Secure Convertible Codes for Passive Eavesdroppers

Large-scale distributed storage systems rely on erasure codes to ensure fault tolerance against node failures. Due to the observed changing failure rates within these systems, code redundancy tuning, or code conversion has been shown to reduce storage cost. Previous work has developed theoretical bounds and constructions for convertible codes, a specialized class of erasure codes optimizing either access or bandwidth costs during conversion. In this paper, we address the challenge of securing convertible codes in the presence of an eavesdropper. We introduce an eavesdropper-secrecy model for convertible codes wherein an eavesdropper gaining read access to a subset of the codeword symbols learns nothing (information-theoretically) about the underlying message. We then focus on access-cost optimal convertible codes, and we then derive the information-theoretic upper bound on the number of message symbols that can be stored securely. Finally, we provide an explicit construction that simultaneously reaches this secrecy bound while admitting accesscost optimal conversion using concatenation of nested codes with traditional convertible codes. Since our construction works with all traditional access-optimal convertible codes, we show that access-optimal secure convertible codes exist for all message and codeword length parameters.