  We consider a secure source coding problem with side information (S.I.) at
the decoder and the eavesdropper. The encoder has a source that it wishes to
describe with limited distortion through a rate limited link to a legitimate
decoder. The message sent is also observed by the eavesdropper. The encoder
aims to minimize both the distortion incurred by the legitimate decoder; and
the information leakage rate at the eavesdropper. When the encoder has access
to the uncoded S.I. at the decoder, we characterize the
rate-distortion-information leakage rate (R.D.I.) region under a Markov chain
assumption and when S.I. at the encoder does not improve the rate-distortion
region as compared to the case when S.I. is absent. When the decoder also has
access to the eavesdroppers S.I., we characterize the R.D.I. region without the
Markov Chain condition. We then consider a related setting where the encoder
and decoder obtain coded S.I. through a rate limited helper, and characterize
the R.D.I. region for several special cases, including special cases under
logarithmic loss distortion and for special cases of the Quadratic Gaussian
setting. Finally, we consider the amplification measures of list or entropy
constraint at the decoder, and show that the R.D.I. regions for the settings
considered in this paper under these amplification measures coincide with
R.D.I. regions under per symbol logarithmic loss distortion constraint at the
decoder.
