Random digital encryption secure communication system

The design of a secure communication system is described. A product code, formed from two pseudorandom sequences of digital bits, is used to encipher or scramble data prior to transmission. The two pseudorandom sequences are periodically changed at intervals before they have had time to repeat. One of the two sequences is transmitted continuously with the scrambled data for synchronization. In the receiver portion of the system, the incoming signal is compared with one of two locally generated pseudorandom sequences until correspondence between the sequences is obtained. At this time, the two locally generated sequences are formed into a product code which deciphers the data from the incoming signal. Provision is made to ensure synchronization of the transmitting and receiving portions of the system

Pseudorandom number generator based on the Bernoulli map on cubic algebraic integers

We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact computation. In particular, we clarify a way to properly prepare a set of initial points (i.e., seeds), which is needed when generating multiple pseudorandom sequences. With this seed selection method, we can distribute the initial points almost uniformly in the unit interval and can also guarantee that the orbits starting from them do not merge. We also report results of a large variety of tests indicating that the generated pseudorandom sequences have good statistical properties as well as an advantage over what is probably the most popular generator, the Mersenne Twister MT19937

Підходи до визначення випадкових послідовностей

Приводяться та порівнюються різні означення випадкових та псевдовипадкових послідовностей. Розглядається питання про тестування послідовностей.Different definitions of random and pseudorandom sequences are compared. Question about testing of sequences is considered. Random and pseudorandom sequences, testing

Generation of further pseudorandom binary sequences, I (Blowing up a single sequence)

Assume that a binary sequence is given with strong pseudorandom properties. An algorithm is presented and studied which prepares many further binary sequences from the given one. It is shown that if certain conditions hold then each of the sequences obtained in this way also possesses strong pseudorandom properties. Moreover, it is proved that certain large families of these sequences also posses strong pseudorandom properties

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