On Entropy and Bit Patterns of Ring Oscillator Jitter

Thermal jitter (phase noise) from a free-running ring oscillator is a common, easily implementable physical randomness source in True Random Number Generators (TRNGs). We show how to evaluate entropy, autocorrelation, and bit pattern distributions of ring oscillator noise sources, even with low jitter levels or some bias. Entropy justification is required in NIST 800-90B and AIS-31 testing and for applications such as the RISC-V entropy source extension. Our numerical evaluation algorithms outperform Monte Carlo simulations in speed and accuracy. We also propose a new lower bound estimation formula for the entropy of ring oscillator sources which applies more generally than previous ones.Comment: 6 page

Performance analysis of random number generator based on breakdown diode noise

Generatorji naključnih števil igrajo pomembno vlogo pri zagotavljanju varnosti podatkov. Omogočajo večjo varnost podatkov uporabnikov na spletu, uporabljajo se v mnogih industrijskih aplikacijah, medicini, vojski, policiji, igrah na srečo in drugje. V diplomskem delu opišemo osnovne tipe generatorjev naključnih števil. Možen izvor naključnosti predstavlja šum elektronskih elementov, v delu se osredotočimo na generator naključnih števil na osnovi šuma prebojnih diod. Za analizo stopnje naključnosti naredimo poenostavljeni model vezja in izpeljemo analitično enačbo za določitev entropije generatorja. Na koncu opišemo kako lahko zagotovimo višjo entropijo, ne da bi pri tem spremenili vezje.Random numbers generators play an important role in data security. They are used for bigger security of users online, in many industrial applications, in medical, military and police facilities, they are being used in gambling and elsewhere. In this thesis we describe basic types of random numbers generators and possible source of randomness as noise of electrical components. In this thesis we focus on random numbers generators with principle of avalanche diode. For analysis of randomness we make a simplified circuit model and derive an analytical formula for entropy of simplified circuit. In the end, we describe how we can ensure a higher entropy, without changing the circuit

A Design for a Physical RNG with Robust Entropy Estimators

We briefly address general aspects that reliable security evaluations of physical RNGs should consider. Then we discuss an efficient RNG design that is based on a pair of noisy diodes. The main contribution of this paper is the formulation and the analysis of the corresponding stochastic model which interestingly also fits to other RNG designs. We prove a theorem that provides tight lower bounds for the entropy per random bit, and we apply our results to a prototype of a particular physical RNG

Grained integers and applications to cryptography

To meet the requirements of the modern communication society, cryptographic techniques are of central importance. In modern cryptography, we try to build cryptographic primitives, whose security can be reduced to solving a particular number theoretic problem for which no fast algorithmic method is known by now. Thus, any advance in the understanding of the nature of such problems indirectly gives insight in the analysis of some of the most practical cryptographic techniques. In this work we analyze exactly this aspect much more deeply: How can we use some of the purely theoretical results in number theory to answer very practical questions on the security of widely used cryptographic algorithms and how can we use such results in concrete implementations? While trying to answer these kinds of security-related questions, we always think two-fold: From a cryptographic, security-ensuring perspective and from a cryptanalytic one. After we outlined -- with a special focus on the historical development of these results -- the necessary analytic and algorithmic foundations of number theory, we first delve into the question how point addition on certain elliptic curves can be done efficiently. The resulting formulas have their application in the cryptanalysis of crypto systems that are insecure if factoring integers can be done efficiently. The rest of the thesis is devoted to the study of integers, all of whose prime factors are neither too small nor too large. We show with the help of two applications how one can use the properties of such kinds of integers to answer very practical questions in the design and the analysis of cryptographic primitives: The optimization of a hardware-realization of the cofactorization step of the General Number Field Sieve and the analysis of different standardized key-generation algorithms