This work presents a new and efficient approach to discriminative speaker verification in the i-vector space. We illustrate the development of a linear discriminative classifier that is trained to discriminate between the hypothesis that a pair of feature vectors in a trial belong to the same speaker or to different speakers. This approach is alternative to the usual discriminative setup that discriminates between a speaker and all the other speakers. We use a discriminative classifier based on a Support Vector Machine (SVM) that is trained to estimate the parameters of a symmetric quadratic function approximating a log-likelihood ratio score without explicit modeling of the i-vector distributions as in the generative Probabilistic Linear Discriminant Analysis (PLDA) models. Training these models is feasible because it is not necessary to expand the i -vector pairs, which would be expensive or even impossible even for medium sized training sets. The results of experiments performed on the tel-tel extended core condition of the NIST 2010 Speaker Recognition Evaluation are competitive with the ones obtained by generative models, in terms of normalized Detection Cost Function and Equal Error Rate. Moreover, we show that it is possible to train a gender-independent discriminative model that achieves state-of-the-art accuracy, comparable to the one of a gender-dependent system, saving memory and execution time both in training and in testing.