  A $K$-user secure Gaussian Multiple-Access-Channel (MAC) with an external
eavesdropper is considered in this paper. An achievable rate region is
established for the secure discrete memoryless MAC. The secrecy sum capacity of
the degraded Gaussian MIMO MAC is proven using Gaussian codebooks. For the
non-degraded Gaussian MIMO MAC, an algorithm inspired by interference alignment
technique is proposed to achieve the largest possible total
Secure-Degrees-of-Freedom (S-DoF). When all the terminals are equipped with a
single antenna, Gaussian codebooks have shown to be inefficient in providing a
positive S-DoF. Instead, a novel secure coding scheme is proposed to achieve a
positive 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. It is proven that the total S-DoF of $\frac{K-1}{K}$ can be
achieved for almost all channel gains. For the other channel gains, a
multi-layer coding scheme is proposed to achieve a positive S-DoF. As a
function of channel gains, therefore, the achievable S-DoF is discontinued.
