Nadir Murru

Gessica Alecci, Simone Dutto, Nadir Murru

We present a study on the use of Pell hyperbolas in cryptosystems with security based on the discrete logarithm problem. Specifically, after introducing the group's structure over generalized Pell conics (and also giving the explicit isomorphisms with the classical Pell hyperbolas), we provide a parameterization with both an algebraic and a geometrical approach. The particular parameterization that we propose appears to be useful from a cryptographic point of view because the product that arises over the set of parameters is connected to the Rédei rational functions, which can be evaluated in a fast way. Thus, we exploit these constructions for defining three different public key cryptosystems based on the ElGamal scheme. We show that the use of our parameterization allows to obtain schemes more efficient than the classical ones based on finite fields.

Nadir Murru, Rosaria Rossini

Convergence rate of training algorithms for neural networks is heavily affected by initialization of weights. In this paper, an original algorithm for initialization of weights in backpropagation neural net is presented with application to character recognition. The initialization method is mainly based on a customization of the Kalman filter, translating it into Bayesian statistics terms. A metrological approach is used in this context considering weights as measurements modeled by mutually dependent normal random variables. The algorithm performance is demonstrated by reporting and discussing results of simulation trials. Results are compared with random weights initialization and other methods. The proposed method shows an improved convergence rate for the backpropagation training algorithm.

Giuseppe Airò Farulla, Nadir Murru, Rosaria Rossini

The problem of correctly segmenting touching characters is an hard task to solve and it is of major relevance in pattern recognition. In the recent years, many methods and algorithms have been proposed; still, a definitive solution is far from being found. In this paper, we propose a novel method based on fuzzy logic. The proposed method combines in a novel way three features for segmenting touching characters that have been already proposed in other studies but have been exploited only singularly so far. The proposed strategy is based on a 3--input/1--output fuzzy inference system with fuzzy rules specifically optimized for segmenting touching characters in the case of Latin printed and handwritten characters. The system performances are illustrated and supported by numerical examples showing that our approach can achieve a reasonable good overall accuracy in segmenting characters even on tricky conditions of touching characters. Moreover, numerical results suggest that the method can be applied to many different datasets of characters by means of a convenient tuning of the fuzzy sets and rules.

Giuseppe Airò Farulla, Tiziana Armano, Anna Capietto et al.

Optical Character Recognition software (OCR) are important tools for obtaining accessible texts. We propose the use of artificial neural networks (ANN) in order to develop pattern recognition algorithms capable of recognizing both normal texts and formulae. We present an original improvement of the backpropagation algorithm. Moreover, we describe a novel image segmentation algorithm that exploits fuzzy logic for separating touching characters.

Emanuele Bellini, Nadir Murru

We define an isomorphism between the group of points of a conic and the set of integers modulo a prime equipped with a non-standard product. This product can be efficiently evaluated through the use of Rédei rational functions. We then exploit the isomorphism to construct a novel RSA-like scheme. We compare our scheme with classic RSA and with RSA-like schemes based on the cubic or conic equation. The decryption operation of the proposed scheme turns to be two times faster than RSA, and involves the lowest number of modular inversions with respect to other RSA-like schemes based on curves. Our solution offers the same security as RSA in a one-to-one communication and more security in broadcast applications.