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The Computer Journal

Almost-Tight Identity Based Encryption Against Selective Opening Attack

Junqing Gong, Xiaolei Dong, Zhenfu Cao, Jie Chen

Published Aug 12, 2016• 3 citations
Publisher

Abstract

The paper presents an identity based encryption (IBE) under selective opening attacks (SOA) whose security is almost-tightly related to a set of computational assumptions in composite-order bilinear groups. Our result is a combination of Bellare, Waters and Yilek's method [TCC, 2011] for constructing (not tightly) SOA secure IBE and Hofheinz, Koch and Striecks’ technique [PKC, 2015] on building almost-tightly secure IBE in the multi-ciphertext setting. In the paper, we first tune Bellare et al.’s generic construction for SOA secure IBE to show that a one-bit IBE achieving ciphertext indistinguishability under chosen plaintext attack in the multi-ciphertext setting (with one-sided public openability) tightly implies a multi-bit IBE secure under the selective opening attack. Next, we almost tightly reduce such a one-bit IBE to static assumptions in the composite-order bilinear groups employing the technique of Hofheinz et al. This yields the first SOA secure IBE with almost-tight reduction.

DOI
10.1093/comjnl/bxw030

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The paper presents an identity based encryption (IBE) under selective opening attacks (SOA) whose security is almost-tightly related to a set of computational assumptions in composite-order bilinear groups. Our result is a combination of Bellare, Waters and Yilek's method [TCC, 2011] for constructing (not tightly) SOA secure IBE and Hofheinz, Koch and Striecks’ technique [PKC, 2015] on building almost-tightly secure IBE in the multi-ciphertext setting. In the paper, we first tune Bellare et al.’s generic construction for SOA secure IBE to show that a one-bit IBE achieving ciphertext indistinguishability under chosen plaintext attack in the multi-ciphertext setting (with one-sided public openability) tightly implies a multi-bit IBE secure under the selective opening attack. Next, we almost tightly reduce such a one-bit IBE to static assumptions in the composite-order bilinear groups employing the technique of Hofheinz et al. This yields the first SOA secure IBE with almost-tight reduction.
The paper presented an identity based encryption (IBE) under selective opening attack (SOA) whose security is almost-tightly related to a set of computational assumptions. Our result is a combination of Bellare, Waters, and Yilek’s method [TCC, 2011] for constructing (not tightly) SOA secure IBE and Hofheinz, Koch, and Striecks ’ technique [PKC, 2015] on building almost-tightly secure IBE in the multi-ciphertext setting. In particular, we first tuned Bellare et al.’s generic construction for SOA secure IBE to show that a one-bit IBE achieving ciphertext indistinguishability under chosen plaintext attack in the multi-ciphertext setting (with one-sided publicly openability) tightly implies a multi-bit IBE secure under selective opening attack. Next, we almost-tightly reduced such a one-bit IBE to static assumptions in the composite-order bilinear groups
Security against selective opening attack (SOA) for receivers requires that in a multi-user setting, even if an adversary has access to all ciphertexts, and adaptively corrupts some fraction of the users to obtain the decryption keys corresponding to some of the ciphertexts, the remaining (potentially related) ciphertexts retain their privacy. In this paper, we study simulation-based selective opening security for receivers of public key encryption (PKE) schemes under chosen-ciphertext attacks (RSIM-SO-CCA). Concretely, we first show that some known PKE schemes meet RSIM-SO-CCA security. Then, we introduce the notion of master-key SOA security for identity-based encryption (IBE), and extend the Canetti–Halevi–Katz transformation to show generic PKE constructions achieving RSIM-SO-CCA security. Finally, we show how to construct an IBE scheme achieving master-key SOA security.
Abstract We construct an identity-based encryption (IBE) scheme that is tightly secure in a very strong sense. Specifically, we consider a setting with many instances of the scheme and many encryptions per instance. In this setting, we reduce the security of our scheme to a variant of a simple assumption used for a similar purpose by Chen and Wee (CRYPTO 2013, Springer, 2013). The security loss of our reduction is O(k)\textbf{O} (k)O(k) O(k) (where kk k k is the security parameter). Our scheme is the first IBE scheme to achieve this strong flavor of tightness under a simple assumption. Technically, our scheme is a variation of the IBE scheme by Chen and Wee. However, in order to “lift” their results to the multi-instance, multi-ciphertext case, we need to develop new ideas. In particular, while we build on (and extend) their high-level proof strategy, we deviate significantly in the low-level proof steps.
We propose two efficient Identity-Based threshold decryption schemes.They are proved secure against chosen ciphertext attacks under the standard decisional bilinear Diffie-Hellman assumption.The first one is constructed from(one of) the Selective ID-Based Encryption(Selective-IBE) scheme proposed by Boneh and Boyen recently,yet the second one is transformed from the Full ID-Based Encryption(Full-IBE) scheme obtained by Waters.As the based IBE schemes,the attacker in the first proposal has to choose the challenge identity before the common parameter is generated.while the attacker in the second one could choose the identity adaptively.To the best of our knowledge,previous related schemes could only be proved secure in the random oracle model.
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.
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.