Correlation measures of binary sequences derived from Euler quotients
This work addresses the suitability of specific number-theoretic sequences for cryptography, but it is incremental as it builds on prior studies of these sequences.
The paper tackled the problem of evaluating the correlation measures of pseudorandom binary sequences derived from Euler quotients, finding that the 4-order correlation measures are very large, which suggests these sequences may not be suitable for cryptographic applications.
Fermat-Euler quotients arose from the study of the first case of Fermat's Last Theorem, and have numerous applications in number theory. Recently they were studied from the cryptographic aspects by constructing many pseudorandom binary sequences, whose linear complexities and trace representations were calculated. In this work, we further study their correlation measures by using the approach based on Dirichlet characters, Ramanujan sums and Gauss sums. Our results show that the $4$-order correlation measures of these sequences are very large. Therefore they may not be suggested for cryptography.