A Lower Bound on the Key Length of Information-Theoretic Forward-Secure Storage Schemes

Forward-Secure Storage (FSS) was introduced by Dziembowski (CRYPTO 2006). Informally, FSS is an encryption scheme (Encr, Decr) that has the following non-standard property: even if the adversary learns the value of some function h of the ciphertext C = Encr(K,M), he should have essentially no information on the corresponding plaintext M, even if he knows the key K. The only restriction is that h is input-shrinking, i.e. |h(R)| ≤ σ, where σ is some parameter such that σ ≤ |C|. We study the problem of minimizing the length of the secret key in the IT-secure FSS, and we establish an almost optimal lower bound on the length of the secret key. The secret key of the FSS scheme of Dziembowski has length |M|+O(log σ). We show that in every FSS the secret key needs to have length at least |M| + log2 σ-O(log2 log2 σ).

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