An Efficient and Verifiable Solution to the Millionaire Problem

A new solution to the millionaire problem is designed on the base of two new techniques: zero test and batch equation. Zero test is a technique used to test whether one or more ciphertext contains a zero without revealing other information. Batch equation is a technique used to test equality of multiple integers. Combination of these two techniques produces the only known solution to the millionaire problem that is correct, private, publicly verifiable and efficient at the same time.

Creative design and the generative evolutionary paradigm

Design as seen from the designer's perspective is a series of amazing imaginative jumps or creative leaps. But design as seen by the design historian is a smooth progression or evolution of ideas that they seem self-evident and inevitable after the event. But the next step is anything but obvious for the artist/creator/inventor/designer stuck at that point just before the creative leap. They know where they have come from and have a general sense of where they are going, but often do not have a precise target or goal. This is why it is misleading to talk of design as a problem-solving activity - it is better defined as a problem-finding activity. This has been very frustrating for those trying to assist the design process with computer-based, problem-solving techniques. By the time the problem has been defined, it has been solved. Indeed the solution is often the very definition of the problem. Design must be creative-or it is mere imitation. But since this crucial creative leap seem inevitable after the event, the question must arise, can we find some way of searching the space ahead? Of course there are serious problems of knowing what we are looking for and the vastness of the search space. It may be better to discard altogether the term "searching" in the context of the design process: Conceptual analogies such as search, search spaces and fitness landscapes aim to elucidate the design process. However, the vastness of the multidimensional spaces involved make these analogies misguided and they thereby actually result in further confounding the issue. The term search becomes a misnomer since it has connotations that imply that it is possible to find what you are looking for. In such vast spaces the term search must be discarded. Thus, any attempt at searching for the highest peak in the fitness landscape as an optimal solution is also meaningless. Futhermore, even the very existence of a fitness landscape is fallacious. Although alternatives in the same region of the vast space can be compared to one another, distant alternatives will stem from radically different roots and will therefore not be comparable in any straightforward manner (Janssen 2000). Nevertheless we still have this tantalizing possibility that if a creative idea seems inevitable after the event, then somehow might the process be rserved? This may be as improbable as attempting to reverse time. A more helpful analogy is from nature, where it is generally assumed that the process of evolution is not long-term goal directed or teleological. Dennett points out a common minsunderstanding of Darwinism: the idea that evolution by natural selection is a procedure for producing human beings. Evolution can have produced humankind by an algorithmic process, without its being true that evolution is an algorithm for producing us. If we were to wind the tape of life back and run this algorithm again, the likelihood of "us" being created again is infinitesimally small (Gould 1989; Dennett 1995). But nevertheless Mother Nature has proved a remarkably successful, resourceful, and imaginative inventor generating a constant flow of incredible new design ideas to fire our imagination. Hence the current interest in the potential of the evolutionary paradigm in design. These evolutionary methods are frequently based on techniques such as the application of evolutionary algorithms that are usually thought of as search algorithms. It is necessary to abandon such connections with searching and see the evolutionary algorithm as a direct analogy with the evolutionary processes of nature. The process of natural selection can generate a wealth of alternative experiements, and the better ones survive. There is no one solution, there is no optimal solution, but there is continuous experiment. Nature is profligate with her prototyping and ruthless in her elimination of less successful experiments. Most importantly, nature has all the time in the world. As designers we cannot afford prototyping and ruthless experiment, nor can we operate on the time scale of the natural design process. Instead we can use the computer to compress space and time and to perform virtual prototyping and evaluation before committing ourselves to actual prototypes. This is the hypothesis underlying the evolutionary paradigm in design (1992, 1995).