Cryptographic properties of some binary generalized cyclotomic sequences with the length p2☆

New generalized cyclotomic binary sequences of period $$p^2$$ p 2

“…We calculate the well-distribution measure and correlation measure of the cyclotomic sequences of period p 2 constructed in this paper. The numerical results show that in the case f = 2, the correlation measure of order 2 of all sequences in this paper are smaller than that of the sequences in [7,9,23]. Moreover, both the well-distribution measure and the correlation measure of order k for 1 ≤ k ≤ 4 of all sequences are below the upper bound p log(p 2 ), which indicates that the cyclotomic sequences in this paper are potentially " good " in terms of these pseudorandomness measures.…”

“…Several binary sequences of period p 2 were constructed from this generalized cyclotomy [7,9,13]. In the case of f = 2, the generalized cyclotomic binary sequences of period p 2 with the characteristic set pZ p ∪ D were introduced in [7,9] and their properties were further investigated in [23]. Recently, the linear complexity of the generalized cyclotomic binary sequences with the characteristic set…”

“…, the linear complexity of these sequences is larger than that of those cyclotomic sequences in [7,23,13]. For cryptographic applications, high linear complexity does not necessarily guarantee the cryptographic strength of a sequence and the linear complexity profile should be also taken into consideration.…”

“…The analysis of the number of solutions to the system enables us to characterize necessary and sufficient conditions for the polynomial p 2 −1 i=0 s i x i to share roots with x p 2 − 1, and to eventually determine the linear complexity of the new generalized cyclotomic sequences. The linear complexity of the constructed cyclotomic sequences is, in general, larger than that of the generalized cyclotomic sequences of period p 2 in [7], [23] and [13]. For small primes p, the numerical result indicates that the cyclotomic sequences are "good" in terms of the linear complexity profile [20], the well-distribution measure and the correlation measure [19] of pseudorandom sequences.…”

Linear complexity of binary Whiteman generalized cyclotomic sequences of order 2k

“…Although most of these new sequences have been proved to possess good linear complexity [2,10,11,[13][14][15][16], but their properties of correlation are not good enough [14,16].…”