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 $\ell_1$ number of storage nodes in the system and the data downloaded during the bandwidth efficient repair of an additional $\ell_2$ 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 $\ell_2$ 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 $\ell_2$ ouf of $n$ nodes in the system and characterizes the secrecy capacity of linear repairable MSR codes. 
Ankit Singh Rawat
cs.IT math.IT