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21.
The inversive congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. In this paper we present the first nontrivial bounds on the discrepancy of individual sequences of inversive congruential pseudorandom numbers in parts of the period. The proof is based on a new bound for certain incomplete exponential sums.
22.
We present a new method to study the power generator of pseudorandom numbers modulo a Blum integer . This includes as special cases the RSA generator and the Blum-Blum-Shub generator. We prove the uniform distribution of these, provided that the period with fixed 0$\"> and, under the same condition, the uniform distribution of a positive proportion of the leftmost and rightmost bits. This sharpens and generalizes previous results which dealt with the RSA generator, provided the period . We apply our results to deduce that the period of the binary sequence of the rightmost bit has exponential length.
23.
The authors carry out numerical experiments with regard to the Monte Carlointegration method, using as input the pseudorandom vectors that are generated by thealgorithm proposed in [Mok, C. P., Pseudorandom Vector Generation Using Elliptic Curvesand Applications to Wiener Processes, Finite Fields and Their Applications, 85, 2023,102129], which is based on the arithmetic theory of elliptic curves over finite fields. Theyconsider integration in the following two cases: The case of Lebesgue measure on theunit hypercube [0, 1]d, and as well as the case of Wiener measure. In the case of Wienermeasure, the construction gives discrete time simulation of an independent sequence ofstandard Wiener processes, which is then used for the numerical evaluation of FeynmanKac formulas. 相似文献
24.
Hans Ekkehard Plesser Anders Grønvik Jahnsen 《Applied mathematics and computation》2010,217(1):339-346
Kim et al. [C. Kim, G.H. Choe, D.H. Kim, Test of randomness by the gambler’s ruin algorithm, Applied Mathematics and Computation 199 (2008) 195-210] recently presented a test of random number generators based on the gambler’s ruin problem and concluded that several generators, including the widely used Mersenne Twister, have hidden defects. We show here that the test by Kim et al. suffers from a subtle, but consequential error: re-seeding the pseudorandom number generator with a fixed seed for each starting point of the gambler’s ruin process induces a random walk of the test statistic as a function of the starting point. The data presented by Kim et al. are thus individual realizations of a random walk and not suited to judge the quality of pseudorandom number generators. When generating or analyzing the gambler’s ruin data properly, we do not find any evidence for weaknesses of the Mersenne Twister and other widely used random number generators. 相似文献
25.
This paper proposes a performance-enhanced code-division-multiple-access (CDMA) system using modified pseudorandom noise (PN) coded fiber Bragg gratings (FBGs) with a bipolar optical CDMA encoder/decoder. The data were encoded either by a unipolar signature sequence of modified PN code or by its complement, depending on whether the data bit was ‘1’ or ‘0’. Numerical simulation confirmed that bit error rate (BER) performance largely improved due to the increased decision margin at the receiver. Furthermore, at the BER of 10−9, the tolerance of spectral power distortion in the optical source appeared to be nearly twice that of conventional optical CDMA systems. 相似文献
26.
On Some Properties of the Shrinking Generator 总被引：1，自引：0，他引：1
Igor Shparlinski 《Designs, Codes and Cryptography》2001,23(2):147-156
We obtain several results about the output rate and distribution ofzeros and ones of the shrinking generator associated with two linear recurringsequences. These results are based on various bounds on the number of zeros of linearrecurring sequences. Non-linear recurring sequences are considered aswell. 相似文献
27.
Huaning Liu 《Proceedings of the American Mathematical Society》2007,135(5):1309-1318
Let be an odd prime. Define where is the multiplicative inverse of modulo such that . This paper shows that the sequence is a ``good\" pseudorandom sequence, by using the properties of exponential sums, character sums, Kloosterman sums and mean value theorems of Dirichlet -functions.
28.
刘华宁 《数学年刊A辑(中文版)》2007,(3)
设p为奇素数,x为整数且满足1≤x≤p-1．定义数列其中■是n模p的乘法逆,满足n■≡1 mod p以及1≤■≤p-1．证明了(x_n)是一致分布数列,(e_n)是好的伪随机数列．这表明在二进制数列与[0,1)数列之间存在某种联系． 相似文献