I'm working on a security project. I need to perform a sorting on the lists of encrypted integers and strings. The encryption used is symmetric. The clients send the encrypted data in a list to the server (encrypted by different symmetric keys, each key is shared b/w a client and the server). On receiving the list, server may again encrypt it using another key shared between the server (such as authentication server) and the service provider's server. If service provider server wish to sort the encrypted data, then how can it be achieved? It cannot decrypt the original messages encrypted by different users' keys. I found a paper, https://eprint.iacr.org/2014/1017.pdf, however, it performs sort over the data encrypted with same key. But in my project requirements are different where each data element is encrypted by a different key of the client. (each key shared b/w a client and the server).
Any help is appreciated.