Nina Brandstätter

Some notes on the two-prime generator of order 2

The two-prime generator of order 2 has several desirable randomness properties if the two primes are chosen properly. In particular, Ding deduced exact formulas for the (periodic) autocorrelation and the linear complexity of these sequences. In this note, we analyze parts of the period of the two-prime generator of order 2 and obtain bounds on the aperiodic autocorrelation and linear complexity profile.

Linear complexity profile of binary sequences with small correlation measure

SummaryA high linear complexity profile is a desirable feature of sequences used for cryptographical purposes. For a given binary sequence we estimate its linear complexity profile in terms of the correlation measure, which was introduced by Mauduit and Sárközy. We apply this result to certain periodic sequences including Legendre sequences, Sidelnikov sequences and other sequences related to the discrete logarithm.

Correlation of the two-prime Sidel'nikov sequence

Motivated by the concepts of Sidel’nikov sequences and two-prime generator (or Jacobi sequences) we introduce and analyze some new binary sequences called two-prime Sidel’nikov sequences. In the cases of twin primes and cousin primes equivalent 3 modulo 4 we show that these sequences are balanced. In the general case, besides balancedness we also study the autocorrelation, the correlation measure of order k and the linear complexity profile of these sequences showing that they have many nice pseudorandom features.

-error linear complexity over p of subsequences of Sidelnikov sequences of period (pr – 1)/3

Abstract Subsequences of Sidelnikov sequences have several desirable cryptographic features such as high linear complexity over 𝔽2 and small aperiodic autocorrelation. Here we analyse the k-error linear complexity over 𝔽 p of subsequences of Sidelnikov sequences of length (q –1)/3. The proofs are based on results on equations with binomial coefficients modulo p partly obtained using character sum techniques.