Shunsuke Araki

A study on relations between loops in sequences generated by the logistic map over integers and real numbers

We are interested in properties of the logistic maps with finite precision and theirs sequences. In this paper, we focus on a cyclic part, which we call a loop, in a sequence generated by the logistic map over integers successively, since the loop always exists in the sequence. We can observe loops in sequences generated by the logistic map with irrational numbers as initial values. We will show the relations between loops in sequences generated by the map over integers and real numbers. We will also show a correspondence between these loops by averages of squared differences.

A study on occurrence rates per bit for the logistic map over integers

We are investigating the logistic map over integers with finite precisions and sequences out-putted by the iterative mapping. In our proposed simple pseudo-random number generator with the logistic map over integers, we implicitly assumed that 0 and 1 occurrence frequencies per bit of outputs by the map are nearly equal. By some numerical experiments, we got the conjecture that occurrence rates per bit are nearly equal for many bits of 2n-bit values in the intermediate step of the map by one iteration and many iterations.

A study on initial values of the logistic map over integers

We are investigating the logistic may over intergers with finite precision and sequences outputted by the interative mapping. One of our goals is to provide a guide-line for design of pseudorandom number generators with the map. In this paper, we set a basic model in which internal initial values are updated after a certain iteration, and show that an updating way of the internal initial value does not have a critical influence on radomness of output by the basic model with minor exceptions.

Suitable representation of values on the logistic map with finite precision

We are investigating the logistic map over integers and its pseudorandom number generator. Focusing on differences between the logistic maps over floating-point numbers and over integers, we herein show that the integer format is a suitable representation for implementing the logistic map on computers with limited memories.

Period and link length of logistic map over integers

On the designing of a pseudo-random number generator from a sequence generated by the logistic map, period and link length of the sequence are important for good randomness. In this paper, we focus loops and links of sequences generated by the logistic map over integers. Since their periods and link lengths of them depend on an available bit. We consider the relation between the available bit and expected values of them.

Improvement of Tseng et al.'s authenticated encryption scheme with message linkages

An authenticated encryption scheme is a message transmission scheme which sends messages in a secure and authentic way. In large message transmission, traditional authenticated encryption scheme has the disadvantage that the communication and the computation costs are too high. Recently, Tseng et al. proposed an authenticated encryption scheme with message linkages to reduce the computation time and communication costs for large message transmission. In this paper, the authors point out a weakness in Tseng et al.s scheme. Finally, we present a new authenticated encryption scheme with message linkages to overcome the weakness in Tseng et al.s scheme. The proposed scheme is based on the Meta-message recovery signature scheme and it is efficient in the terms of communication and computation costs.

Analysis and Visualization of Traffic Conditions of Road Network by Route Bus Probe Data

In recent years, route bus service systems have been collecting and accumulating bus probe data such as GPS positions and traffic speeds from all route buses, day after day. In the present paper, we propose a method to analyze the conditions of a road traffic network from a huge amount of the route bus probe data. First, we show a conversion method from the probe data to a road segment data set. Second, we introduce analysis methods that compute the degree of congestion and reachable areas from the road segment data set. Finally, we discuss road segment data structures for rapid calculations of these analytical methods.

Relations between periods and control parameters in the logistic map over integers

In this present paper, we give results that a decrease of the control parameter in the logistic map over integers causes to disappear several loops which have specified periods. We derive the theoretical lower bound of the control parameter for a potential of existing the loop with an odd period on the logistic map over integers.

A study on differences in properties of the logistic maps over integers affected by rounding

On the studies of the logistic map, many reports are presented because of the simple structure of the equation. Calculations with finite precision are usually used for implementations of the map for computers. Then a rounding is needed to these calculations. There are five major methods to implement rounding, but there was not any paper on the rounding of the map. In the present paper, we get some experimental results that the properties of sequences change greatly by roundings, and give some theoretical analyses of them. Then we will give principal reasons that the map with a floor function for rounding generates long aperiodic subsequences.

A terminal authentication with transiting nodes by SymPC on an ad-hoc network

In this paper, we propose an one-sided authentication method by the SymPC which is a homomorphic symmetric encryption in an ad-hoc network such as a sensor network. In our protocol, a manager can authorize a node and know transiting nodes between them by using secret keys of their nodes.