In this paper a new variant of the linear cryptanalysis method for block ciphers is proposed. It is based on the existing method of multidimensional linear cryptanalysis, but offers the option of discarding a whole half-space of linear approximations that do not contribute to statistical nonrandomness of the multidimensional linear cryptanalysis, and keep only the information extracted from an affine subspace for statistical inference. Also the connections of the new affine cryptanalysis with conditional linear cryptanalysis and multiple linear cryptanalysis are described and demonstrated in the context of state-of-the-art ciphers.