Interactivity in Constructive Cryptography : Modeling and Applications to Updatable Encryption and Private Information Retrieval

04/25/2022

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by   Françoise Levy-dit-Vehel, et al.

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In this work, we extend the Constructive Cryptography (CC) framework introduced by Maurer in 2011 so as to handle interactive protocols. We design and construct a so-called Interactive Server Memory Resource (ISMR), that is an augmented version of the basic instantiation of a client-server protocol in CC, namely the Server Memory Resource. We then apply our ISMR construction to two types of interactive cryptographic protocols for remote storage : Updatable Encryption (UE) and Private Information Retrieval (PIR). Concerning UE, our results are a composable version of those protocols, clarifying the security guarantees achieved by any UE scheme. Namely, we give the relevant security notion to consider according to a given leakage context. Letting USMR denote our ISMR adapted to the UE application, we prove that 𝖨𝖭𝖣-𝖴𝖤-𝖢𝖯𝖠 security is sufficient for a secure construction of a confidential USMR that hides the age of ciphertexts; and 𝖨𝖭𝖣-(𝖤𝖭𝖢+𝖴𝖯𝖣)-𝖢𝖯𝖠 security is sufficient for a secure construction of a confidential USMR in case of unrestricted leakage. As a consequence, contrary to what was claimed before, the 𝖨𝖭𝖣-𝖴𝖤 security notion is not always stronger than the 𝖨𝖭𝖣-(𝖤𝖭𝖢+𝖴𝖯𝖣) one. Concerning PIR, we also give a composable version of PIR protocols, yielding a unique model that unifies different notions of PIR : IT-PIR, C-PIR, one- or multi- server PIR. Using the flexibility of CC, we are also able to model PIR variants, such as SPIR.