Optimal Weakly Secure Minimum Storage Regenerating Codes Scheme

In a distributed storage system, regenerating codes can be utilized to ensure data availability. This reduces the repair bandwidth but increases the risk of data eavesdropping on each node. Previous studies in this area generally only provided an approximate analysis of the security of schemes with information-theoretic security or weak security. Some researchers have further divided weak security into block security; however, they only analyzed several the regenerating codes schemes and proposed improved schemes with specific eavesdropping capabilities. In this study, we analyze the block security of a Cauchy-matrix-based product-matrix minimum storage regenerating(MSR) scheme and determine the optimal block security of MSR codes. Lastly, an improved MSR codes scheme for achieving optimal block security is proposed, and the relevant proof is provided.