Can't touch this: unconditional tamper evidence from short keys

Storing data on an external server with information-theoretic security, while using a key shorter than the itself, is impossible. As alternative, we propose scheme that achieves information-theoretically secure tamper evidence: The able to obtain information about stored data, but not staying undetected. Moreover, client only needs remember whose length much data. We provide security proof for our scheme, based entropic uncertainty relation, similar QKD proofs. Our works if Alice (reversibly) randomise message almost-uniformity short key. By constructing explicit attack show short-key unconditional evidence cannot be achieved without this randomisability.