Volume 5 (2009) Article 2 pp. 43-67
Deterministic History-Independent Strategies for Storing Information on Write-Once Memories
by
Motivated by the challenging task of designing “secure” vote storage mechanisms, we study information storage mechanisms that operate in extremely hostile environments. In such environments, the majority of existing techniques for information storage and for security are susceptible to powerful adversarial attacks. We propose a mechanism for storing a set of at most $K$ elements from a large universe of size $N$ on write-once memories in a manner that does not reveal the insertion order of the elements. We consider a standard model for write-once memories, in which the memory is initialized to the all-zero state, and the only operation allowed is flipping bits from $0$ to $1$. Whereas previously known constructions were either inefficient (required $\Theta(K^2)$ memory), randomized, or employed cryptographic techniques which are unlikely to be available in hostile environments, we eliminate each of these undesirable properties. The total amount of memory used by the mechanism is linear in the number of stored elements and poly-logarithmic in the size of the universe of elements.