  Strong gravitational lensing is a unique tool to model with great accuracy
the inner mass distribution of massive galaxy clusters. In particular, clusters
with large Einstein radii provide a wealth of multiply imaged systems in the
cluster core allowing to determine precisely the shape of the central dark
matter profile. This paper presents a spectroscopic survey in the massive
cluster Abell 1703, displaying a large Einstein radius (28" at z=2.8) and a
high number of strongly-lensed systems including a central ring-like
configuration. We used LRIS on Keck to target multiple images and lensed galaxy
candidates, and use the measured redshifts to constrain the mass distribution
of the cluster using a parametric model. The data enable us to measure accurate
redshifts in good agreement with their photometric redshifts, and to update the
identification of multiply imaged systems by discovering 3 new systems and a
radial counter image. We also report the discovery of a remarkably bright ~3.6
L* i-band dropout at z=5.827 in our mask which is only moderately magnified by
the cluster (~3.0+/-0.08). The improved parametric mass model, including 16
multiple systems with 10 spectroscopic redshifts, further constrains the
cluster-scale mass distribution with a generalized NFW profile of best-fit
logarithmic slope alpha=0.92+/-0.04, concentration c200=4.72+/-0.40 and scale
radius rs=476+/-45 kpc. Our strong-lensing model predicts a large scale shear
signal consistent with Subaru weak-lensing measurements out to 4 Mpc h^-1.
Together with the fact that the strong-lensing modeling requires a single dark
matter clump, this suggests that Abell 1703 is a relaxed, unimodal cluster.
This unique cluster could be probed further using deep X-ray, SZ and dynamics
analysis, for a detailed study of the physics in a relaxed cluster. (abridged)
