Analysis and design of stream ciphers
Analysis and design of stream ciphers
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Finite fields
Linear complexity, k-error linear complexity, and the discrete Fourier transform
Journal of Complexity
A Fourier Transform Approach to the Linear Complexity of Nonlinearly Filtered Sequences
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
The expected value of the joint linear complexity of periodic multisequences
Journal of Complexity
IEEE Transactions on Information Theory
Counting functions and expected values for the lattice profile at n
Finite Fields and Their Applications
On the structure of inversive pseudorandom number generators
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Recent results on recursive nonlinear pseudorandom number generators
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Structure of pseudorandom numbers derived from fermat quotients
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
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The lattice profile analyzes the intrinsic structure of pseudorandom number sequences with applications in Monte Carlo methods and cryptology. In this paper, using the discrete Fourier transform for periodic sequences and the relation between the lattice profile and the linear complexity, we give general formulas for the expected value, variance, and counting function of the lattice profile of periodic sequences with fixed period. Moreover, we determine in a more explicit form the expected value, variance, and counting function of the lattice profile of periodic sequences for special values of the period.