On Optimal Information-Theoretic Security in Symmetric Encryption under Low-Entropy Keys

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We study the achievable level of information-theoretic security for symmetric encryption under low-entropy keys (e.g., passwords and biometrics), where classical notions such as perfect secrecy and entropic security are usually unattainable. We consider a model in which messages $M$ and keys $K$ are drawn independently from distributions $(p_{\mathrm{m}}, p_{\mathrm{k}})$. Prior work on homophonic ciphers (HC) and honey encryption (HE) suggests that randomized encryption tailored to $p_{\mathrm{