Cryptography, Statistics and Pseudo-Randomness (Part II) (original) (raw)

Cryptography, Statistics and Pseudo-Randomness (Part I)

In the classical approach to pseudo-random number generators, a generator is considered to perform well if its output sequences pass a battery of statistical tests that has become standard. In recent years, it has turned out that this approach is not satisfactory. Many generators have turned out to seriously bias the outcome of some simulation experiments in which they were put to use. From a theoretical point of view, the classical approach does not at all explain in what way a completely deterministic algorithm can be said to simulate randomness.

A simple secure pseudo-random number generator

Siam Journal on Computing, 1982

Two closely-related pseudo-random sequence generators are presented: The \/P-generator t with input P a prime, outputs the quotient digits obtained on dividing 1 by P. The x2 mod^-generator with inputs N, x0 (where N = P-Q is a product of distinct primes, each congruent to 3 mod 4, and Xq is a quadratic residue mod N), outputs &o&i^2 ' ' ' where 6^= parityfe) and *i+i = x\ Tnod N. From short seeds each generator efficiently produces long well-distributed sequences. Moreover, both generators have computationally hard problems at their core. The first generator's sequences, however, are completely inferable (from any small segment of 2|.P|+1 consecutive digits one can infer the "seed," P), while the second, on the other hand, is cryptographically secure (no polynomial (| N \)-time statistical test can distinguish such sequences from ran dom uniformly-distributed sequences). The second generator has additional interesting properties: from knowledge of x0 and N but not P or Q, one can generate the sequence forwards but not backwards. From the additional knowledge of P and Q, one can generate the sequence backwards. Yet more knowledge about N, including the factors of P-1 and Q-l, enable one to "jump" about from any point in the sequence to any other. Because of these properties, the x2 mod jV-generator promises many interesting applications, e.g., to publickey cryptography. To use these generators in practice, an analysis is needed of various properties of these sequences such as their periods. This analysis is begun here. Keywords, random, pseudo-random, Monte Carlo, computational complex ity, secure transactions, public-key encryption, cryptography, one-time pad, Jacobi symbol, quadratic residuocity. What do we want from a pseudo-random sequence generator? Ideally, we would like a pseudo-random sequence generator to quickly produce, from short seeds, long sequences (of bits) that appear in every way to be generated by suc cessive flips of a fair coin.

Random Number Generators Survey

IJCSIS Vol. 18 No. 10 OCT 2020, 2020

The use of random numbers is essential in random-ized algorithms, and many statistical methods are using them on random sampling, this is due to the fact that examining all the possible cases is unpractical. Nowadays, the most common used of random numbers is in simulation studies of stochastic processes. In fact, the security of many cryptographic systems relies on the generating of random numbers. However, cryptographic applications require random numbers with different criteria than those used in simulation. This study investigates pseudo-random numbers PRN, Quasi-random numbers QRN, and cryptographic random numbers CRN. The survey goal is to cover several random number generators and examining their statistic proprietaries using several testing algorithms.

A New Trend of Pseudo Random Number Generation using QKD

International Journal of Computer Applications, 2014

Random Numbers determine the security level of cryptographic applications as they are used to generate padding schemes in the encryption/decryption process as well as used to generate cryptographic keys. This paper utilizes the QKD to generate a random quantum bit rely on BB84 protocol, using the NIST and DIEHARD randomness test algorithms to test and evaluate the randomness rates for key generation. The results show that the bits generated using QKD are truly random, which in turn, overcomes the distance limitation (associated with QKD) issue, its well-known challenges with the sending/ receiving data process between different communication parties.

A Simple Unpredictable Pseudo-Random Number Generator

SIAM Journal on Computing, 1986

Two closely-related pseudo-random sequence generators are presented: The lIP generator, with input P a prime, outputs the quotient digits obtained on dividing by P. The x mod N generator with inputs N, Xo (where N P. Q is a product of distinct primes, each congruent to 3 mod 4, and x 0 is a quadratic residue mod N), outputs bob1 b2" where bi parity (xi) and xi+ x mod N. From short seeds each generator efficiently produces long well-distributed sequences. Moreover, both generators have computationally hard problems at their core. The first generator's sequences, however, are completely predictable (from any small segment of 21PI + consecutive digits one can infer the "seed," P, and continue the sequence backwards and forwards), whereas the second, under a certain intractability assumption, is unpredictable in a precise sense. The second generator has additional interesting properties: from knowledge of Xo and N but not P or Q, one can generate the sequence forwards, but, under the above-mentioned intractability assumption, one can not generate the sequence backwards. From the additional knowledge of P and Q, one can generate the sequence backwards; one can even "jump" about from any point in the sequence to any other. Because of these properties, the x mod N generator promises many interesting applications, e.g., to public-key cryptography. To use these generators in practice, an analysis is needed of various properties of these sequences such as their periods. This analysis is begun here.

Hybrid quantum random number generator for cryptographic algorithms

RADIOELECTRONIC AND COMPUTER SYSTEMS, 2021

The subject matter of the article is pseudo-random number generators. Random numbers play the important role in cryptography. Using not secure pseudo-random number generators is a very common weakness. It is also a fundamental resource in science and engineering. There are algorithmically generated numbers that are similar to random distributions but are not random, called pseudo-random number generators. In many cases the tasks to be solved are based on the unpredictability of random numbers, which cannot be guaranteed in the case of pseudo-random number generators, true randomness is required. In such situations, we use real random number generators whose source of randomness is unpredictable random events. Quantum Random Number Generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. The goal is to develop a mathematical model of the generator, which generates fast random numbers at a lower cost. At the same time, a high level of r...

A simple quantum generator of random numbers

Emergent Scientist

Cryptography techniques rely on chains of random numbers used to generate safe encryption keys. Since random number generator algorithms are in fact pseudo-random their behavior can be predicted if the generation method is known and as such they cannot be used for perfectly safe communications. In this article, we present a perfectly random generator based on quantum measurement processes. The main advantage of such a generator is that using quantum mechanics, its behavior cannot be predicted in any way. We verify the randomness of our generator and compare it to commonly used pseudo-random generators.

Random Number Generators: Principles and Applications

this paper we present approaches for generating random numbers along with potential applications. Rather than trying to provide extensive coverage of several techniques or algorithms that have appeared in the scientific literature, we focus on some representative approaches presenting their workings and properties in detail. Our goal is to delineate their strengths and weaknesses as well as their potential application domains so as the reader can judge what would be the best approach for the application in hand, possibly a combination of the available approaches. For instance, a physical source of randomness can be used for the initial seed, then suitable preprocessing can enhance its randomness and then the output of the preprocessing can feed different types of generators, e.g. a linear congruential generator, a cryptographically secure one and one based on the combination of one way hash functions and shared key cryptoalgorithms in various modes of operation. Then, if desired, th...