  We construct locally decodable codes (LDCs) to correct insertion-deletion
errors in the setting where the sender and receiver share a secret key or where
the channel is resource-bounded. Our constructions rely on a so-called
"Hamming-to-InsDel" compiler (Ostrovsky and Paskin-Cherniavsky, ITS '15 & Block
et al., FSTTCS '20), which compiles any locally decodable Hamming code into a
locally decodable code resilient to insertion-deletion (InsDel) errors. While
the compilers were designed for the classical coding setting, we show that the
compilers still work in a secret key or resource-bounded setting. Applying our
results to the private key Hamming LDC of Ostrovsky, Pandey, and Sahai (ICALP
'07), we obtain a private key InsDel LDC with constant rate and polylogarithmic
locality. Applying our results to the construction of Blocki, Kulkarni, and
Zhou (ITC '20), we obtain similar results for resource-bounded channels; i.e.,
a channel where computation is constrained by resources such as space or time.
