Topic
Inversive congruential generator
About: Inversive congruential generator is a research topic. Over the lifetime, 23 publications have been published within this topic receiving 248 citations.
Papers
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TL;DR: This paper revisits the modular inversion hidden number problem and the inversive congruential pseudo random number generator and considers how to more efficiently attack them in terms of fewer samples or outputs, and presents two strategies to construct lattices in Coppersmith's lattice-based root-finding technique for the solving of the equations.
Abstract: In this paper we revisit the modular inversion hidden number problem and the inversive congruential pseudo random number generator and consider how to more efficiently attack them in terms of fewer samples or outputs. We reduce the attacking problem to finding small solutions of systems of modular polynomial equations of the form ai+bix0+cixi+x0xi = 0 (mod p), and present two strategies to construct lattices in Coppersmith’s lattice-based root-finding technique for the solving of the equations. Different from the choosing of the polynomials used for constructing lattices in previous methods, a part of polynomials chosen in our strategies are linear combinations of some polynomials generated in advance and this enables us to achieve a larger upper bound for the desired root. Applying the solving of the above equations to analyze the modular inversion hidden number problem, we put forward an explicit result of Boneh et al. which was the best result so far, and give a further improvement in the involved lattice construction in the sense of requiring fewer samples. Our strategies also give a method of attacking the inversive congruential pseudo random number generator, and the corresponding result is the best up to now.
1 citations
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TL;DR: For anys ≥ 2, the set of all nonoverlappings-tuples X ns =(x ns,x ns +1,...,x ns+s−1) ∈I s,n=0, 1,,..., (M/2)−1, is the same as the intersection of I s with a union of some number of grids with explicitly known shift vectors and lattice bases as discussed by the authors.
Abstract: Let {x n } be pseudorandom numbers inI=[0,1) of the maximal period, generated by the modified inversive method with modulusM, M=2α. We show that, for anys≥2, the set of all nonoverlappings-tuples X ns =(x ns ,x ns +1, ...,x ns +s−1) ∈I s ,n=0,1, ..., (M/2)−1, is the same as the intersection ofI s with a union of some number of grids with explicitly known shift vectors and lattice bases. Our arguments follow closely those in the paper by Eichnauer-Herrmann, Grothe, Niederreiter and Topuzoglu.
1 citations
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TL;DR: This paper slightly modify this notion to obtain the so-called irreducible-expansion complexity which is more suitable for certain applications and analyzes both the classical and modified expansion complexity.
Abstract: In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. In this paper, we slightly modify this notion to obtain the so-called irreducible-expansion complexity which is more suitable for certain applications. We analyze both, the classical and the modified expansion complexity. Moreover, we also study the expansion complexity of the explicit inversive congruential generator.
1 citations
01 Jan 2019
TL;DR: In this article, a period length of pseudorandom numbers with coefficients A j, B (n) j, j = 0, 1, 2, 3 can be defined as the polynomials fi(k) for n = 3k + i, i = 0.
Abstract: where the coefficients A j , B (n) j , j = 0, 1, 2, 3 can be prescribe as the polynomials fi(k) for n = 3k + i, i = 0, 1, 2. We determinate a period length of the sequence {yn}, besides this period reaches a maximum τ = 3pm−ν0−α if νp(y0y 1 − a) < νp(b) = α. Moreover, we prove that the sequence of pseudorandom numbers passes 3-dimensional test on the statistical independence. Obtained results are analogue of similar results for the congruential inversive pseudorandom sequences of the first order investigated in [1],[2].
01 Jan 2013
TL;DR: In this article, the authors give a description for elements of the sequence of inversive congru- ential pseudorandom numbers yn as polynomials on number n and initial value y 0.
Abstract: We give the description for elements of the sequence of inversive congru- ential pseudorandom numbers yn as polynomials on number n and initial value y0. We also estimate some exponential sums over yn.