Abstract
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(logσ). 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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Dziembowski, S. (2010). A Lower Bound on the Key Length of Information-Theoretic Forward-Secure Storage Schemes. In: Kurosawa, K. (eds) Information Theoretic Security. ICITS 2009. Lecture Notes in Computer Science, vol 5973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14496-7_2
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DOI: https://doi.org/10.1007/978-3-642-14496-7_2
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