A simple unpredictable pseudo random number generator
SIAM Journal on Computing
Toward a theory of Pollard's rho method
Information and Computation
Algorithmic number theory
Finite fields
Analysis of Iterated Modular Exponentiation: The Orbitsof x^α mod N
Designs, Codes and Cryptography
Cryptography: Theory and Practice
Cryptography: Theory and Practice
Handbook of Applied Cryptography
Handbook of Applied Cryptography
On the distribution of the power generation
Mathematics of Computation
Period of the power generator and small values of Carmichael's function
Mathematics of Computation
The Security of Individual RSA Bits
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The Security of Individual RSA Bits
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Stronger security proofs for RSA and rabin bits
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Properties of the x2 mod N pseudorandom number generator
IEEE Transactions on Information Theory
Designs, Codes and Cryptography
Deterministic Computation of Pseudorandomness in Sequences of Cryptographic Application
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
Recent results on recursive nonlinear pseudorandom number generators
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
A deterministic approach to balancedness and run quantification in pseudorandom pattern generators
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
Interpolation of functions related to the integer factoring problem
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
On the power generator and its multivariate analogue
Journal of Complexity
Finite Fields and Their Applications
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We obtain a lower bound on the linear complexity of the powergenerator of pseudo-random numbers, which in some special cases is alsoknown as the RSA generator and as the Blum–Blum–Shubgenerator. In some very important cases this bound is essentially thebest possible. In particular, this implies that lattice reductionattacks on such generators are not feasible.