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Pseudorandom number generation and space complexity

Merrick Furst, Richard Lipton, Larry Stockmeyer
1985 Information and Control  
INTRODUCTION Recently, Blum and Micali (1982) described a pseudorandum number generator that transforms m-bit seeds to ink-bit pseudorandom numbers, for any integer k.  ...  Yao (1982) has shown under the same assumption about the nonpolynomial complexity of the discrete logarithm problem, that these pseudorandom numbers can be used in place of truly random numbers by any  ...  ACKNOWLEDGMENT We thank Andy Yao, Tom Leighton, and Silvio Micali for very helpful discussions about the results of Blum and Micali (1982) and Yao (1982) .  ... 
doi:10.1016/s0019-9958(85)80043-7 fatcat:2tubjsn4tfbsjmtea3f7luap64

Pseudorandomness for network algorithms

Russell Impagliazzo, Noam Nisan, Avi Wigderson
1994 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing - STOC '94  
We define pseudorandom generators for Yao's twoparty communication complexity model and exhibit a simple construction, based on expanders, for it.  ...  As mentioned above, a large number of models can be viewed as algorithms performed by communication networks. For these we can apply our general theorem and obtain specific generators.  ...  In short we say that g is a c-generator if it is a pseudorandom generator for communication complexity c with parameter 2 −c .  ... 
doi:10.1145/195058.195190 dblp:conf/stoc/ImpagliazzoNW94 fatcat:cfsf2cfn7ffapjfsxzeiqtd3zm

A Self-perturbed Pseudo-random Sequence Generator Based on Hyperchaos

Yi Zhao, Changyuan Gao, Jie Liu, Shaozeng Dong
2020 Chaos, Solitons & Fractals: X  
expand the period of pseudo-random sequence  Increase the complexity of system dynamic behavior and improve the random performance  This scheme has a larger key space and a higher level of security  ...  Based on the proposed hyper-chaotic system, a pseudorandom number generator is designed. The dynamic behavior of the hyper-chaotic system is analyzed.  ...  [12] combined chaos with variable perturbation parameters to construct the pseudorandom number generator.  ... 
doi:10.1016/j.csfx.2020.100023 fatcat:hhqocl6ddraetly5cxjvrjqccm

Space Pseudorandom Generators by Communication Complexity Lower Bounds

Anat Ganor, Ran Raz, Marc Herbstritt
2014 International Workshop on Approximation Algorithms for Combinatorial Optimization  
In 1989, Babai, Nisan and Szegedy [2] gave a construction of a pseudorandom generator for logspace, based on lower bounds for multiparty communication complexity.  ...  Subsequently, pseudorandom generators for logspace with seed length O(log 2 n) were given by [19] and [15].  ...  Our pseudorandom generator construction is based on a lower bound for a certain model of multiparty communication complexity, relying on the pseudorandom generator construction of Babai, Nisan and Szegedy  ... 
doi:10.4230/lipics.approx-random.2014.692 dblp:conf/approx/GanorR14 fatcat:zgrsvyodbna2zid3hnktfx3qla

Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Chuanfu Wang, Qun Ding
2019 Complexity  
a secure pseudorandom sequence generator for information encryption.  ...  Furthermore, experimental implementation shows that the digitized chaotic time series has great complexity, approximate entropy, and randomness, and the perturbed digitized logistic map can be used as  ...  Suppose the perturbation sources is the pseudorandom number generator, and its output pseudorandom number is ( ), the diagram of perturbed digitized logistic map is shown in Figure 3 .  ... 
doi:10.1155/2019/5942121 fatcat:c23xjsbcujdcfnnogdneldshge

Page 2489 of Mathematical Reviews Vol. , Issue 89E [page]

1989 Mathematical Reviews  
The author gives a generalization of these theo- rems for sequences of the form (5>7_, pi(k)a*)xen, where the p; are polynomials and the a; complex numbers.  ...  Let X be a compact metric space and @(X) the space of continuous functions from X to C.  ... 

Page 4098 of Mathematical Reviews Vol. , Issue 91G [page]

1991 Mathematical Reviews  
Summary: “We show how to predict a large class of pseudorandom number generators.  ...  generating the correct authentication check for a different message in the source space.  ... 

Construction of pseudorandom binary sequences using chaotic maps

Dimo Malchev, Ilhan Ibryam
2015 Applied Mathematical Sciences  
This paper proposes a modified construction of pseudorandom binary sequences using chaotic maps. The output binary digits are statistically tested with NIST, DIEHARD and ENT packages.  ...  A novel variable parameters hyperchaotic pseudorandom number generation structure which is composed by homogenized Logistic chaos and unified hyperchaos cascade, is presented in [17] .  ...  In [6] , a pseudorandom sequence generator based on two Circle maps and XOR function is designed. The Chen chaotic map is proposed as pseudorandom sequence generator in [3] .  ... 
doi:10.12988/ams.2015.52149 fatcat:jfcyft3w55aonkbgsyfz3bdvgq

Pseudorandom Bit Generator Based On Chaotic Parameter Hopping Chaos

Ahmed I. El-Naggary, Karim H. Moussa
2019 International Journal of Engineering and Technology  
Random number generators (RNGs) can be broadly classified as true RNGs (TRNGs), and pseudo RNGs (PRNGs).  ...  The main aspect of the cryptographic system is to generate artificially unpredictable random numbers (RNs) as a source for key generation and encryption applications.  ...  STATISTICAL TESTS RESULTS The National Institute of Standards and Technology (NIST) formulated some specific statistical tests to measure the randomness behavior for the pseudorandom number generators  ... 
doi:10.21817/ijet/2019/v11i6/191106013 fatcat:zcol5c4ui5glhiyb32sub4icr4

Targeted Pseudorandom Generators, Simulation Advice Generators, and Derandomizing Logspace [article]

William M. Hoza, Chris Umans
2017 arXiv   pre-print
We prove that _α > 0promise-BPSPACE(^1 + α n) = _α > 0promise-DSPACE(^1 + α n) if and only if for every targeted pseudorandom generator against logspace, there is a simulation advice generator for logspace  ...  Assume that for every derandomization result for logspace algorithms, there is a pseudorandom generator strong enough to nearly recover the derandomization by iterating over all seeds and taking a majority  ...  CCF-1423544 and by a Simons Investigator grant.  ... 
arXiv:1610.01199v4 fatcat:fh3wx2iolndtrcp6hdbyacnx6m

Hardness vs randomness

Noam Nisan, Avi Wigderson
1994 Journal of computer and system sciences (Print)  
We present a simple new construction of a pseudorandom bit generator.  ...  This construction reveals an equivalence between the problem of proving lower bounds and the problem of generating good pseudorandom sequences. Our construction has many consequences.  ...  There is no known construction of pseudorandom generators for NC that is based on a general complexity assumption about NC.  ... 
doi:10.1016/s0022-0000(05)80043-1 fatcat:vqgigqdbhzehzohlyvvhqga7cu

Pseudorandom permutations with the fast forward property [article]

Boaz Tsaban
2003 arXiv   pre-print
In order to shift to the pseudorandom case, we need to have some pseudorandom number generator to generate the random choices of the s i 's in the CCL process.  ...  The space complexity of our algorithm is equal to the size of the sequence created by the CCL process, that is, O(log n).  ... 
arXiv:cs/0112016v2 fatcat:am4c4a5iyjgqhi2fwfgqpyadri

Ternary pseudorandom encoding of Fourier transform holograms

Robert W. Cohn, Markus Duelli
1999 Optical Society of America. Journal A: Optics, Image Science, and Vision  
These algorithms are notable because their computational overhead is low and because the space-bandwidth product of the encoded signal is identical to the number of modulator pixels.  ...  Pseudorandom encoding is a statistical method for designing Fourier transform holograms by mapping ideal complex-valued modulations onto spatial light modulators that are not fully complex.  ...  In these calculations we use N ϭ 128 2 for the number of SLM pixels, and, considering a diffraction-limited spot to have a space-bandwidth product of 1, we use B ϭ 7 2 for the space-bandwidth product of  ... 
doi:10.1364/josaa.16.000071 pmid:9919694 fatcat:i3itr4lewbbw5c25oehoygdiwi

Hardness vs. randomness

N. Nisan, A. Wigderson
1988 [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science  
We present a simple new construction of a pseudorandom bit generator.  ...  This construction reveals an equivalence between the problem of proving lower bounds and the problem of generating good pseudorandom sequences. Our construction has many consequences.  ...  There is no known construction of pseudorandom generators for NC that is based on a general complexity assumption about NC.  ... 
doi:10.1109/sfcs.1988.21916 dblp:conf/focs/NisanW88 fatcat:qtvqglf5yzbnbmjrapdz6rzc7a

Analyzing the encoding range of amplitude-phase coupled spatial light modulators

Robert W. Cohn
1999 Optical Engineering: The Journal of SPIE  
While the method approximates fairly arbitrary complex modulations, there are always some complex values that are outside the encoding range for each SLM coupling characteristic and for each specific pseudorandom  ...  For coherently illuminated SLMs in a Fourier transform arrangement, pseudorandom encoding can be used.  ...  Acknowledgments This study was supported by the National Aeronautics and Space Administration ͑NASA͒ cooperative agreement No. NCC5-222 and Office of Naval Research ͑ONR͒ grant No. N00014-96-1-1296.  ... 
doi:10.1117/1.602095 fatcat:7dcwiezpjzcizntjwhi76c7gya
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