Paper 2014/774

Automated Analysis and Synthesis of Block-Cipher Modes of Operation

Alex J. Malozemoff, Jonathan Katz, and Matthew D. Green

Abstract

Block ciphers such as AES are deterministic, keyed functions that operate on small, fixed-size blocks. Block-cipher \emph{modes of operation} define a mechanism for probabilistic encryption of arbitrary length messages using any underlying block cipher. A mode of operation can be proven secure (say, against chosen-plaintext attacks) based on the assumption that the underlying block cipher is a pseudorandom function. Such proofs are complex and error-prone, however, and must be done from scratch whenever a new mode of operation is developed. We propose an \emph{automated} approach for the security analysis of block-cipher modes of operation based on a ``local'' analysis of the steps carried out by the mode when handling a \emph{single} message block. We model these steps as a directed, acyclic graph, with nodes corresponding to instructions and edges corresponding to intermediate values. We then introduce a set of \emph{labels} and \emph{constraints} on the edges, and prove a meta-theorem showing that any mode for which there exists a labeling of the edges satisfying these constraints is secure (against chosen-plaintext attacks). This allows us to reduce security of a given mode to a constraint-satisfaction problem, which in turn can be handled using an SMT solver. We couple our security-analysis tool with a routine that automatically generates viable modes; together, these allow us to synthesize hundreds of secure modes.

Note: Full version of paper published at CSF 2014