Secure Multiparty Computation based on Samir Secret sharing methods rely on Polynomials. Imagine corpus of data should be outsourced to bunch of untrusted servers for any computations. Now the data could be split by a trusted client using Secret Sharing and distributed among the multiple untrusted servers. Subsequently any operations on the data could done using Secure Multiparty Computation protocols such that no single untrusted server has access to complete data in clear.
If the corpus of data are confidential documents and the client tokenizes them into each word then secret shares those words into say three shares. Distribute them to three untrusted servers. So that subsequently the client could search the documents for keyword using some SMC protocol.
Should the client use different polynomials for each word (or collection of words) or same polynomial could be used for entire corpus of document
- If same polynomial is used for secret sharing all the words then searching the corpus with the share of keyword would be easy. But then the secret shares of each word would be pretty deterministic and frequency analysis could be launched to identify the words.
- If different polynomial is used then how is the search for keywords work on the entire corpus ?
The same might hold good not only for search , for any other operation including arithmetic. Any help ?