The majority-gate and the inverter-gate together make a universal set of Boolean primitives in Quantum-dot Cellular Automata (QCA) circuits. An important step in designing QCA circuits is reducing the number of required primitives to implement a given Boolean function. This paper presents a method to reduce the number of primitive gates in a multi-output Boolean circuit. It extends the previous methodology based on genetic algorithm for converting sum of product expressions into a reduced number of QCA primitive gates in a single-output Boolean circuit. Simulation results show that the proposed method is able to reduce the number of primitive gates.

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In this paper an estimation technique for the data hiding capacity in biometric images is presented. We consider the QSWT algorithm for data hiding in biometric images and investigate the effect of message strength in increasing capacity in the presence of different types of attacks.Index terms-data hiding, image watermarking, DWT, QSWT, channel capacity. I-IntroductionData hiding refers to embedding information within a host data such as text, audio, image or video. In watermarking applications, the hidden data represents authorship information, a time stamp or copyright information [1]. Data hiding in biometric images has been proposed to make the biometric systems secure and resilient to deliberate manipulations and attacks.Data hiding capacity is a measure of the amount of information that can be hidden in a digital image while satisfying requirements such as robustness and invisibility. Estimating the capacity can set an upperbound to the amount of data that can be hidden in an image, therefore it can help in the design of efficient data hiding algorithms. There has been ongoing research in data hiding capacity estimation in recent years. In [2], each pixel is considered as an independent channel and the capacity is calculated based on the theory of parallel Gaussian channels. Reference [3] presents an information theoretic model for data hiding and studies the capacity problem under several types of attacks. In [4], zero-error information hiding capacity in JPEG-compressed domain is presented. Reference [5], presents an analysis of watermarking capacity based on the content of wavelet sub-bands and uses the concept of wavelet quantization matrix and Noise Visibility Function.The factors determining data hiding capacity include (1) the statistical model used for the host image, (2) the distortion constraints placed on the data hider and the attacker, and (3) the information available to the data hider, attacker and decoder. In fact, the content of an image has great influence on its data hiding capacity.Data hiding capacity can also be influenced by the watermark strength, but high strength does not necessarily imply high capacity, as will be shown in simulation results. In previous works [2][3][4][5], capacity is estimated for data hiding in wavelet domain. In those works, the watermark strength is constrained based on the content of wavelet sub-bands.In this paper, a framework for estimating the capacity of data hiding in biometric images based on QSWT algorithm is presented. Automated biometrics can provide accurate and reliable user authentication method. Watermarking biometric images can guarantee secure transmission of acquired images from intelligence agencies to a central image data base [6]. We assume that these watermarked biometric images are used for automatic user recognition and authentication. Since authentication will be done automatically, considerations of Human Visual System in watermarking can be ignored to some extent. In other words, in this proposed scheme, watermark (message) streng...