Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences Année : 2021

Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences

Résumé

Automatic sequences are not suitable sequences for cryptographic applications since both their subword complexity and their expansion complexity are small, and their correlation measure of order 2 is large. These sequences are highly predictable despite having a large maximum order complexity. However, recent results show that polynomial subsequences of automatic sequences, such as the Thue–Morse sequence, are better candidates for pseudorandom sequences. A natural generalization of automatic sequences are morphic sequences, given by a fixed point of a prolongeable morphism that is not necessarily uniform. In this paper we prove a lower bound for the maximum order complexity of the sum of digits function in Zeckendorf base which is an example of a morphic sequence. We also prove that the polynomial subsequences of this sequence keep large maximum order complexity, such as the Thue–Morse sequence.

Dates et versions

hal-03283528 , version 1 (10-07-2021)

Identifiants

Citer

Damien Jamet, Pierre Popoli, Thomas Stoll. Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences. Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences , 2021, ⟨10.1007/s12095-021-00507-w⟩. ⟨hal-03283528⟩
72 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More