279/1454-864x-20-i1-034 ◽

2020 ◽

Vol XXIII (1) ◽

pp. 248-252

Author(s):

Veronica Cornaciu

Keyword(s):

Detailed Analysis ◽

Random Number ◽

Statistical Tests ◽

Random Numbers ◽

Random Number Generators ◽

Pseudo Random Number ◽

First Category ◽

Mouse Movement ◽

The One ◽

Special Category

The generation of random numbers is a important topic in cryptography. Random number generators are bradly divided into two categories: random number generators(RNGs) and pseudo-random number generators(PRNGs). If the PRNGs werw intensively studied in the specialized literature, many such generators being built and analyzed, the topic of RNGs did not capture the researchers atention so much. Candidates in this first category generate nondeterministic sequences and are often based on physical reactions, such as radioactive degradation or mouse movement. A special category of generators is the one that combines the two categories, namely, the category of hybrid generators (HRGs). The purpose of this paper is to study in detail the category of hybrid generators and to provide a detailed analysis of the results of statistical tests, security , portability and how to improve some of the generators of this category.

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Design and Analysis of Configurable Ring Oscillators for True Random Number Generation Based on Coherent Sampling

ACM Transactions on Reconfigurable Technology and Systems ◽

10.1145/3433166 ◽

2021 ◽

Vol 14 (2) ◽

pp. 1-20

Author(s):

Adriaan Peetermans ◽

Vladimir Rožić ◽

Ingrid Verbauwhede

Keyword(s):

Random Number ◽

Statistical Tests ◽

Random Number Generation ◽

Ring Oscillator ◽

Security Requirements ◽

Random Number Generators ◽

High Entropy ◽

Field Programmable ◽

Automatic Placement ◽

Easy Integration

True Random Number Generators (TRNGs) are indispensable in modern cryptosystems. Unfortunately, to guarantee high entropy of the generated numbers, many TRNG designs require a complex implementation procedure, often involving manual placement and routing. In this work, we introduce, analyse, and compare three dynamic calibration mechanisms for the COherent Sampling ring Oscillator based TRNG: GateVar , WireVar , and LUTVar , enabling easy integration of the entropy source into complex systems. The TRNG setup procedure automatically selects a configuration that guarantees the security requirements. In the experiments, we show that two out of the three proposed mechanisms are capable of assuring correct TRNG operation even when an automatic placement is carried out and when the design is ported to another Field-Programmable Gate Array (FPGA) family. We generated random bits on both a Xilinx Spartan 7 and a Microsemi SmartFusion2 implementation that, without post processing, passed the AIS-31 statistical tests at a throughput of 4.65 Mbit/s and 1.47 Mbit/s, respectively.

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True Random Number Generator Based on Wake-Up Ring Oscillator Utilizing Post-Processing Optimization to Generate Random Bit Sequence

2020 2nd International Conference on Industrial Electrical and Electronics (ICIEE) ◽

10.1109/iciee49813.2020.9277075 ◽

2020 ◽

Author(s):

Anang Adi Permana ◽

Aprilia Kusuma Dewi ◽

Magfirawaty Magfirawaty

Keyword(s):

Random Number ◽

Random Number Generator ◽

Ring Oscillator ◽

Number Generator ◽

Post Processing ◽

True Random Number Generator ◽

Processing Optimization

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Enhancing the operational efficiency of quantum random number generators

Infocommunications journal ◽

10.36244/icj.2021.2.2 ◽

2021 ◽

Vol 13 (2) ◽

pp. 10-18

Author(s):

Botond L. Márton ◽

Dóra Istenes ◽

László Bacsárdi

Keyword(s):

Random Number ◽

Statistical Tests ◽

Practical Implementation ◽

Random Numbers ◽

Random Number Generators ◽

Original Source ◽

Negative Effect ◽

Quantum Phenomena ◽

The Right

Random numbers are of vital importance in today’s world and used for example in many cryptographical protocols to secure the communication over the internet. The generators producing these numbers are Pseudo Random Number Generators (PRNGs) or True Random Number Generators (TRNGs). A subclass of TRNGs are the Quantum based Random Number Generators (QRNGs) whose generation processes are based on quantum phenomena. However, the achievable quality of the numbers generated from a practical implementation can differ from the theoretically possible. To ease this negative effect post-processing can be used, which contains the use of extractors. They extract as much entropy as possible from the original source and produce a new output with better properties. The quality and the different properties of a given output can be measured with the help of statistical tests. In our work we examined the effect of different extractors on two QRNG outputs and found that witg the right extractor we can improve their quality.

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SRAM Based Random Number Generator for Non-Repeating Pattern Generation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.573.181 ◽

2014 ◽

Vol 573 ◽

pp. 181-186 ◽

Cited By ~ 3

Author(s):

G.P. Ramesh ◽

A. Rajan

Keyword(s):

Random Number ◽

Statistical Tests ◽

Random Number Generator ◽

Random Number Generation ◽

Pattern Generation ◽

Storage Device ◽

Number Generator ◽

Random Number Generators ◽

Field Programmable ◽

The Look

—Field-programmable gate array (FPGA) optimized random number generators (RNGs) are more resource-efficient than software-optimized RNGs because they can take advantage of bitwise operations and FPGA-specific features. A random number generator (RNG) is a computational or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e. appear random. The many applications of randomness have led to the development of several different methods for generating random data. Several computational methods for random number generation exist, but often fall short of the goal of true randomness though they may meet, with varying success, some of the statistical tests for randomness intended to measure how unpredictable their results are (that is, to what degree their patterns are discernible).LUT-SR Family of Uniform Random Number Generators are able to handle randomness only based on seeds that is loaded in the look up table. To make random generation efficient, we propose new approach based on SRAM storage device.Keywords: RNG, LFSR, SRAM

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Delay-Based True Random Number Generator in Sub-Nanomillimeter IoT Devices

Electronics ◽

10.3390/electronics9050817 ◽

2020 ◽

Vol 9 (5) ◽

pp. 817

Author(s):

Maulana Randa ◽

Mohammad Samie ◽

Ian K. Jennions

Keyword(s):

Random Number ◽

Promising Result ◽

Physical Phenomenon ◽

Random Number Generator ◽

Ring Oscillator ◽

Random Number Generators ◽

Propagation Delays ◽

Field Programmable ◽

Iot Devices ◽

Non Gaussian

True Random Number Generators (TRNGs) use physical phenomenon as their source of randomness. In electronics, one of the most popular structures to build a TRNG is constructed based on the circuits that form propagation delays, such as a ring oscillator, shift register, and routing paths. This type of TRNG has been well-researched within the current technology of electronics. However, in the future, where electronics will use sub-nano millimeter (nm) technology, the components become smaller and work on near-threshold voltage (NTV). This condition has an effect on the timing-critical circuit, as the distribution of the process variation becomes non-gaussian. Therefore, there is an urge to assess the behavior of the current delay-based TRNG system in sub-nm technology. In this paper, a model of TRNG implementation in sub-nm technology was created through the use of a specific Look-Up Table (LUT) in the Field-Programmable Gate Array (FPGA), known as SRL16E. The characterization of the TRNG was presented and it shows a promising result, in that the delay-based TRNG will work properly, with some constraints in sub-nm technology.

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