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arXiv:2204.11653

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

Françoise Levy-dit-Vehel, Maxime Roméas

Published Apr 25, 2022• 0 citations
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Abstract

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 {\em 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 {\em 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 $\mathsf{IND}\text{-}\mathsf{UE}\text{-}\mathsf{CPA}$ security is sufficient for a secure construction of a confidential USMR that hides the age of ciphertexts; and $\mathsf{IND}\text{-}(\mathsf{ENC}+\mathsf{UPD})\text{-}\mathsf{CPA}$ 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 $\mathsf{IND}\text{-}\mathsf{UE}$ security notion is not always stronger than the $\mathsf{IND}\text{-}(\mathsf{ENC+UPD})$ 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.

DOI
10.48550/arxiv.2204.11653

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We revisit the problem of low-memory robust simulation of interactive protocols over noisy channels. Haeupler [FOCS 2014] considered robust simulation of two-party interactive protocols over oblivious, as well as adaptive, noisy channels. Since the simulation does not need to have fixed communication pattern, the achieved communication rates can circumvent the lower bound proved by Kol and Raz [STOC 2013]. However, a drawback of this approach is that each party needs to remember the whole history of the simulated transcript. In a subsequent manuscript, Haeupler and Resch considered low-memory simulation. The idea was to view the original protocol as a computational DAG and only the identities of the nodes are saved (as opposed to the whole transcript history) for backtracking to reduce memory usage. In this paper, we consider low-memory robust simulation of more general client-server interactive protocols, in which a leader communicates with other members/servers, who do not communicate among themselves; this setting can be applied to information-theoretic multi-server Private Information Retrieval (PIR) schemes. We propose an information-theoretic technique that converts any correct PIR protocol that assumes reliable channels, into a protocol which is both correct and private in the presence of a noisy channel while keeping the space complexity to a minimum. Despite the huge attention that PIR protocols have received in the literature, the existing works assume that the parties communicate using noiseless channels. Moreover, we observe that the approach of Haeupler and Resch to just save the nodes in the aforementioned DAG without taking the transcript history into account will lead to a correctness issue even for oblivious corruptions. We resolve this issue by saving hashes of prefixes of past transcripts. Departing from the DAG representation also allows us to accommodate scenarios where a party can simulate its part of the protocol without any extra knowledge (such as the DAG representation of the whole protocol). In the the two-party setting, our simulation has the same dependence on the error rate as in the work of Haeupler, and in the client-server setting it also depends on the number of servers. Furthermore, since our approach does not remember the complete transcript history, our current technique can defend only against oblivious corruptions.
Abstract. A receiver-anonymous channel allows a sender to send a message to a receiver without an adversary learning for whom the message is intended. Wireless broadcast channels naturally provide receiver anonymity, as does multi-casting one message to a receiver population containing the intended receiver. While anonymity and confidentiality appear to be orthogonal properties, making anonymous communication confidential is more involved than one might expect, since the ciphertext might reveal which public key has been used to encrypt. To address this problem, public-key cryptosystems with enhanced security properties have been proposed. We investigate constructions as well as limitations for preserving receiver anonymity when using public-key encryption (PKE). We use the constructive cryptography approach by Maurer and Renner and interpret cryptographic schemes as constructions of a certain ideal resource (e.g. a confidential anonymous channel) from given real resources (e.g. a broadcast channel). We define appropriate anonymous communication resources and show that a very natural resource can be constructed by using a PKE scheme which fulfills three properties that appear in cryptographic literature (IND-CCA, key-privacy, weak robustness). We also show that a desirable stronger variant, preventing the adversary from selective “trial-deliveries ” of messages, is unfortunately unachievable by any PKE scheme, no matter how strong. The constructive approach makes the guarantees achieved by applying a cryptographic scheme explicit in the constructed (ideal) resource; this specifies the exact requirements for the applicability of a cryptographic scheme in a given context. It also allows to decide which of the existing security properties of such a cryptographic scheme are adequate for the considered scenario, and which are too weak or too strong. Here, we show that weak robustness is necessary but that so-called strong robustness is unnecessarily strong in that it does not construct a (natural) stronger resource.
The Private Information Retrieval protocol(PIR) is an important secure multi-party computation protocol.In PIR,a user can perform a query from a database without revealing his private information;meanwhile the privacy of the database will be protected,too.This paper proposes a new scheme in which we apply cryptographic technology on the auxiliary random servers protocol to solve the problem of PIR.This scheme is efficient in computational complexity and doesn't increase the cost of communication.It is very practical and can retrieve a block of bits.Detailed analysis of security,computational complexity and communicational complexity to the scheme is also given in this paper.
The universal composability (UC) framework enables the modular design of cryptographic protocols by allowing arbitrary compositions of lower-level building blocks. Public-key encryption is unarguably a very important such building block. However, so far no UC-functionality exists that offers non-interactive encryption necessary for modular protocol construction. We provide an ideal functionality for non-committing encryption (i.e., public-key encryption secure against adaptive corruptions) with locally generated, and therefore non-interactive, ciphertexts. As a sanity check, we also provide a property-based security notion that we prove to be equivalent to the UC notion. We then show that the encryption scheme of Camenisch et al. (SCN '16) based on trapdoor permutations securely implements our notion in the random-oracle model without assuming secure erasures. This is the best one can hope to achieve as standard-model constructions do not exist due to the uninstantiability of round-optimal adaptively secure message transfer in the standard model (Nielsen, Crypto '02). We illustrate the modular reusability of our functionality by constructing the first non-interactive signcryption scheme secure against adaptive corruptions without secure erasures in the UC framework.
In this paper, we consider encryption systems with two-out-of-two threshold decryption, where one of the parties (the client) initiates the decryption and the other one (the server) assists. Existing threshold decryption schemes disclose to the server the ciphertext that is being decrypted. We give a construction, where the identity of the ciphertext is not leaked to the server, and the client's privacy is thus preserved. While showing the security of this construction, we run into the issue of defining the security of a scheme with blindly assisted decryption. We discuss previously proposed security definitions for similar cryptographic functionalities and argue why they do not capture the expected meaning of security. We propose an ideal functionality for the encryption with server-supported blind threshold decryption in the universal composability model, carefully balancing between the meaning of privacy, and the ability to implement it. We construct a protocol and show that it is a secure implementation of the proposed functionality in the random oracle model.
In (single-server) Private Information Retrieval (PIR), a server holds a large database DBDBDB of size nnn, and a client holds an index i∈[n]i \in [n]i∈[n] and wishes to retrieve DB[i]DB[i]DB[i] without revealing iii to the server. It is well known that information theoretic privacy even against an `honest but curious' server requires Ω(n)Ω(n)Ω(n) communication complexity. This is true even if quantum communication is allowed and is due to the ability of such an adversarial server to execute the protocol on a superposition of databases instead of on a specific database (`input purification attack'). Nevertheless, there have been some proposals of protocols that achieve sub-linear communication and appear to provide some notion of privacy. Most notably, a protocol due to Le Gall (ToC 2012) with communication complexity O(n)O(\sqrt{n})O(n​), and a protocol by Kerenidis et al. (QIC 2016) with communication complexity O(log⁡(n))O(\log(n))O(log(n)), and O(n)O(n)O(n) shared entanglement. We show that, in a sense, input purification is the only potent adversarial strategy, and protocols such as the two protocols above are secure in a restricted variant of the quantum honest but curious (a.k.a specious) model. More explicitly, we propose a restricted privacy notion called \emph{anchored privacy}, where the adversary is forced to execute on a classical database (i.e. the execution is anchored to a classical database). We show that for measurement-free protocols, anchored security against honest adversarial servers implies anchored privacy even against specious adversaries. Finally, we prove that even with (unlimited) pre-shared entanglement it is impossible to achieve security in the standard specious model with sub-linear communication, thus further substantiating the necessity of our relaxation. This lower bound may be of independent interest (in particular recalling that PIR is a special case of Fully Homomorphic Encryption).