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On the Provable Security of an Efficient RSABased Pseudorandom Generator. Cryptology ePrint Archive, Report 2006/206
, 2006
"... Abstract. Pseudorandom Generators (PRGs) based on the RSA inversion (onewayness) problem have been extensively studied in the literature over the last 25 years. These generators have the attractive feature of provable pseudorandomness security assuming the hardness of the RSA inversion problem. How ..."
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Abstract. Pseudorandom Generators (PRGs) based on the RSA inversion (onewayness) problem have been extensively studied in the literature over the last 25 years. These generators have the attractive feature of provable pseudorandomness security assuming the hardness of the RSA inversion problem. However, despite extensive study, the most efficient provably secure RSAbased generators output asymptotically only at most O(log n) bits per multiply modulo an RSA modulus of bitlength n, and hence are too slow to be used in many practical applications. To bring theory closer to practice, we present a simple modification to the proof of security by Fischlin and Schnorr of an RSAbased PRG, which shows that one can obtain an RSAbased PRG which outputs Ω(n) bits per multiply and has provable pseudorandomness security assuming the hardness of a wellstudied variant of the RSA inversion problem, where a constant fraction of the plaintext bits are given. Our result gives a positive answer to an open question posed by Gennaro (J. of Cryptology, 2005) regarding finding a PRG beating the rate O(log n) bits per multiply at the cost of a reasonable assumption on RSA inversion.
On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators
 MATH. COMP
, 2010
"... In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degree growth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical systems and show that they admit much stronger estimates ..."
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In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degree growth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical systems and show that they admit much stronger estimates than in the general case and thus can be of use for pseudorandom number generation.
Pseudorandom numbers and hash functions from iterations of multivariate polynomials’, Cryptography and Communications
"... Abstract. Dynamical systems generated by iterations of multivariate polynomials with slow degree growth have proved to admit good estimates of exponential sums along their orbits which in turn lead to rather stronger bounds on the discrepancy for pseudorandom vectors generated by these iterations. H ..."
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Abstract. Dynamical systems generated by iterations of multivariate polynomials with slow degree growth have proved to admit good estimates of exponential sums along their orbits which in turn lead to rather stronger bounds on the discrepancy for pseudorandom vectors generated by these iterations. Here we add new arguments to our original approach and also extend some of our recent constructions and results to more general orbits of polynomial iterations which may involve distinct polynomials as well. Using this construction we design a new class of hash functions from iterations of polynomials and use our estimates to motivate their “mixing ” properties. Subject Classification (2000). 11K45; 11T23; 11T71; 94A60 1.
Analyzing a Class of PseudoRandom Bit Generator through Inductive Machine Learning Paradigm
"... Abstract. Random number generation is an integral part of strong cipher systems. If a pseudorandom sequence can be predicted with better than chance probability then the generator is considered to be cryptographically weak. This paper deals with next bit prediction of pseudorandom binary sequences ..."
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Abstract. Random number generation is an integral part of strong cipher systems. If a pseudorandom sequence can be predicted with better than chance probability then the generator is considered to be cryptographically weak. This paper deals with next bit prediction of pseudorandom binary sequences generated by Linear Feedback Shift Register (LFSR) and LFSRbased pseudorandom bit generators (PRBG), using Inductive Machine Learning (ML) paradigm, namely C4.5 the most common and widely used inductive data mining algorithm. This machine learning technique has been introduced to convert the theoretical prediction problem into a classification problem, which we coined as Classificatory Prediction problem. We further extended the use of 2 Corresponding Author 1 this technique to predict next bit without having any knowledge of subsequent bits of the PRBG and can be termed as true Next Bit Predictor. The technique used is independent of the parameters and domain knowledge of the pseudorandom bit generators. The present study is a comprehensive extension of the work done by Hernandez et al [15]. We performed meticulous experiments (over wide range of LFSRs) and came out with a more explanatory analysis. Our classificatory prediction results paved the way for the evolution of the next bit prediction model.