Recovering Reed-Solomon codes privately

Abstract

We investigate the problems of privately repairing erasures and evaluating their linear combinations for Reed-Solomon codes with low communication bandwidths. We propose two approaches: one based on hiding subspaces used to form parity-check equations, and another based on multiplying parity-check equations with random polynomials. We also derive a lower bound on the repair bandwidth for the single erasure case under reasonable assumptions about the schemes being used and demonstrate the optimality of the proposed schemes for codes of specific lengths.Ministry of Education (MOE)National Research Foundation (NRF)Submitted/Accepted versionThis research is supported by the National Research Foundation, Singapore under its Strategic Capability Research Centres Funding Initiative, Ministry of Education, Singapore, under its MOE Academic Research Fund Tier 2 Grants MOE-T2EP20121-0007 and MOE-000623-00, Tier 1 Grant RG19/23, Australia Research Council (ARC) DECRA Grant DE180100768, Israel Science Foundation (ISF) under Grant 2462/24. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore