4 research outputs found
Maximum-order Complexity and Correlation Measures
We estimate the maximum-order complexity of a binary sequence in terms of its
correlation measures. Roughly speaking, we show that any sequence with small
correlation measure up to a sufficiently large order cannot have very small
maximum-order complexity
Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences
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.Comment: 23 pages, 5 figures, 4 table
Cryptography / Maximum-order complexity and correlation measures
We estimate the maximum-order complexity of a binary sequence in terms of its correlation measures. Roughly speaking, we show that any sequence with small correlation measure up to a sufficiently large order k cannot have very small maximum-order complexity.(VLID)219511