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This paper presents an optimized method to reduce the points number to be used in order to identify a person using fuzzy fingerprints. Two fingerprints are similar if n out of N points from the skin are identical. We discuss the criteria used for choosing these points. We also describe the properties of fuzzy logic and the classical methods applied on fingerprints. Our method compares two matching sets and selects the optimal set from these, using a fuzzy reasoning system. The advantage of our method with respect to the classical existing methods consists in a smaller number of calculations.

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In order to construct the border solutions for nonsupersingular elliptic curve equations, some common used models need to be adapted from linear treated cases for use in particular nonlinear cases. There are some approaches that conclude with these solutions. Optimization in this area means finding the majority of points on the elliptic curve and minimizing the time to compute the solution in contrast with the necessary time to compute the inverse solution. We can compute the positive solution of PDE (partial differential equation) like oscillations of f (s)/s around the principal eigenvalueTranslating mathematics into cryptographic applications will be relevant in everyday life, wherein there are situations in which two parts that communicate need a third part to confirm this process. For example, if two persons want to agree on something they need an impartial person to confirm this agreement, like a notary. This third part does not influence in any way the communication process. It is just a witness to the agreement. We present a system where the communicating parties do not authenticate one another. Each party authenticates itself to a third part who also sends the keys for the encryption/decryption process. Another advantage of such a system is that if someone (sender) wants to transmit messages to more than one person (receivers), he needs only one authentication, unlike the classic systems where he would need to authenticate himself to each receiver. We propose an authentication method based on zero-knowledge and elliptic curves.