Secrecy capacity of minimum storage regenerating codes

This paper revisits the problem of designing secure minimum storage regenerating (MSR) codes for distributed storage systems (DSS). A secure MSR code ensures that a DSS does not reveal the stored information to a passive eavesdropper. The eavesdropper is assumed to have access to the content stored on ℓ
₁
number of storage nodes in the system and the data downloaded during the bandwidth efficient repair of an additional ℓ
₂
number of storage nodes. This paper combines the Gabidulin codes based precoding [1] and a new construction of MSR codes (without security requirements) by Ye and Barg [2] in order to obtain secure MSR codes. Such optimal secure MSR codes were previously known only in the setting where the eavesdropper was allowed to observe the repair of ℓ
₂
nodes among a specific subset of k nodes [1], [3]. The secure coding scheme presented in this paper allows the eavesdropper to observe repair of any ℓ
₂
out of ii nodes in the system and characterizes the secrecy capacity of linear repairable MSR codes.