A simple unpredictable pseudo random number generator
SIAM Journal on Computing
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
On the Linear Complexity of the Power Generator
Designs, Codes and Cryptography
On the Distribution of Nonlinear Recursive Congruential Pseudorandom Numbers of Higher Orders
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Iterations of Multivariate Polynomials and Discrepancy of Pseudorandom Numbers
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
The security of all RSA and discrete log bits
Journal of the ACM (JACM)
Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
On the provable security of an efficient RSA-Based pseudorandom generator
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Pseudorandom vector sequences of maximal period generated by triangular polynomial dynamical systems
Designs, Codes and Cryptography
On the linear complexity profile of the power generator
IEEE Transactions on Information Theory
Properties of the x2 mod N pseudorandom number generator
IEEE Transactions on Information Theory
Multivariate permutation polynomial systems and nonlinear pseudorandom number generators
Finite Fields and Their Applications
On pseudorandom numbers from multivariate polynomial systems
Finite Fields and Their Applications
Exponential sums for nonlinear recurring sequences
Finite Fields and Their Applications
On the Average Distribution of Inversive Pseudorandom Numbers
Finite Fields and Their Applications
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We obtain a new estimate on the discrepancy of the power generator over a part of the period that improves several previous results. We also introduce a multidimensional analogue and show that the corresponding vector sequence is uniformly distributed, provided it is of a sufficiently large period. This result is based on a recent estimate of T. Cochrane and C. Pinner on binomial exponential sums. Our construction extends the class of nonlinear pseudorandom number generators for which a power saving against the trivial bound is possible in estimates of their discrepancy. It has several additional properties such as high nonlinearity and inhomogeneity which may be useful for its cryptographic applications.