Lower bounds for the linear complexity of sequences over residue rings
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Binary sequences derived from ML-sequences over rings I: periods and minimal polynomials
Journal of Cryptology
A New Class of Invertible Mappings
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Distribution properties of compressing sequences derived from primitive sequences over Z/(pe)
IEEE Transactions on Information Theory
Random properties of the highest level sequences of primitive sequences over Z(2e)
IEEE Transactions on Information Theory
The most significant bit of maximum-length sequences over Z2l: autocorrelation and imbalance
IEEE Transactions on Information Theory
Compression mappings on primitive sequences over Z/(pe)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Injectivity of Compressing Maps on Primitive Sequences Over Z/(pe)
IEEE Transactions on Information Theory
Further Result of Compressing Maps on Primitive Sequences Modulo Odd Prime Powers
IEEE Transactions on Information Theory
Typical primitive polynomials over integer residue rings
Finite Fields and Their Applications
On the distinctness of maximal length sequences over Z/(pq) modulo 2
Finite Fields and Their Applications
A new result on the distinctness of primitive sequences over Z/ (pq) modulo 2
Finite Fields and Their Applications
Compressing Mappings on Primitive Sequences over Z/(2e) and Its Galois Extension
Finite Fields and Their Applications
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This paper studies the distinctness of modular reductions of primitive sequences over $${\mathbf{Z}/(2^{32}-1)}$$ . Let f(x) be a primitive polynomial of degree n over $${\mathbf{Z}/(2^{32}-1)}$$ and H a positive integer with a prime factor coprime with 232驴1. Under the assumption that every element in $${\mathbf{Z}/(2^{32}-1)}$$ occurs in a primitive sequence of order n over $${\mathbf{Z}/(2^{32}-1)}$$ , it is proved that for two primitive sequences $${\underline{a}=(a(t))_{t\geq 0}}$$ and $${\underline{b}=(b(t))_{t\geq 0}}$$ generated by f(x) over $${\mathbf{Z}/(2^{32}-1), \underline{a}=\underline{b}}$$ if and only if $${a\left( t\right) \equiv b\left( t\right) \bmod{H}}$$ for all t 驴 0. Furthermore, the assumption is known to be valid for n between 7 and 100, 000, the range of which is sufficient for practical applications.