Information Theoretically Secure Communication in the Limited Storage Space Model

We provide a simple secret-key two-party secure communication scheme, which is provably information-theoretically secure in the limited-storage-space model. The limited-storage-space model postulates an eavesdropper who can execute arbitrarily complex computations, and is only limited in the total amount of storage space (not computation space) available to him. The bound on the storage space can be arbitrarily large (e.g. terabytes), as long as it is fixed. Given this bound, the protocol guarantees that the probability of the eavesdropper of gaining any information on the message is exponentially small. The proof of our main results utilizes a novel combination of linear algebra and Kolmogorov complexity considerations.