You could zip the files with a password, and use a Phonegap FileTransfer and ZIP plugin to download the zip and extract it. There's a few ZIP plugins out there, and FileTransfer is part of Phonegap, and Javascript
http://docs.phonegap.com/en/3.3.0/cordova_file_file.md.html#FileTransfer https://github.com/phonegap/phonegap-plugins/tree/DEPRECATED/iOS/ExtractZipFile (deprecated - not sure where the current version is)
If the JSON files are small enough you can also encrypt them into a AES encoded string, using the Javacsript Crypto Library:
https://code.google.com/p/crypto-js/#AES
Or you can do it all, encrypt your data, ZIP it with a password, transfer over HTTPS