  Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor
fields) belong, together with Majorana spinor fields, to a wider class of
spinor fields, the so-called flagpole spinor fields, corresponding to the class
(5), according to Lounesto spinor field classification based on the relations
and values taken by their associated bilinear covariants. There exists only six
such disjoint classes: the first three corresponding to Dirac spinor fields,
and the other three respectively corresponding to flagpole, flag-dipole and
Weyl spinor fields. This paper is devoted to investigate and provide the
necessary and sufficient conditions to map Dirac spinor fields to ELKO, in
order to naturally extend the Standard Model to spinor fields possessing mass
dimension one. As ELKO is a prime candidate to describe dark matter, an
adequate and necessary formalism is introduced and developed here, to better
understand the algebraic, geometric and physical properties of ELKO spinor
fields, and their underlying relationship to Dirac spinor fields.
