Paper 2019/506

Forward Integrity and Crash Recovery for Secure Logs

Erik-Oliver Blass and Guevara Noubir

Abstract

Logging is a key mechanism in the security of computer systems. Beyond supporting important forward security properties, it is critical that logging withstands both failures and intentional tampering to prevent subtle attacks leaving the system in an inconsistent state with inconclusive evidence. We propose new techniques combining forward integrity with crash recovery for secure log data storage. As the support of forward integrity and online nature of logging prevent the use of conventional coding, we propose and analyze a coding scheme resolving these unique design constraints. Specifically, our coding enables forward integrity, online encoding, and most importantly a constant number of operations per encoding. It adds a new log item by XORing it to forward-securely selected $k$ cells of a table. If up to a certain threshold of cells is modified by the adversary, or lost due to a crash, we still guarantee recovery of all stored log items. The main advantage of the coding scheme is its efficiency and compatibility with forward integrity. A key contribution of the paper is the use of spectral graph theory techniques to prove that $k$ is constant in the number $n$ of all log items ever stored and small in practice, e.g., $k=5$. Moreover, we prove that to cope with up to $\sqrt{n}$ lost log items, storage expansion is asymptotically constant in $n$ and small in practice. For $k=5$, the total size of the table is only $12\%$ more than the simple concatenation of all $n$ items. We instantiate our scheme into an abstract data structure which allows to either detect adversarial modifications to log items or treat modifications like data loss in a system crash. The data structure can recover lost log items, thereby effectively reverting adversarial modifications.