A Note on Secure Minimum Storage Regenerating Codes

This short note revisits the problem of designing secure minimum storage regenerating (MSR) codes for distributed storage systems. A secure MSR code ensures that a distributed storage system does not reveal the stored information to a passive eavesdropper. The eavesdropper is assumed to have access to the content stored on l1 number of storage nodes in the system and the data downloaded during the bandwidth efficient repair of an additional l2 number of storage nodes. This note combines the Gabidulin codes based precoding [18] and a new construction of MSR codes (without security requirements) by Ye and Barg [27] in order to obtain secure MSR codes. Such optimal secure MSR codes were previously known in the setting where the eavesdropper was only allowed to observe the repair of l2 nodes among a specific subset of k nodes [7, 18]. The secure coding scheme presented in this note allows the eavesdropper to observe repair of any l2 ouf of n nodes in the system and characterizes the secrecy capacity of linear repairable MSR codes.