Welcome to the resource topic for
**2023/409**

**Title:**

Somewhere Randomness Extraction and Security against Bounded-Storage Mass Surveillance

**Authors:**
Jiaxin Guan, Daniel Wichs, Mark Zhandry

**Abstract:**

Consider a state-level adversary who observes and stores large amounts of encrypted data from all users on the Internet, but does not have the capacity to store it all. Later, it may target certain “persons of interest” in order to obtain their decryption keys. We would like to guarantee that, if the adversary’s storage capacity is only (say) 1\% of the total encrypted data size, then even if it can later obtain the decryption keys of arbitrary users, it can only learn something about the contents of (roughly) 1\% of the ciphertexts, while the rest will maintain full security. This can be seen as an extension of incompressible cryptography (Dziembowski CRYPTO '06, Guan, Wichs and Zhandry EUROCRYPT '22) to the multi-user setting. We provide solutions in both the symmetric key and public key setting with various trade-offs in terms of computational assumptions and efficiency.

As the core technical tool, we study an information-theoretic problem which we refer to as “somewhere randomness extraction”. Suppose X_1, \ldots, X_t are correlated random variables whose total joint min-entropy rate is \alpha, but we know nothing else about their individual entropies. We choose t random and independent seeds S_1, \ldots, S_t and attempt to individually extract some small amount of randomness Y_i = \mathsf{Ext}(X_i;S_i) from each X_i. We’d like to say that roughly an \alpha-fraction of the extracted outputs Y_i should be indistinguishable from uniform even given all the remaining extracted outputs and all the seeds. We show that this indeed holds for specific extractors based on Hadamard and Reed-Muller codes.

**ePrint:**
https://eprint.iacr.org/2023/409

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