Methods, systems, and apparatus for efficiently authenticating a document (e.g. a credit card) having a magnetic stripe are provided. The magnetic field at different points of the magnetic stripe are measured, e.g., by a checkout scanner to create a magnetic signature. Digital samples of the measurements may be transformed into coefficients of continuous basis functions, e.g., a Fourier transform. These coefficients are then compared to reference values (e.g. corresponding coefficients) to produce a measure of the authenticity of the document. The number of coefficients used can advantageously be smaller than the number of digital samples without compromising accuracy, thus using less bandwidth between a scanner and an authentication entity.