Takeru Miyazaki

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.

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 consideration on a common template-based biometric cryptosystem using on-line signatures

Recently, with the rapid spread of smartphones and tablet PCs, biometric authentication using handwritten signatures has been attracting much interest. However, little research has been reported on biometric template protection, which is indispensable for protecting ones privacy, especially when those devices are used in a network environment. Therefore, as a means of (biometric) template protection, we propose a common template-based biometric cryptosystem that is suitable for signature-based biometric authentication. The results of the simulation using signature data confirmed the effectiveness of the proposed method.

Linear complexity of pseudo random binary sequence generated by trace function and Legendre symbol over proper sub extension field

The authors have proposed an approach for generating a pseudo random binary sequence by using primitive polynomial, trace function, and Legendre symbol over the proper sub extension field. There are many uses of pseudo random binary sequence in security applications. The linear complexity of a sequence is considered as the most important property to be analyzed in these types of applications. In this paper, the authors have restricted the discussion on the linear complexity and linear complexity profile properties of the proposed sequence based on some experimental results. According to the results, the proposed sequence always holds a maximum value of the linear complexity.

Biometric Bit String Generation from Handwritten Signatures on Smart Device

Recently, with the rapid spread of smart devices, such as smart-phones and tablet PCs, biometric authentication using handwritten signatures on such devices has been attracting much interest. However, little research has been reported on biometric-bit-string generation from handwritten signatures, which is indispensable for biometric-template protection on smart devices. Therefore, for designing a more secure template-protection method for smart devices, we propose a biometric-bit-string-generation method from handwritten signatures collected on such devices. The simulation results confirmed the effectiveness of the proposed method.