  A new achievability rate region for the secure discrete memoryless
Multiple-Access-Channel (MAC) is presented. Thereafter, a novel secure coding
scheme is proposed to achieve a positive Secure Degrees-of-Freedom (S-DoF) in
the single-antenna MAC. This scheme converts the single-antenna system into a
multiple-dimension system with fractional dimensions. The achievability scheme
is based on the alignment of signals into a small sub-space at the
eavesdropper, and the simultaneous separation of the signals at the intended
receiver. Tools from the field of Diophantine Approximation in number theory
are used to analyze the probability of error in the coding scheme.
