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Permutations mostly in the form of sboxes are very efficient components largely present in cryptographic artifacts either hardware or software. They have been well studied as an individual component and have a large body of knowledge. Here we look at the properties of tiny transformations employing permutations and a few field operations. That gives functions with few components, which can be safely used either as PRG building blocks or as a component in lightweight ciphers. At the end, we propose a PRG implementation with those components. Lastly, we formalize a key assumption over the system functions and give a theorem for the equivalence of some system instances. [ABSTRACT FROM AUTHOR]

Simplices are the fundamental domain when integrating over convex polytopes. The aim of this work is to establish a novel framework of Monte Carlo integration over simplices, throughout from sampling to variance reduction. Namely, we develop a uniform sampling method on the standard simplex consisting of two independent procedures and construct theories on change of measure on each of the two independent elements in the developed sampling technique with a view towards variance reduction by importance sampling. We provide illustrative figures and numerical results to support our theoretical findings and demonstrate the strong potential of the developed framework for effective implementation and acceleration of Monte Carlo integration over simplices. [ABSTRACT FROM AUTHOR]

As the first generic method for finding the optimal differentialand linear characteristics, Matsui's branch and bound search algorithm has played an important role in evaluating the security of symmetric ciphers. By combining Matsui's bounding conditions with automatic search models, search efficiency can be improved. In this paper, by studying the properties of Matsui's bounding conditions, we give the general form of bounding conditions that can eliminate all the impossible solutions determined by Matsui's bounding conditions. Then, a new method of combining bounding conditions with sequential encoding method is proposed. With the help of some small size Mixed Integer Linear Programming (MILP) models, we can use fewer variables and clauses to build Satisfiability Problem (SAT) models. As applications, we use our new method to search for the optimal differential and linear characteristics of some SPN, Feistel, and ARX block ciphers. The number of variables and clauses and the solving time of the SAT models are decreased significantly. In addition, we find some new differential and linear characteristics covering more rounds. [ABSTRACT FROM AUTHOR]

A regression model, based on the well-known log-logistic distribution is proposed. This model is parameterized in terms of the median of the distribution, through a link function. The regression model assumes the censored data structure. The unknown parameters are estimated by maximum likelihood. Monte Carlo simulations with censoring and application to real censored data show the good quality of the proposed regression model. [ABSTRACT FROM AUTHOR]

A quaternary sequence is said to be good if its maximum nontrivial autocorrelation is very low relative to its period. In this paper, we present some new classes of quaternary sequences with low autocorrelation of period N via two binary cyclotomic sequences, where N ≡ 1 (mod 4) is an odd prime. Furthermore, we determine the linear complexity and minimal polynomials of these quaternary sequences over F 2 2 as well. [ABSTRACT FROM AUTHOR]

Traditional global stability measure for sequences is hard to determine because of large search space. We propose the k-error linear complexity with a zone restriction for measuring the local stability of sequences. For several classes of sequences, we demonstrate that the k-error linear complexity is identical to the k-error linear complexity within a zone, while the length of a zone is much smaller than the whole period when the k-error linear complexity is large. These sequences have periods 2 n , or 2 v r (r odd prime and 2 is primitive modulo r), or 2 v p 1 s 1 ⋯ p n s n ( p i is an odd prime and 2 is primitive modulo p i 2 , where 1 ≤ i ≤ n ) respectively. In particular, we completely determine the spectrum of 1-error linear complexity with any zone length for an arbitrary 2 n -periodic binary sequence. [ABSTRACT FROM AUTHOR]

R. Hofer and A. Winterhof proved that the 2-adic complexity of the two-prime (binary) generator of period pq with two odd primes p ≠ q is close to its period and it can attain the maximum in many cases. When the two-prime generator is applied to producing quaternary sequences, we need to determine the 4-adic complexity. It is proved that there are only two possible values of the 4-adic complexity for the two-prime quaternary generator, which are at least p q - 1 - max { log 4 (p q 2) , log 4 (p 2 q) } . Examples for primes p and q with 5 ≤ p , q < 10000 illustrate that the 4-adic complexity only takes one value larger than p q - max { log 4 (p) , log 4 (q) } , which is close to its period. So it is good enough to resist the attack of the rational approximation algorithm. [ABSTRACT FROM AUTHOR]

Discrete tempered stable distributions are a large and flexible class of models for heavy tailed and overdispersed count data. In this paper we derive various properties of these distributions and develop an exact simulation method based on rejection sampling and a compound Poisson representation. We extend this method to exact simulation of the corresponding bilateral distributions and Lévy processes. [ABSTRACT FROM AUTHOR]

Linear complexity test included in the NIST test suite only checks whether or not the observed linear complexity is close to the expected linear complexity. To take full advantage of the information of the linear complexity profile, we propose two randomness tests including a jump test based on the jump complexity, i. e., the number of changes in the linear complexity profile of a sequence, and a hop test checking the sum of jump heights at intervals. By using an iterative algorithm we calculate some necessary statistical measures of a random sequence of length M, and combining with hypothesis test we determine whether a given binary sequence is random or not. Moreover, we provide the explicit formulae of the expectation and the variance of the statistical measure of the hop test. The computational complexity of the jump test and the hop test is the same as that of the linear complexity test. Additionally, we provide a type of sample which, having passed all tests in the NIST test suite, is rejected by the jump test and hop test. So the proposed tests deserve to be considered. [ABSTRACT FROM AUTHOR]

A projected extrapolated gradient method is designed for solving monotone variational inequality in Hilbert space. Requiring local Lipschitz continuity of the operator, our proposed method improves the value of the extrapolated parameter and admits larger step sizes, which are predicted based a local information of the involved operator and corrected by bounding the distance between each pair of successive iterates. The correction will be implemented when the distance is larger than a given constant and its main cost is to compute a projection onto the feasible set. In particular, when the operator is the gradient of a convex function, the correction step is not necessary. We establish the convergence and ergodic convergence rate in theory under the larger range of parameters. Related numerical experiments illustrate the improvements in efficiency from the larger step sizes. [ABSTRACT FROM AUTHOR]

We propose Tseng's extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudomonotone and Lipschitz continuous vector fields, we prove that any sequence generated by the proposed methods converges to a solution of variational inequality problem, whenever it exits. Moreover, we give some numerical experiments to illustrate our main results. [ABSTRACT FROM AUTHOR]

NIST SP800-22 is one of the most widely used statistical testing tools for pseudorandom number generators (PRNGs). This tool consists of 15 tests (one-level tests) and two additional tests (two-level tests). Each one-level test provides one or more p-values. The two-level tests measure the uniformity of the obtained p-values for a fixed one-level test. One of the two-level tests categorizes the p-values into ten intervals of equal length, and apply a chi-squared goodness-of-fit test. This two-level test is often more powerful than one-level tests, but sometimes it rejects even good PRNGs when the sample size at the second level is too large, since it detects approximation errors in the computation of p-values. In this paper, we propose a practical upper limit of the sample size in this two-level test, for each of six tests appeared in SP800-22. These upper limits are derived by the chi-squared discrepancy between the distribution of the approximated p-values and the uniform distribution U(0, 1). We also computed a "risky" sample size at the second level for each one-level test. Our experiments show that the two-level test with the proposed upper limit gives appropriate results, while using the risky size often rejects even good PRNGs. We also propose another improvement: to use the exact probability for the ten categories in the computation of goodness-of-fit at the two-level test. This allows us to increase the sample size at the second level, and would make the test more sensitive than the NIST's recommending usage. [ABSTRACT FROM AUTHOR]

For distinct odd primes N and p, we view the N-periodic binary Legendre sequence as a p-ary sequence and present its trace representation via trace functions over F p . We use a skill to calculate the Mattson–Solomon polynomials of Legendre sequences and then describe the Mattson–Solomon polynomials by means of trace functions over F p . [ABSTRACT FROM AUTHOR]

T-functions have been widely used in the design of symmetric ciphers, hash functions, and fast cryptographic primitives. Single cycle polynomial T-functions are a special category. If they are used as state transition functions of stream ciphers, the security of the generated sequences is crucial. In 2008, Kolokotronis proposed a conjecture regarding the autocorrelation function’s values of coordinate sequences generated by single cycle polynomial T-functions. In this paper, we show that the conjecture does not hold in general and prove the conditions under which it holds. [ABSTRACT FROM AUTHOR]

Pseudo-random sequences with good statistical properties, such as low autocorrelation, high linear complexity and large 2-adic complexity, have been used in designing reliable stream ciphers. In this paper, we obtain the exact autocorrelation distribution of a class of binary sequences with three-level autocorrelation and analyze the 2-adic complexity of this class of sequences. Our results show that the 2-adic complexity of such a binary sequence with period N is at least (N + 1) − log2 (N + 1). We further show that it is maximal for infinitely many cases. This indicates that the 2-adic complexity of this class of sequences is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs). [ABSTRACT FROM AUTHOR]

For an elliptic curve E over a finite field we define the point sequence (Pn) recursively by Pn=ϑ(Pn-1)=ϑn(P0) with an endomorphism ϑ∈End(E) and with some initial point P0 on E. We study the distribution and the linear complexity of sequences obtained from (Pn). [ABSTRACT FROM AUTHOR]

Trustworthy generation of public random numbers is necessary for the security of a number of cryptographic applications. It was suggested to use the inherent unpredictability of blockchains as a source of public randomness. Entropy from the Bitcoin blockchain in particular has been used in lotteries and has been suggested for a number of other applications ranging from smart contracts to election auditing. In this Arcticle, we analyse this idea and show how an adversary could manipulate these random numbers, even with limited computational power and financial budget. [ABSTRACT FROM AUTHOR]

We define a family of quaternary sequences over the residue class ring modulo 4 of length pq, a product of two distinct odd primes, using the generalized cyclotomic classes modulo pq and calculate the discrete Fourier transform (DFT) of the sequences. The DFT helps us to determine the exact values of linear complexity and the trace representation of the sequences. [ABSTRACT FROM AUTHOR]

For a given elliptic curve $$\mathbf {E}$$ over a finite field of odd characteristic and a rational function f on $$\mathbf {E}$$ we first study the linear complexity profiles of the sequences f( nG), $$n=1,2,\dots $$ which complements earlier results of Hess and Shparlinski. We use Edwards coordinates to be able to deal with many f where Hess and Shparlinski's result does not apply. Moreover, we study the linear complexities of the (generalized) elliptic curve power generators $$f(e^nG)$$ , $$n=1,2,\dots $$ We present large families of functions f such that the linear complexity profiles of these sequences are large. [ABSTRACT FROM AUTHOR]

We introduce the new concept of joint nonlinear complexity for multisequences over finite fields and we analyze the joint nonlinear complexity of two families of explicit inversive multisequences. We also establish a probabilistic result on the behavior of the joint nonlinear complexity of random multisequences over a fixed finite field. [ABSTRACT FROM AUTHOR]

When a system consisting of independent components of the same type, some appropriate actions may be done as soon as a portion of them have failed. It is, therefore, important to be able to predict later failure times from earlier ones. One of the well-known failure distributions commonly used to model component life, is the modified Weibull distribution ( MWD ). In this paper, two pivotal quantities are proposed to construct prediction intervals for future unobservable lifetimes based on generalized order statistics (gos) from MWD . Moreover, a pivotal quantity is developed to reconstruct missing observations at the beginning of experiment. Furthermore, Monte Carlo simulation studies are conducted and numerical computations are carried out to investigate the efficiency of presented results. Finally, two illustrative examples for real data sets are analyzed. [ABSTRACT FROM AUTHOR]

We present a survey of applications of finite fields to cryptography, digital nets, and pseudorandom number generation. [ABSTRACT FROM AUTHOR]

We give the trace representation of a family of binary sequences derived from Euler quotients by determining the corresponding defining polynomials. The result extends an earlier result of Z. Chen on the trace of binary sequences derived from Fermat quotients modulo a prime. However, the case of composite modulus brings some interesting twists. Trace representation can help us producing the sequences efficiently and analyzing their cryptographic properties, such as linear complexity. [ABSTRACT FROM AUTHOR]

Linear complexity is an important cryptographic index of sequences. We study the linear complexity of $$p(q-1)$$ -periodic Legendre-Sidelnikov sequences, which combine the concepts of Legendre sequences and Sidelnikov sequences. We get lower and upper bounds on the linear complexity in different cases, and experiments show that the upper bounds can be attained. Remarkably, we associate the linear complexity of Legendre-Sidelnikov sequences with some famous primes including safe prime and Fermat prime. If $$2$$ is a primitive root modulo $$\frac{q-1}{2}$$ , and $$q$$ is a safe prime greater than 7, the linear complexity is the period if $$p\equiv 3 \pmod 8$$ ; $$p(q-1)-p+1$$ if $$p\equiv q \equiv 7 \pmod 8$$ , and $$p(q-1)-\frac{p-1}{2}$$ if $$p \equiv 7 \pmod 8, q \equiv 3 \pmod 8$$ . If $$q$$ is a Fermat prime, the linear complexity is the period if $$p \equiv 3 \pmod 8$$ , and $$p(q-1)-q+2$$ if $$p \equiv 5 \pmod 8$$ . It is very interesting that the Legendre-Sidelnikov sequence has maximal linear complexity and is balanced if we choose $$p=q$$ to be some safe prime. [ABSTRACT FROM AUTHOR]

In this paper, we present a random number generation method, which is one of the rejection methods. To accelerate ratio-of-uniform method, we use an efficiency variabler. After finding the optimal value of r with respect to interesting distribution with proportional density, random numbers can be generated in acceleration. [ABSTRACT FROM AUTHOR]