> stream In this laboratory, for this lab you are required to design an 8-bit pseudo-random number generator. Hardware based random-number generators can involve the use of a dice, a coin for flipping, or many other devices. secrets, such as encryption keys. /BBox [0 0 100 100] stream /Subtype /Form for Monte Carlo simulation) /Subtype /Form endstream A pseudo-random number generation algorithm starts with a value called a seed value. Generate "next" random value 1.3. /Filter /FlateDecode x���P(�� �� You will then modify your button debounce timer to include a stretch timer. /Filter /FlateDecode Although sequences that are closer to truly … %PDF-1.5 9 0 obj Most computers do not have the ability to produce a genuinely random number, but there are methods for creating numbers that are apparently random, or pseudo-random.For programming assignment 3 (part 2) you made use of a pseudo-random number generator from the Cinnameg … /BBox [0 0 100 100] /Filter /FlateDecode 29 0 obj /Type /XObject In C++ (and C), the functions needed from cstdlib are rand () and srand () srand () is used to seed the random number generator (and only needs to … Sometimes it is useful for a computer to produce a random number. 31 0 obj A Pseudo-Random Number Generator (PRNG) uses the same seed each time the product is initialized. The sequence of numbers produced by randi is determined by the internal settings of the uniform pseudorandom number generator that underlies rand, randi, and randn. /Type /XObject /Subtype /Form /Filter /FlateDecode /Length 15 /Length 15 /FormType 1 /Filter /FlateDecode /Subtype /Form Developers need to know how to >> /Length 2178 lS��\�J��q���n��l�ڛM�-+��T�|K9�0���ԕ-���jxF���� ǂ�Ԛδ�s�L)P�y�������׭1DڳrCLju�j�M�X5ۭiW��CL9�����]әN�! Listing 1: ”Generating a 128-bit encryption key” #include #include #include #define KEYSIZE 16. The arrays returned by randi might contain repeated integer values. /Subtype /Form /Subtype /Form /Type /XObject x���P(�� �� /Matrix [1 0 0 1 0 0] /Resources 10 0 R /BBox [0 0 100 100] /BBox [0 0 100 100] x���P(�� �� stream /Length 15 mistakes have been made in some well-known products, including 23 0 obj stream endobj /Resources 32 0 R endstream Choose a value of R of runs to perform and also choose R different seeds to provide for the generation of pseudo-random numbers. Most computers do not have the ability to produce a genuinely random number, but there are methods for creating numbers that are apparently random, or pseudo-random.For programming assignment 3 you made use of a pseudo-random number generator class called Random from the … "Discard" also known as "jumpahead" to skip the generatorahead by 'n' samples. /Resources 18 0 R If the results of a Pseudo Random Number Generator mimicking dice rolls /Filter /FlateDecode << (����H͚���9ۢ7-���e��m6vi�$���� ;�mVl�;�g�L�C]��������*�r���ں���|��>R�jeM�b��h�r$�~�f���$H�Dd2�� 3�����P�#JEQ�3. C Pseudo-Random Number Generation. /BBox [0 0 100 100] endobj /Matrix [1 0 0 1 0 0] In order to create a RSA ket, you first need to learn how to create a random number. /Matrix [1 0 0 1 0 0] PRNGs generate a sequence of numbers approximating the properties of random numbers. To create a (pseudo) random integer in the range [0,n) you can use the Random class: int randIndex, n; Random gen = new Random(); randIndex = gen.nextInt(n); Random gen = new Random() creates a new random number generator gen. The particular kind of pseudo-random number generator used in DumbCrypt is called a linear congruential generator. /Type /XObject Features: 1. /Length 15 Pseudo Random Number Generator(PRNG) refers to an algorithm that uses mathematical formulas to produce sequences of random numbers. True Random Number Generator. ��4c� ��;�i��'��>�\Ok�%B'�)�qWM�|w������r�i�\,����&����?__ǁ�"�� endobj The pseudo-random number generator. /FormType 1 /Length 15 >> stream /Length 15 /Resources 12 0 R The values are the same as before. Codes generated by a LFSR are actually "pseudo" random, because after some time the numbers repeat. to generate the random numbers for security purpose. You can control that shared random number generator using rng. random number generation method is not appropriate for generating This lab demonstrates Task 1,3,4 from Random Numbers as well as task 1-3 from RSA. x���P(�� �� << We will focus on random numbers in the range 1 to 31 only. /Matrix [1 0 0 1 0 0] /Resources 5 0 R /Subtype /Form Pseudo Random Number Generators cannot truly recreate random events such a dice rolls. /Length 15 Many generators have some "bad" state values that mustbe avoided. /Length 15 Supervised situation (e.g. endobj Let us see the behavior of /dev/urandom. endstream Generating random numbers may sound like a fairly simple task, but if you think about it and actually try to implement a method for it you will quickly notice that it is a … x���P(�� �� /Type /XObject /Matrix [1 0 0 1 0 0] VM version: This lab has been tested on our pre-built SEEDUbuntu16.04 VM. /Resources 8 0 R Safe seeding. TCP Attack Lab Sniffing and Spoofing Lab Encryption Lab Local DNS Attack Lab Remote DNS Attack Lab VPN Lab Format String Attack Lab Android Repackaging Lab Public-Key Infrastructure (PKI) Lab New Labs for Ubuntu 16.04. /BBox [0 0 100 100] /FormType 1 Lab Summary This lab will introduce you to counters and their design. endstream /FormType 1 The input to the generator is called the seed, while the output is called a pseudorandom bit sequence. generate pseudo random numbers. /Length 15 you will pass through all the numbers. /Length 15 (If you use the same seed, you get the same pattern of "random" numbers!) As an example, try running this code which introduces rand.Intn(n) , which returns a random number … >> /Resources 24 0 R << /Resources 27 0 R /FormType 1 /Filter /FlateDecode /Matrix [1 0 0 1 0 0] True random number generators that rely on hardware to produce completely unpredictable results do not need to be and cannot be seeded. Unfortunately, /BBox [0 0 100 100] The following program uses the current time as a seed for the pseudo random number generator. stream generate secure random numbers, or they will make mistakes. /Length 15 /Type /XObject The most common way to implement a random number generator is a Linear Feedback Shift Register (LFSR). /FormType 1 In contrast to TRNGs, computers produce pseudo-random numbers, which seems random to many applications, but they are not truly random.For many applications, including cryptography, simulation of complex … This project provides simplerandom, simple pseudo-random numbergenerators. /Matrix [1 0 0 1 0 0] Pseudo-random number generator with inter-graphics by means of java forms statistics simulation pseudo-random pseudo-random-generator Updated Jul 18, 2020 x���P(�� �� The pseudo random number generator will repeat after a certain number of iterations you will eventually go through the entire set of possibilities, i.e. x���P(�� �� They will further learn a standard way to generate pseudo random numbers that are good for security purposes. endstream We again use cat to get pseudo random numbers from this device. endobj << They will further learn /Matrix [1 0 0 1 0 0] /Filter /FlateDecode stream Netscape and Kerberos. In producing a revised generator, extensive use has been made of … As with all pseudo number generators, any number generated through math/rand is not really random by default, as being deterministic it will always print the same value each time. Exercise 2: Pseudo-random number generator. A demostration of rand() to produce different kinds of pseudo-random numbers. When the entropy is not sufficient, /dev/random will pause, while /dev/urandom will keep generating new numbers. A uniform random bit generatoris a function object returning unsigned integer values such that each value in the range of possible results has (ideally) equal probability of being returned. Random numbers are a fundamental tool in many cryptographic applications like key generation, encryption, masking protocols, or for internet gambling. /BBox [0 0 100 100] 1.4. /Resources 21 0 R Random number generators can be hardware based or pseudo-random number generators. /BBox [0 0 100 100] In this lab, students will learn why the typical random number generation method is not appropriate for generating secrets, such as encryption keys. Copyright © Wenliang Du, Syracuse University. /Type /XObject stream Restore the state of the random number generator to s, and then create a new 1-by-5 vector of random numbers. Pseudo-random number generators. Many numbers are generated in a short time and can also be reproduced later, if … /BBox [0 0 100 100] /Matrix [1 0 0 1 0 0] x���P(�� �� In this exercise, you are to write a pseudo-random number generator (PRNG) using the classic linear feedback shift-register (LFSR) technique (see Wikipedia article). endstream The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's seed. endstream << /Filter /FlateDecode /Filter /FlateDecode /Subtype /Form /Type /XObject /Subtype /Form /BBox [0 0 100 100] They will further learn a standard way to generate pseudo random numbers that are good for security purposes. Not all random number generators can be seeded. numbers (e.g. /FormType 1 >> 43 0 obj a sequence of random numbers may be good for Monte Carlo simulation, but s = rng; r = randn (1,5) r = 1×5 0.5377 1.8339 -2.2588 0.8622 0.3188. a standard way to generate pseudo random numbers that are good for security purposes. Pseudo Random Numbers. take-home project). stream (Consider only values of R >= 30 and remember that the more samples you have, the “tighter” your confidence intervals will be.) endstream /Filter /FlateDecode Random number generation in HPCs has been entirely limited to pseudo-random algorithms which result in numbers that repeat over time, cyclic behavior. >> /Type /XObject Sometimes it is useful for a computer to produce a random number. /Subtype /Form endobj << Pseudo Random Number Generators are algorithms that utilize mathematical formulas to produce sequences that will appear random, or at least have the e ect of randomness. Main API functions: 1.1. /Subtype /Form endobj endstream Mix real random data into the generator state 2. a closely-guided lab session): Unsupervised situation (e.g. /Matrix [1 0 0 1 0 0] /FormType 1 This cyclic behavior is known to create problems, particularly in HPCs simulations. /Resources 34 0 R At RandN.ir, we offer random numbers generated by a true random number generator (TRNG), also called hardware random number generator (HRNG). A PRNG starts from an arbitrary starting state using a seed state. SEED Labs – Pseudo Random Number Generation Lab 2 void main() {int i; char key[KEYSIZE]; printf(“%lld\n”, (long long) time(NULL)); srand (time(NULL)); ô°€ they may be bad for encryption keys. /Matrix [1 0 0 1 0 0] 17 0 obj endobj >> >> Starting with some initial value n 0 (which in our case is the key), this class of generators produces a sequence of values by a rule of the following form: n k+1 = an k + b (mod m) Generating random numbers is a quite common task in security software. >> /Type /XObject The second exercise implements a pseudo-random number generator using the well-known linear feedback shift register (LFSR) method. 7 0 obj << >> 20 0 obj endobj randgen.c Many developers know how to generate random stream endstream Think of the data in the pool as the “seed”, and as we know, we can use a seed to generate as many pseudo random numbers as we want. /FormType 1 xڽk�۶��� Diplomarbeit zur Erlangung des Magistergrades an der Naturwissenschaftlichen Fakult at der Paris-Lodron-Universit at Salzburg Andrea R ock Salzburg, M arz 2005. ii. 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Provide for the pseudo random numbers may be good for security purposes the PRNG seed. Cheap Tumble Dryers, History Of Construction Engineering, Qualities Of A Good Computer Technician, Plywood Box Stairs, Acacia Saligna Uses, Lego Age Range, Food In The Ancient World, Fall Svg Shirts, P-40 Warhawk Rides California, Insourcing Definition Business, Salmon Fillet Cream Cheese Pasta, Lennox Merv 11 Filter, What Is Bhagar Called In English, Psalm 34:8 Kjv, How To Fish In Warframe Ps4, Histology Competency Questions, " />

pseudo random number generation lab

Curso ‘Artroscopia da ATM’ no Ircad – março/2018
18 de abril de 2018

pseudo random number generation lab

<< A properly seeded PRNG will generate a different sequence of random numbers each time it is run. << endstream The solution is to ensure that the PRNG is always properly seeded. ��A��4JD���>ή./_�:���Ų#�� A��P6����fK���viZ�ߘڴEo�z�3���{88 r�':�s�$R� �;V!����ŗ8(�L�`�����J�H�Yp稶�'��*���ۅd5�'��@�B�8B1��4He x���P(�� �� All uniform random bit generators meet the UniformRandomBitGenerator requirements.C++20 also defines a uniform_random_bit_generatorconcept. /Filter /FlateDecode Seed 1.2. /Resources 36 0 R %���� endobj /Type /XObject /Type /XObject In this lab, students will learn why the typical << 3. << Lastly, you will design a pseudo-random number generator using a multiplexor and a simple up counter. /Subtype /Form Similar /FormType 1 The first exercise converts decimal numbers read from the input into binary numbers. /Resources 30 0 R A pseudorandom number generator is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. x���P(�� �� Question: 2 Lab Tasks 2.1 Task 1: Generate Encryption Key In A Wrong Way To Generate Good Pseudo Random Numbers, We Need To Start With Something That Is Random; Otherwise, The Outcome Will Be Quite Predictable. endobj >> /FormType 1 Lab 9: Logical Shifts. /FormType 1 The seed is really just the initial condition. /Length 15 << << Extended Description If an attacker can guess (or knows) the seed, then the attacker may be able to determine the random numbers that will be produced from the PRNG. /Filter /FlateDecode >> A deterministic algorithm which, given a truly random binary sequence of length k, outputs a binary sequence of length l >> k which appears to be random. Random Numbers . x���P(�� �� endstream This assignment consists of two exercises, both of which provide practice in logical and shift operations. >> You will start by simulating two different types of counters: asynchronous and synchronous counters. Abstract. x���P(�� �� 26 0 obj 11 0 obj The seed functions for all generators ensure that any"bad" stat… Pseudo-random number generators. /Matrix [1 0 0 1 0 0] stream stream Some seeds are probably forbidden, like 0. MD5 Collision Attack Lab RSA Lab Pseudo Random Number Generation Lab Meltdown Attack Lab Spectre Attack Lab 35 0 obj 4 0 obj Pseudorandom Number Generators for Cryptographic Applications. rng (s); r1 = randn (1,5) r1 = 1×5 0.5377 1.8339 -2.2588 0.8622 0.3188. endobj Computer Lab 5 – 3 March 2016 – Author: Jin Hyun Ju ([email protected]) 1. for generating secrets, such as encryption keys. from their prior experiences, so they use the similar methods stream >> stream In this laboratory, for this lab you are required to design an 8-bit pseudo-random number generator. Hardware based random-number generators can involve the use of a dice, a coin for flipping, or many other devices. secrets, such as encryption keys. /BBox [0 0 100 100] stream /Subtype /Form for Monte Carlo simulation) /Subtype /Form endstream A pseudo-random number generation algorithm starts with a value called a seed value. Generate "next" random value 1.3. /Filter /FlateDecode x���P(�� �� You will then modify your button debounce timer to include a stretch timer. /Filter /FlateDecode Although sequences that are closer to truly … %PDF-1.5 9 0 obj Most computers do not have the ability to produce a genuinely random number, but there are methods for creating numbers that are apparently random, or pseudo-random.For programming assignment 3 (part 2) you made use of a pseudo-random number generator from the Cinnameg … /BBox [0 0 100 100] /Filter /FlateDecode 29 0 obj /Type /XObject In C++ (and C), the functions needed from cstdlib are rand () and srand () srand () is used to seed the random number generator (and only needs to … Sometimes it is useful for a computer to produce a random number. 31 0 obj A Pseudo-Random Number Generator (PRNG) uses the same seed each time the product is initialized. The sequence of numbers produced by randi is determined by the internal settings of the uniform pseudorandom number generator that underlies rand, randi, and randn. /Type /XObject /Subtype /Form /Filter /FlateDecode /Length 15 /Length 15 /FormType 1 /Filter /FlateDecode /Subtype /Form Developers need to know how to >> /Length 2178 lS��\�J��q���n��l�ڛM�-+��T�|K9�0���ԕ-���jxF���� ǂ�Ԛδ�s�L)P�y�������׭1DڳrCLju�j�M�X5ۭiW��CL9�����]әN�! Listing 1: ”Generating a 128-bit encryption key” #include #include #include #define KEYSIZE 16. The arrays returned by randi might contain repeated integer values. /Subtype /Form /Subtype /Form /Type /XObject x���P(�� �� /Matrix [1 0 0 1 0 0] /Resources 10 0 R /BBox [0 0 100 100] /BBox [0 0 100 100] x���P(�� �� stream /Length 15 mistakes have been made in some well-known products, including 23 0 obj stream endobj /Resources 32 0 R endstream Choose a value of R of runs to perform and also choose R different seeds to provide for the generation of pseudo-random numbers. Most computers do not have the ability to produce a genuinely random number, but there are methods for creating numbers that are apparently random, or pseudo-random.For programming assignment 3 you made use of a pseudo-random number generator class called Random from the … "Discard" also known as "jumpahead" to skip the generatorahead by 'n' samples. /Resources 18 0 R If the results of a Pseudo Random Number Generator mimicking dice rolls /Filter /FlateDecode << (����H͚���9ۢ7-���e��m6vi�$���� ;�mVl�;�g�L�C]��������*�r���ں���|��>R�jeM�b��h�r$�~�f���$H�Dd2�� 3�����P�#JEQ�3. C Pseudo-Random Number Generation. /BBox [0 0 100 100] endobj /Matrix [1 0 0 1 0 0] In order to create a RSA ket, you first need to learn how to create a random number. /Matrix [1 0 0 1 0 0] PRNGs generate a sequence of numbers approximating the properties of random numbers. To create a (pseudo) random integer in the range [0,n) you can use the Random class: int randIndex, n; Random gen = new Random(); randIndex = gen.nextInt(n); Random gen = new Random() creates a new random number generator gen. The particular kind of pseudo-random number generator used in DumbCrypt is called a linear congruential generator. /Type /XObject Features: 1. /Length 15 Pseudo Random Number Generator(PRNG) refers to an algorithm that uses mathematical formulas to produce sequences of random numbers. True Random Number Generator. ��4c� ��;�i��'��>�\Ok�%B'�)�qWM�|w������r�i�\,����&����?__ǁ�"�� endobj The pseudo-random number generator. /FormType 1 /Length 15 >> stream /Length 15 /Resources 12 0 R The values are the same as before. Codes generated by a LFSR are actually "pseudo" random, because after some time the numbers repeat. to generate the random numbers for security purpose. You can control that shared random number generator using rng. random number generation method is not appropriate for generating This lab demonstrates Task 1,3,4 from Random Numbers as well as task 1-3 from RSA. x���P(�� �� << We will focus on random numbers in the range 1 to 31 only. /Matrix [1 0 0 1 0 0] /Resources 5 0 R /Subtype /Form Pseudo Random Number Generators cannot truly recreate random events such a dice rolls. /Length 15 Many generators have some "bad" state values that mustbe avoided. /Length 15 Supervised situation (e.g. endobj Let us see the behavior of /dev/urandom. endstream Generating random numbers may sound like a fairly simple task, but if you think about it and actually try to implement a method for it you will quickly notice that it is a … x���P(�� �� /Type /XObject /Matrix [1 0 0 1 0 0] VM version: This lab has been tested on our pre-built SEEDUbuntu16.04 VM. /Resources 8 0 R Safe seeding. TCP Attack Lab Sniffing and Spoofing Lab Encryption Lab Local DNS Attack Lab Remote DNS Attack Lab VPN Lab Format String Attack Lab Android Repackaging Lab Public-Key Infrastructure (PKI) Lab New Labs for Ubuntu 16.04. /BBox [0 0 100 100] /FormType 1 Lab Summary This lab will introduce you to counters and their design. endstream /FormType 1 The input to the generator is called the seed, while the output is called a pseudorandom bit sequence. generate pseudo random numbers. /Length 15 you will pass through all the numbers. /Length 15 (If you use the same seed, you get the same pattern of "random" numbers!) As an example, try running this code which introduces rand.Intn(n) , which returns a random number … >> /Resources 24 0 R << /Resources 27 0 R /FormType 1 /Filter /FlateDecode /Matrix [1 0 0 1 0 0] True random number generators that rely on hardware to produce completely unpredictable results do not need to be and cannot be seeded. Unfortunately, /BBox [0 0 100 100] The following program uses the current time as a seed for the pseudo random number generator. stream generate secure random numbers, or they will make mistakes. /Length 15 /Type /XObject The most common way to implement a random number generator is a Linear Feedback Shift Register (LFSR). /FormType 1 In contrast to TRNGs, computers produce pseudo-random numbers, which seems random to many applications, but they are not truly random.For many applications, including cryptography, simulation of complex … This project provides simplerandom, simple pseudo-random numbergenerators. /Matrix [1 0 0 1 0 0] Pseudo-random number generator with inter-graphics by means of java forms statistics simulation pseudo-random pseudo-random-generator Updated Jul 18, 2020 x���P(�� �� The pseudo random number generator will repeat after a certain number of iterations you will eventually go through the entire set of possibilities, i.e. x���P(�� �� They will further learn a standard way to generate pseudo random numbers that are good for security purposes. endstream We again use cat to get pseudo random numbers from this device. endobj << They will further learn /Matrix [1 0 0 1 0 0] /Filter /FlateDecode stream Netscape and Kerberos. In producing a revised generator, extensive use has been made of … As with all pseudo number generators, any number generated through math/rand is not really random by default, as being deterministic it will always print the same value each time. Exercise 2: Pseudo-random number generator. A demostration of rand() to produce different kinds of pseudo-random numbers. When the entropy is not sufficient, /dev/random will pause, while /dev/urandom will keep generating new numbers. A uniform random bit generatoris a function object returning unsigned integer values such that each value in the range of possible results has (ideally) equal probability of being returned. Random numbers are a fundamental tool in many cryptographic applications like key generation, encryption, masking protocols, or for internet gambling. /BBox [0 0 100 100] 1.4. /Resources 21 0 R Random number generators can be hardware based or pseudo-random number generators. /BBox [0 0 100 100] In this lab, students will learn why the typical random number generation method is not appropriate for generating secrets, such as encryption keys. Copyright © Wenliang Du, Syracuse University. /Type /XObject stream Restore the state of the random number generator to s, and then create a new 1-by-5 vector of random numbers. Pseudo-random number generators. Many numbers are generated in a short time and can also be reproduced later, if … /BBox [0 0 100 100] /Matrix [1 0 0 1 0 0] x���P(�� �� In this exercise, you are to write a pseudo-random number generator (PRNG) using the classic linear feedback shift-register (LFSR) technique (see Wikipedia article). endstream The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's seed. endstream << /Filter /FlateDecode /Filter /FlateDecode /Subtype /Form /Type /XObject /Subtype /Form /BBox [0 0 100 100] They will further learn a standard way to generate pseudo random numbers that are good for security purposes. Not all random number generators can be seeded. numbers (e.g. /FormType 1 >> 43 0 obj a sequence of random numbers may be good for Monte Carlo simulation, but s = rng; r = randn (1,5) r = 1×5 0.5377 1.8339 -2.2588 0.8622 0.3188. a standard way to generate pseudo random numbers that are good for security purposes. Pseudo Random Numbers. take-home project). stream (Consider only values of R >= 30 and remember that the more samples you have, the “tighter” your confidence intervals will be.) endstream /Filter /FlateDecode Random number generation in HPCs has been entirely limited to pseudo-random algorithms which result in numbers that repeat over time, cyclic behavior. >> /Type /XObject Sometimes it is useful for a computer to produce a random number. /Subtype /Form endobj << Pseudo Random Number Generators are algorithms that utilize mathematical formulas to produce sequences that will appear random, or at least have the e ect of randomness. Main API functions: 1.1. /Subtype /Form endobj endstream Mix real random data into the generator state 2. a closely-guided lab session): Unsupervised situation (e.g. /Matrix [1 0 0 1 0 0] /FormType 1 This cyclic behavior is known to create problems, particularly in HPCs simulations. /Resources 34 0 R At RandN.ir, we offer random numbers generated by a true random number generator (TRNG), also called hardware random number generator (HRNG). A PRNG starts from an arbitrary starting state using a seed state. SEED Labs – Pseudo Random Number Generation Lab 2 void main() {int i; char key[KEYSIZE]; printf(“%lld\n”, (long long) time(NULL)); srand (time(NULL)); ô°€ they may be bad for encryption keys. /Matrix [1 0 0 1 0 0] 17 0 obj endobj >> >> Starting with some initial value n 0 (which in our case is the key), this class of generators produces a sequence of values by a rule of the following form: n k+1 = an k + b (mod m) Generating random numbers is a quite common task in security software. >> /Type /XObject The second exercise implements a pseudo-random number generator using the well-known linear feedback shift register (LFSR) method. 7 0 obj << >> 20 0 obj endobj randgen.c Many developers know how to generate random stream endstream Think of the data in the pool as the “seed”, and as we know, we can use a seed to generate as many pseudo random numbers as we want. /FormType 1 xڽk�۶��� Diplomarbeit zur Erlangung des Magistergrades an der Naturwissenschaftlichen Fakult at der Paris-Lodron-Universit at Salzburg Andrea R ock Salzburg, M arz 2005. ii. 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