Random Number Generation
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Sensor-Seeded Cryptographically Secure Random Number Generation
International Journal of Recent Technology and Engineering (IJRTE) ISSN: 2277-3878, Volume-8 Issue-3, September 2019 Sensor-Seeded Cryptographically Secure Random Number Generation K.Sathya, J.Premalatha, Vani Rajasekar Abstract: Random numbers are essential to generate secret keys, AES can be executed in various modes like Cipher initialization vector, one-time pads, sequence number for packets Block Chaining (CBC), Cipher Feedback (CFB), Output in network and many other applications. Though there are many Feedback (OFB), and Counter (CTR). Pseudo Random Number Generators available they are not suitable for highly secure applications that require high quality randomness. This paper proposes a cryptographically secure II. PRNG IMPLEMENTATIONS pseudorandom number generator with its entropy source from PRNG requires the seed value to be fed to a sensor housed on mobile devices. The sensor data are processed deterministic algorithm. Many deterministic algorithms are in 3-step approach to generate random sequence which in turn proposed, some of widely used algorithms are fed to Advanced Encryption Standard algorithm as random key to generate cryptographically secure random numbers. Blum-Blum-Shub algorithm uses where X0 is seed value and M =pq, p and q are prime. Keywords: Sensor-based random number, cryptographically Linear congruential Generator uses secure, AES, 3-step approach, random key where is the seed value. Mersenne Prime Twister uses range of , I. INTRODUCTION where that outputs sequence of 32-bit random Information security algorithms aim to ensure the numbers. confidentiality, integrity and availability of data that is transmitted along the path from sender to receiver. All the III. SENSOR-SEEDED PRNG security mechanisms like encryption, hashing, signature rely Some of PRNGs uses clock pulse of computer system on random numbers in generating secret keys, one time as seeds. -
Lecture 8: Key Derivation, Protecting Passwords, Slow Hashes, Merkle Trees
Lecture 8: Key derivation, protecting passwords, slow hashes, Merkle trees Boaz Barak Last lecture we saw the notion of cryptographic hash functions which are functions that behave like a random function, even in settings (unlike that of standard PRFs) where the adversary has access to the key that allows them to evaluate the hash function. Hash functions have found a variety of uses in cryptography, and in this lecture we survey some of their other applications. In some of these cases, we only need the relatively mild and well-defined property of collision resistance while in others we only know how to analyze security under the stronger (and not precisely well defined) random oracle heuristic. Keys from passwords We have seen great cryptographic tools, including PRFs, MACs, and CCA secure encryptions, that Alice and Bob can use when they share a cryptographic key of 128 bits or so. But unfortunately, many of the current users of cryptography are humans which, generally speaking, have extremely faulty memory capacity for storing large numbers. There are 628 ≈ 248 ways to select a password of 8 upper and lower case letters + numbers, but some letter/numbers combinations end up being chosen much more frequently than others. Due to several large scale hacks, very large databases of passwords have been made public, and one estimate is that the most frequent 10, 000 ≈ 214 passwords account for more than 90% of the passwords chosen. If we choose a password at random from some set D then the entropy of the password is simply log |D|. Estimating the entropy of real life passwords is rather difficult. -
A Secure Authentication System- Using Enhanced One Time Pad Technique
IJCSNS International Journal of Computer Science and Network Security, VOL.11 No.2, February 2011 11 A Secure Authentication System- Using Enhanced One Time Pad Technique Raman Kumar1, Roma Jindal 2, Abhinav Gupta3, Sagar Bhalla4 and Harshit Arora 5 1,2,3,4,5 Department of Computer Science and Engineering, 1,2,3,4,5 D A V Institute of Engineering and Technology, Jalandhar, Punjab, India. Summary the various weaknesses associated with a password have With the upcoming technologies available for hacking, there is a come to surface. It is always possible for people other than need to provide users with a secure environment that protect their the authenticated user to posses its knowledge at the same resources against unauthorized access by enforcing control time. Password thefts can and do happen on a regular basis, mechanisms. To counteract the increasing threat, enhanced one so there is a need to protect them. Rather than using some time pad technique has been introduced. It generally random set of alphabets and special characters as the encapsulates the enhanced one time pad based protocol and provides client a completely unique and secured authentication passwords we need something new and something tool to work on. This paper however proposes a hypothesis unconventional to ensure safety. At the same time we need regarding the use of enhanced one time pad based protocol and is to make sure that it is easy to be remembered by you as a comprehensive study on the subject of using enhanced one time well as difficult enough to be hacked by someone else. -
A Note on Random Number Generation
A note on random number generation Christophe Dutang and Diethelm Wuertz September 2009 1 1 INTRODUCTION 2 \Nothing in Nature is random. number generation. By \random numbers", we a thing appears random only through mean random variates of the uniform U(0; 1) the incompleteness of our knowledge." distribution. More complex distributions can Spinoza, Ethics I1. be generated with uniform variates and rejection or inversion methods. Pseudo random number generation aims to seem random whereas quasi random number generation aims to be determin- istic but well equidistributed. 1 Introduction Those familiars with algorithms such as linear congruential generation, Mersenne-Twister type algorithms, and low discrepancy sequences should Random simulation has long been a very popular go directly to the next section. and well studied field of mathematics. There exists a wide range of applications in biology, finance, insurance, physics and many others. So 2.1 Pseudo random generation simulations of random numbers are crucial. In this note, we describe the most random number algorithms At the beginning of the nineties, there was no state-of-the-art algorithms to generate pseudo Let us recall the only things, that are truly ran- random numbers. And the article of Park & dom, are the measurement of physical phenomena Miller (1988) entitled Random generators: good such as thermal noises of semiconductor chips or ones are hard to find is a clear proof. radioactive sources2. Despite this fact, most users thought the rand The only way to simulate some randomness function they used was good, because of a short on computers are carried out by deterministic period and a term to term dependence. -
Pseudorandomness and Computational Difficulty
PSEUDORANDOMNESS AND COMPUTATIONAL DIFFICULTY RESEARCH THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF SCIENCE HUGO KRAWCZYK SUBMITTED TOTHE SENATEOFTHE TECHNION —ISRAEL INSTITUTE OF TECHNOLOGY SHVAT 5750 HAIFAFEBRUARY 1990 Amis padres, AurorayBernardo, aquienes debo mi camino. ALeonor,compan˜era inseparable. ALiat, dulzuraycontinuidad. This research was carried out in the Computer Science Department under the supervision of Pro- fessor Oded Goldreich. To Oded, my deep gratitude for being both teacher and friend. Forthe innumerable hoursofstimulating conversations. Forhis invaluable encouragement and support. Iamgrateful to all the people who have contributed to this research and given me their support and help throughout these years. Special thanks to Benny Chor,Shafi Goldwasser,Eyal Kushilevitz, Jacob Ukel- son and Avi Wigderson. ToMikeLuby thanks for his collaboration in the work presented in chapter 2. Ialso wish to thank the Wolf Foundation for their generous financial support. Finally,thanks to Leonor,without whom all this would not have been possible. Table of Contents Abstract ............................. 1 1. Introduction ........................... 3 1.1 Sufficient Conditions for the Existence of Pseudorandom Generators ........ 4 1.2 The Existence of Sparse Pseudorandom Distributions . ............ 5 1.3 The Predictability of Congruential Generators ............... 6 1.4 The Composition of Zero-Knowledge Interactive-Proofs . ........... 8 2. On the Existence of Pseudorandom Generators ............... 10 2.1. Introduction .......................... 10 2.2. The Construction of Pseudorandom Generators .............. 13 2.3. Applications: Pseudorandom Generators based on Particular Intractability Assump- tions . ............................ 22 3. Sparse Pseudorandom Distributions ................... 25 3.1. Introduction .......................... 25 3.2. Preliminaries ......................... 25 3.3. The Existence of Sparse Pseudorandom Ensembles ............. 27 3.4. -
Cryptanalysis of the Random Number Generator of the Windows Operating System
Cryptanalysis of the Random Number Generator of the Windows Operating System Leo Dorrendorf School of Engineering and Computer Science The Hebrew University of Jerusalem 91904 Jerusalem, Israel [email protected] Zvi Gutterman Benny Pinkas¤ School of Engineering and Computer Science Department of Computer Science The Hebrew University of Jerusalem University of Haifa 91904 Jerusalem, Israel 31905 Haifa, Israel [email protected] [email protected] November 4, 2007 Abstract The pseudo-random number generator (PRNG) used by the Windows operating system is the most commonly used PRNG. The pseudo-randomness of the output of this generator is crucial for the security of almost any application running in Windows. Nevertheless, its exact algorithm was never published. We examined the binary code of a distribution of Windows 2000, which is still the second most popular operating system after Windows XP. (This investigation was done without any help from Microsoft.) We reconstructed, for the ¯rst time, the algorithm used by the pseudo- random number generator (namely, the function CryptGenRandom). We analyzed the security of the algorithm and found a non-trivial attack: given the internal state of the generator, the previous state can be computed in O(223) work (this is an attack on the forward-security of the generator, an O(1) attack on backward security is trivial). The attack on forward-security demonstrates that the design of the generator is flawed, since it is well known how to prevent such attacks. We also analyzed the way in which the generator is run by the operating system, and found that it ampli¯es the e®ect of the attacks: The generator is run in user mode rather than in kernel mode, and therefore it is easy to access its state even without administrator privileges. -
Random Number Generation Using MSP430™ Mcus (Rev. A)
Application Report SLAA338A–October 2006–Revised May 2018 Random Number Generation Using MSP430™ MCUs ......................................................................................................................... MSP430Applications ABSTRACT Many applications require the generation of random numbers. These random numbers are useful for applications such as communication protocols, cryptography, and device individualization. Generating random numbers often requires the use of expensive dedicated hardware. Using the two independent clocks available on the MSP430F2xx family of devices, software can generate random numbers without such hardware. Source files for the software described in this application report can be downloaded from http://www.ti.com/lit/zip/slaa338. Contents 1 Introduction ................................................................................................................... 1 2 Setup .......................................................................................................................... 1 3 Adding Randomness ........................................................................................................ 2 4 Usage ......................................................................................................................... 2 5 Overview ...................................................................................................................... 2 6 Testing for Randomness................................................................................................... -
A Mathematical Formulation of the Monte Carlo Method∗
A Mathematical formulation of the Monte Carlo method∗ Hiroshi SUGITA Department of Mathematics, Graduate School of Science, Osaka University 1 Introduction Although admitting that the Monte Carlo method has been producing practical results in many fields, a number of researchers have the following serious suspicion about it. The Monte Carlo method needs random numbers. But since no computer program can generate them, we execute a Monte Carlo method using a pseu- dorandom number generated by a computer program. Of course, such an expedient can never have any mathematical justification. As a matter of fact, this suspicion is a misunderstanding caused by prejudice. In this article, we propose a proper mathematical formulation of the Monte Carlo method, which resolves this suspicion. The mathematical definitions of the notions of random number and pseudorandom number have been known for quite some time. Indeed, the notion of random number was defined in terms of computational complexity by Kolmogorov and others in 1960’s ([3, 4, 6]), while the notion of pseudorandom number was defined in the context of cryptography by Blum and others in 1980’s ([1, 2, 14]). But unfortunately, those definitions have been thought to be useless until now in understanding and executing the Monte Carlo method. It is not because their definitions are improper, but because our way of thinking about the Monte Carlo method has been improper. In this article, we propose a mathematical formulation of the Monte Carlo method which is based on and theoretically compatible with those definitions of random number and pseudorandom number. Under our formulation, as a result, we see the following. -
Measures of Pseudorandomness
Katalin Gyarmati Measures of Pseudorandomness Abstract: In the second half of the 1990s Christian Mauduit and András Sárközy [86] introduced a new quantitative theory of pseudorandomness of binary sequences. Since then numerous papers have been written on this subject and the original theory has been generalized in several directions. Here I give a survey of some of the most important results involving the new quantitative pseudorandom measures of finite bi- nary sequences. This area has strong connections to finite fields, in particular, some of the best known constructions are defined using characters of finite fields and their pseudorandom measures are estimated via character sums. Keywords: Pseudorandomness, Well Distribution, Correlation, Normality 2010 Mathematics Subject Classifications: 11K45 Katalin Gyarmati: Department of Algebra and Number Theory, Eötvös Loránd University, Budapest, Hungary, e-mail: [email protected] 1Introduction In the twentieth and twenty-first centuries various pseudorandom objects have been studied in cryptography and number theory since these objects are widely used in modern cryptography, in applications of the Monte Carlo method and in wireless communication (see [39]). Different approaches and definitions of pseudorandom- ness can be found in several papers and books. Menezes, Oorschot and Vanstone [95] have written an excellent monograph about these approaches. The most frequent- ly used interpretation of pseudorandomness is based on complexity theory; Gold- wasser [38] has written a survey paper about this approach. However, recently the complexity theory approach has been widely criticized. One problem is that in this approach usually infinite sequences are tested while in the applications only finite sequences are used. Another problem is that most results are based on certain un- proved hypotheses (such as the difficulty of factorization of integers). -
(Pseudo) Random Number Generation for Cryptography
Thèse de Doctorat présentée à L’ÉCOLE POLYTECHNIQUE pour obtenir le titre de DOCTEUR EN SCIENCES Spécialité Informatique soutenue le 18 mai 2009 par Andrea Röck Quantifying Studies of (Pseudo) Random Number Generation for Cryptography. Jury Rapporteurs Thierry Berger Université de Limoges, France Andrew Klapper University of Kentucky, USA Directeur de Thèse Nicolas Sendrier INRIA Paris-Rocquencourt, équipe-projet SECRET, France Examinateurs Philippe Flajolet INRIA Paris-Rocquencourt, équipe-projet ALGORITHMS, France Peter Hellekalek Universität Salzburg, Austria Philippe Jacquet École Polytechnique, France Kaisa Nyberg Helsinki University of Technology, Finland Acknowledgement It would not have been possible to finish this PhD thesis without the help of many people. First, I would like to thank Prof. Peter Hellekalek for introducing me to the very rich topic of cryptography. Next, I express my gratitude towards Nicolas Sendrier for being my supervisor during my PhD at Inria Paris-Rocquencourt. He gave me an interesting topic to start, encouraged me to extend my research to the subject of stream ciphers and supported me in all my decisions. A special thanks also to Cédric Lauradoux who pushed me when it was necessary. I’m very grateful to Anne Canteaut, which had always an open ear for my questions about stream ciphers or any other topic. The valuable discussions with Philippe Flajolet about the analysis of random functions are greatly appreciated. Especially, I want to express my gratitude towards my two reviewers, Thierry Berger and Andrew Klapper, which gave me precious comments and remarks. I’m grateful to Kaisa Nyberg for joining my jury and for receiving me next year in Helsinki. -
Pseudorandomness
~ MathDefs ~ CS 127: Cryptography / Boaz Barak Pseudorandomness Reading: Katz-Lindell Section 3.3, Boneh-Shoup Chapter 3 The nature of randomness has troubled philosophers, scientists, statisticians and laypeople for many years.1 Over the years people have given different answers to the question of what does it mean for data to be random, and what is the nature of probability. The movements of the planets initially looked random and arbitrary, but then the early astronomers managed to find order and make some predictions on them. Similarly we have made great advances in predicting the weather, and probably will continue to do so in the future. So, while these days it seems as if the event of whether or not it will rain a week from today is random, we could imagine that in some future we will be able to perfectly predict it. Even the canonical notion of a random experiment- tossing a coin - turns out that it might not be as random as you’d think, with about a 51% chance that the second toss will have the same result as the first one. (Though see also this experiment.) It is conceivable that at some point someone would discover some function F that given the first 100 coin tosses by any given person can predict the value of the 101th.2 Note that in all these examples, the physics underlying the event, whether it’s the planets’ movement, the weather, or coin tosses, did not change but only our powers to predict them. So to a large extent, randomness is a function of the observer, or in other words If a quantity is hard to compute, it might as well be random. -
Random-Number Functions
Title stata.com Random-number functions Contents Functions Remarks and examples Methods and formulas Acknowledgments References Also see Contents rbeta(a,b) beta(a,b) random variates, where a and b are the beta distribution shape parameters rbinomial(n,p) binomial(n,p) random variates, where n is the number of trials and p is the success probability rcauchy(a,b) Cauchy(a,b) random variates, where a is the location parameter and b is the scale parameter rchi2(df) χ2, with df degrees of freedom, random variates rexponential(b) exponential random variates with scale b rgamma(a,b) gamma(a,b) random variates, where a is the gamma shape parameter and b is the scale parameter rhypergeometric(N,K,n) hypergeometric random variates rigaussian(m,a) inverse Gaussian random variates with mean m and shape param- eter a rlaplace(m,b) Laplace(m,b) random variates with mean m and scale parameter b p rlogistic() logistic variates with mean 0 and standard deviation π= 3 p rlogistic(s) logistic variates with mean 0, scale s, and standard deviation sπ= 3 rlogistic(m,s) logisticp variates with mean m, scale s, and standard deviation sπ= 3 rnbinomial(n,p) negative binomial random variates rnormal() standard normal (Gaussian) random variates, that is, variates from a normal distribution with a mean of 0 and a standard deviation of 1 rnormal(m) normal(m,1) (Gaussian) random variates, where m is the mean and the standard deviation is 1 rnormal(m,s) normal(m,s) (Gaussian) random variates, where m is the mean and s is the standard deviation rpoisson(m) Poisson(m)