Searching on Non-Systematic Erasure Codes

Non-Systematic erasure codes provide confidentiality of data and can even provide strong security guarantees with appropriate parameter selection. So far however, they have lacked an elegant and efficient method for keyword search over the codes. While the obvious method of reconstruction before search can be too slow, direct search produces inaccurate results. This has been one of the barriers in the wider adoption of non systematic erasure codes in distributed and secure storage. In this paper we present an elegant solution to this problem by building an index data structure that we call the Search Vector, created from the generator matrix of the erasure code. We show that this method introduces a very small amount of delay in return of a high degree of accuracy in search results. We also analyse the security of the scheme in terms of information leakage and show that the information leaked from the index data structure is very small even when one assumes the worst case scenario of the attacker having access to the Search Vector.