The Bare Bounded-Storage Model: The Tight Bound on the Storage Requirement for Key Agreement

摘要

In the bounded-storage model (BSM) for information-theoretic secure encryption and key agreement, one makes use of a random string $R$ whose length $t$ is greater than the assumed bound $s$ on the adversary Eve''s storage capacity. The legitimate parties, Alice and Bob, execute a protocol, over an authenticated channel accessible to Eve, to generate a secret key $K$ about which Eve has essentially no information even if she has infinite computing power. The string $R$ is either assumed to be accessible to all parties or communicated publicly from Alice to Bob. While in the BSM one often assumes that Alice and Bob initially share a short secret key, and the goal of the protocol is to generate a much longer key, in this communication, we consider the bare BSM without any initially shared secret key. It is proved that in the bare BSM, secret key agreement is impossible unless Alice and Bob have themselves very high storage capacity, namely, $O(sqrt {t})$ . This proves the optimality of a scheme proposed by Cachin and Maurer.