Families of sequences with good family complexity and cross-correlation measure

In this paper we study pseudorandomness of a family of sequences in terms of two measures, the family complexity ($f$-complexity) and the cross-correlation measure of order $\ell$. We consider sequences not only on binary alphabet but also on $k$-symbols ($k$-ary) alphabet. We first generalize some known methods on construction of the family of binary pseudorandom sequences. We prove a bound on the $f$-complexity of a large family of binary sequences of Legendre-symbols of certain irreducible polynomials. We show that this family as well as its dual family have both a large family complexity and a small cross-correlation measure up to a rather large order. Next, we present another family of binary sequences having high $f$-complexity and low cross-correlation measure. Then we extend the results to the family of sequences on $k$-symbols alphabet.Comment: 13 pages. Comments are welcome

Construction and Applications of CRT Sequences

Protocol sequences are used for channel access in the collision channel without feedback. Each user accesses the channel according to a deterministic zero-one pattern, called the protocol sequence. In order to minimize fluctuation of throughput due to delay offsets, we want to construct protocol sequences whose pairwise Hamming cross-correlation is as close to a constant as possible. In this paper, we present a construction of protocol sequences which is based on the bijective mapping between one-dimensional sequence and two-dimensional array by the Chinese Remainder Theorem (CRT). In the application to the collision channel without feedback, a worst-case lower bound on system throughput is derived.Comment: 16 pages, 5 figures. Some typos in Section V are correcte

Analysis of symmetric key establishment based on reciprocal channel quantization

Methods of symmetric key establishment using reciprocal quantization of channel parameters in wireless Rayleigh and Rician fading channels are considered. Two important aspects are addressed through generic analysis: impact of a proximity attack by a passive eavesdropper and achievable key establishing rates. The analysis makes use of the National Institute of Standards and Technology statistical test suite applied to the channel quantization bits as the outputs of a random number generator. For proximity attacks, a passive mobile eavesdropper with an ability to approach one of the communicating parties and a possible signal-to-noise ratio advantage is assumed. The minimal required distance from the eavesdropper in order to maintain perfect secrecy during key establishment is evaluated as a function of the Rician factor and quantization depth. For key establishing rates, the maximal rates are evaluated while ensuring that the generated secret key bits pass the entire statistical test suite. The generic analysis is applied to channel-phase quantization and performance in practical systems is considered as well