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Constructions Secure against Receiver Selective Opening and Chosen Ciphertext Attacks.

Dingding Jia, Xianhui Lu, Bao Li

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

In this paper we study public key encryption schemes of indistinguishability security against receiver selective opening (IND-RSO) attacks, where the attacker can corrupt some receivers and get the corresponding secret keys in the multi-party setting. Concretely:

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In the situation where there are one sender and multiple receivers, a receiver selective opening (RSO) attack for an identity-based encryption (IBE) scheme considers adversaries that can corrupt some of the receivers and get their user secret keys and plaintexts. Security against RSO attacks for an IBE scheme ensures confidentiality of ciphertexts of uncorrupted receivers. In this paper, we formalize a definition of RSO security against chosen ciphertext attacks (RSO-CCA security) for IBE and propose the first RSO-CCA secure IBE schemes. More specifically, we construct an RSO-CCA secure IBE scheme based on an IND-ID-CPA secure IBE scheme and a non-interactive zero-knowledge proof system with unbounded simulation soundness and multi-theorem zero-knowledge. Through our generic construction, we obtain the first pairing-based and lattice-based RSO-CCA secure IBE schemes.
We provide the first public key encryption schemes proven secure against selective opening attack (SOA). This means that if an adversary obtains a number of ciphertexts and then corrupts some fraction of the senders, obtaining not only the corresponding messages but also the coins under which they were encrypted then the security of theothermessagesisguaranteed. Whetherornotschemeswith this property exist has been open for many years. Our schemes are based on a primitive we call lossy encryption. Our schemes have short keys (public and secret keys of a fixed length suffice for encrypting an arbitrary number of messages), are stateless, are non-interactive, and security does not rely on erasures. The schemes are without random oracles, proven secure under standard assumptions (DDH, Paillier’s DCR, QR, lattices), and even efficient. We are able to meet both an indistinguishability
In the situation where there are one sender and multiple receivers, a receiver selective opening (RSO) attack for an identity-based encryption (IBE) scheme considers adversaries that can corrupt some of the receivers and get their user secret keys and plaintexts. Security against RSO attacks for an IBE scheme ensures confidentiality of ciphertexts of uncorrupted receivers. In this paper, we formalize a definition of RSO security against chosen ciphertext attacks (RSO-CCA security) for IBE and propose the first RSO-CCA secure IBE schemes. More specifically, we construct an RSO-CCA secure IBE scheme based on an IND-ID-CPA secure IBE scheme and a non-interactive zero-knowledge proof system with unbounded simulation soundness and multi-theorem zero-knowledge. Through our generic construction, we obtain the first pairing-based and lattice-based RSO-CCA secure IBE schemes.
Receiver selective opening (RSO) security considers the security of encryption schemes under the scenario of a single sender and multiple receivers, where an adversary is allowed to adaptively corrupt some receivers’ secret keys. RSO security has been proven to be more secure than indistinguishability-based security notions. A lot of research has focused on RSO security in terms of public-key encryption and identity-based encryption (IBE); however, hierarchical IBE (HIBE), which is a generalization of IBE, is still lacking in the study, and how to obtain such a construction remains an open problem. To address this gap, we initiate a study of RSO security on HIBE in this work. Precisely, we first formalize the definition of simulation-based RSO against identity-chosen-plaintext/ciphertext attacks in the k-challenge setting (SIM-ID-RSO k_kk​ -CPA/CCA) for HIBE. We then present generic SIM-ID-RSO k_kk​ -CCA secure HIBE constructions by introducing the double secret key paradigm. Specifically, we show that a SIM-ID-RSO k_kk​ -CCA secure HIBE scheme can be obtained from an IND-ID-CPA secure HIBE scheme as well as a one-time signature scheme that satisfies strong unforgeability. Through our general construction, we can derive various concrete schemes based on different hard assumptions (e.g., lattice-based and pairing-based SIM-ID-RSO k_kk​ -CCA secure HIBE schemes) according to usage requirements.
In a selective opening (SO) attack an adversary breaks into a subset of honestly created ciphertexts and tries to learn information on the plaintexts of some untouched (but potentially related) ciphertexts. Contrary to intuition, standard security notions do not always imply security against this type of adver-sary, making SO security an important standalone goal. In this paper we study receiver security, where the attacker is allowed to obtain the decryption keys corresponding to some of the ciphertexts. First we study the relation between two existing security definitions, one based on simulation and the other based on indistinguishability, and show that the former is strictly stronger. We continue with feasibility results for both notions which we show can be achieved from (variants of) non-committing encryption schemes. In particular, we show that indistinguishability-based SO security can be achieved from a tweaked variant of non-committing encryption which, in turn, can be instantiated from a variety of basic, well-established, assumptions. We conclude our study by showing that SO security is however strictly weaker than all variants of non-committing encryption that we consider, leaving potentially more efficient constructions as an interesting open problem.
Receiver selective opening (RSO) attack for public key encryption (PKE) captures a situation where one sender sends messages to multiple receivers, an adversary can corrupt a set of receivers and get their messages and secret keys. Security against RSO attack for a PKE scheme ensures confidentiality of other uncorrupted receivers' ciphertexts. Among all of the RSO security notions, simulation-based RSO security against chosen ciphertext attack (SIM-RSO-CCA security) is the strongest notion. In this paper, we explore constructions of SIM-RSO-CCA secure PKE from various computational assumptions. Toward this goal, we show that a SIM-RSO-CCA secure PKE scheme can be constructed based on an IND-CPA secure PKE scheme and a designated-verifier non-interactive zero-knowledge (DV-NIZK) argument satisfying one-time simulation soundness. Moreover, we give the first construction of DV-NIZK argument satisfying one-time simulation soundness. Consequently, through our generic construction, we obtain the first SIM-RSO-CCA secure PKE scheme under the computational Diffie-Hellman (CDH) or learning parity with noise (LPN) assumption.