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 for a long term archive is to set up mechanisms that will ensure the authenticity of the holdings of the archive. 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, as well as auditing upon access, 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 ingested into the archive. Using this approach, a prototype system called ACE (Auditing Control Environment) has been built and tested. ACE is scalable and cost effective, and is completely independent of the archive's underlying architecture.