  Regenerating codes enable trading off repair bandwidth for storage in
distributed storage systems (DSS). Due to their distributed nature, these
systems are intrinsically susceptible to attacks, and they may also be subject
to multiple simultaneous node failures. Cooperative regenerating codes allow
bandwidth efficient repair of multiple simultaneous node failures. This paper
analyzes storage systems that employ cooperative regenerating codes that are
robust to (passive) eavesdroppers. The analysis is divided into two parts,
studying both minimum bandwidth and minimum storage cooperative regenerating
scenarios. First, the secrecy capacity for minimum bandwidth cooperative
regenerating codes is characterized. Second, for minimum storage cooperative
regenerating codes, a secure file size upper bound and achievability results
are provided. These results establish the secrecy capacity for the minimum
storage scenario for certain special cases. In all scenarios, the achievability
results correspond to exact repair, and secure file size upper bounds are
obtained using min-cut analyses over a suitable secrecy graph representation of
DSS. The main achievability argument is based on an appropriate pre-coding of
the data to eliminate the information leakage to the eavesdropper.
