A large portion of the government, business, cultural, and scientific digital data being created today needs to be archived and preserved for future use of periods ranging from a few years to decades and sometimes centuries. A fundamental requirement of a long term archive is to ensure the integrity of its holdings. In this paper, we develop a new methodology to address the integrity of long term archives using rigorous cryptographic techniques. Our approach involves the generation of a small-size integrity token for each digital object to be archived, and some cryptographic summary information based on all the objects handled within a dynamic time period. We present a framework that enables the continuous auditing of the holdings of the archive depending on the policy set by the archive. Moreover, an independent auditor will be able to verify the integrity of every version of an archived digital object as well as link the current version to the original form of the object when it was...