Boolean function

Abstract: We define the notions of reducibility and completeness in multi-party private computations. Let g be an n-argument function. We say that a function f is reducible to g if n honest-but-curious players can compute the function f n-privately, given a black-box for g (for which they secretly give inputs and get the result of operating g on these inputs). We say that g is complete (for multi-party private computations) if every function f is reducible to g. In this paper, we characterize the complete Boolean functions: we show that a Boolean function g is complete if and only if g itself cannot be computed n-privately (when there is no black-box available). Namely, for Boolean functions, the notions of completeness and n-privacy are complementary. This characterization gives a huge collection of complete functions (any non-private Boolean function!) compared to very few examples given (implicitly) in previous work. On the other hand, for non-Boolean functions, we show that these two notions are not complementary. Our results can be viewed as a generalization (for multi-party protocols and for (n/spl ges/2)-argument functions) of the two-party case, where it was known that Oblivious Transfer protocol (and its variants) are complete. >

Abstract: In this paper, a novel method is being proposed to construct a substitution box or Boolean function for block ciphers using Gaussian distribution and linear fractional transform. The substitution box is constructed by employing a linear fractional transform based on Box–Muller transform, polarization decision, and central limit algorithm. The cryptographic strength of the proposed S-boxes is evaluated with standardized tests such as linear approximation probability, unified averaged changed intensity, bit independent criterion, histogram analysis, nonlinearity score, strict avalanche criterion, and differential approximation probability. The results show that the proposed substitution box achieves better cryptographic strength as compared with the state-of-the-art techniques.

Abstract: A reversible circuit maps each output vector into a unique input vector, and vice versa. CMOS reversible / adiabatic circuits are currently the most important approaches to power optimization. This paper introduces an approach to synthesize generalized multi-rail reversible cascades for singleoutput Boolean functions. Minimizing the “garbage bits” is the main challenge of reversible logic synthesis. Experimental results over a set of single output functions (derived from Espresso PLAs) will be presented at IWLS 2002.

Abstract: Very recently a new passive circuit element called memristor has been extensively investigated by researchers, which can be used for a variety of applications. This two-terminal device having few nanometer dimensions has been experimentally shown to possess both memory and resistor properties. This has also received great attention due to the fact that these devices can very easily be integrated on CMOS subsystems. Most of the logic design works in this context are based on material implication operation which can be very efficiently implemented using memristors. In this paper we propose an efficient realization of 2-to-1 multiplexer using memristors, and hence present a synthesis methodology that represents a given Boolean function as a Reduced Ordered Binary Decision Diagram (ROBDD) and then maps the same to memristor implementation.