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Security and Communication Networks

On the application of generic CCA‐secure transformations to proxy re‐encryption

David Núñez, Isaac Agudo, Javier López

Published Feb 19, 2016• 8 citations
Publisher

Abstract

Abstract Several generic methods exist for achieving chosen‐ciphertext attack (CCA)‐secure public‐key encryption schemes from weakly secure cryptosystems, such as the Fujisaki–Okamoto and REACT transformations. In the context of proxy re‐encryption (PRE), it would be desirable to count on analogous constructions that allow PRE schemes to achieve better security notions. In this paper, we study the adaptation of these transformations to proxy re‐encryption and find both negative and positive results. On the one hand, we show why it is not possible to directly integrate these transformations with weakly secure PRE schemes because of general obstacles coming from both the constructions themselves and the security models, and we identify 12 PRE schemes that exhibit these problems. On the other hand, we propose an extension of the Fujisaki–Okamoto transformation for PRE, which achieves a weak form of CCA security in the random oracle model, and we describe the sufficient conditions for applying it. Copyright © 2016 John Wiley & Sons, Ltd.

DOI
10.1002/sec.1434

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Abstract Several generic methods exist for achieving chosen‐ciphertext attack (CCA)‐secure public‐key encryption schemes from weakly secure cryptosystems, such as the Fujisaki–Okamoto and REACT transformations. In the context of proxy re‐encryption (PRE), it would be desirable to count on analogous constructions that allow PRE schemes to achieve better security notions. In this paper, we study the adaptation of these transformations to proxy re‐encryption and find both negative and positive results. On the one hand, we show why it is not possible to directly integrate these transformations with weakly secure PRE schemes because of general obstacles coming from both the constructions themselves and the security models, and we identify 12 PRE schemes that exhibit these problems. On the other hand, we propose an extension of the Fujisaki–Okamoto transformation for PRE, which achieves a weak form of CCA security in the random oracle model, and we describe the sufficient conditions for applying it. Copyright © 2016 John Wiley & Sons, Ltd.
ABSTRACT In this paper, we present a more efficient chosen‐ciphertext secure proxy re‐encryption scheme in the standard model with less ciphertext size and without any strong unforgeable one‐time signature. Our scheme is unidirectional and single‐hop. The security of our scheme is under the reasonable complexity assumption—the decisional bilinear Diffie–Hellman assumption in bilinear groups. There are no proxy re‐encryption schemes achieving chosen‐ciphertext security in the standard model without a strong unforgeable one‐time signature in the literature. Copyright © 2012 John Wiley & Sons, Ltd.
The Fujisaki-Okamoto (FO) conversion is a generic conversion to enhance a public key encryption scheme with security of one-way against chosen plaintext attacks (OW-CPA) to security of indistinguishable against adaptive chosen ciphertext attacks (IND-CCA) in the random oracle model. Existing works have shown that the FO conversion also can generically upgrade the security of the identity-based encryption (IBE) schemes or certificateless public key encryption (CL-PKE) schemes. However, it is still unknown if the same holds for certificate-based encryption (CBE) schemes. In this paper, we investigate the generic security of the CBE scheme obtained by applying the FO conversion to an arbitrary underlying OW-CBE-CPA secure CBE scheme and confirm that the FO conversion can generically convert any OW-CBE-CPA secure CBE into an IND-CBE-CCA secure CBE. We also note that the straightforward application of the FO conversion only leads to a CBE scheme with a loose reduction. To solve this problem, we propose an enhanced FO conversion which just introduces minor extra computation overhead, but results in considerably more efficient security reduction.
In proxy re-encryption (PRE), a semi-trusted proxy can convert a ciphertext originally intended for Alice into one which can be decrypted by Bob, while the proxy cannot know the corresponding plaintext. PRE can be classified as single-use PRE and multi-use PRE according to the times the ciphertext can be transformed. In multi-use PRE schemes, the ciphertext can be transformed from A to B and to C and so on. In CCS’09 (post session), Wang et al. proposed a multi-use unidirectional CCA-secure proxy re-encryption scheme. Unfortunately, we show their proposal is not CCA-secure in the corresponding security models by giving concrete attacks. In 2010, Ren et al. proposed a hierarchical identity-based proxy re-encryption scheme without random oracles, and claimed their scheme was also multi-use and CCA-secure, we also show their scheme is not secure.
A proxy re-encryption (PRE) scheme allows a designated proxy, that has beforehand received aso-called re-encryption key, to translate a ciphertext intended to one user to a ciphertext intendedto another one. Traditionally, the re-encryption key is generated at the initiative of the initialreceiver and ideally, no secret keys should be known to the proxy. Such scheme is said unidirectionalif the transformation from one user to another does not necessarily imply the possibility tomake the inverse transformation. Regarding the literature on unidirectional proxy re-encryption, itseems hard to prove the strongest security level (namely indistinguishability under chosen ciphertextattacks - IND-CCA) of such schemes. Most of the time, PRE either reaches a chosen-plaintextsecurity or a replayable CCA security. At Africacrypt 2010, Chow, Weng, Yang and Deng proposeda scheme that satisfies CCA security in the random oracle model. However, their modelcan actually be strengthen. Indeed, we show in this paper how to modify this scheme so that itsimproved security achieves a full CCA security. In particular, we now allow the adversary of theCCA security for re-encryption to corrupt the user i′ who is the initial receiver of the challengedciphertext and at the same time to obtain the re-encryption key from i′ to the targeted users. Theresulting scheme is therefore a fully secure PRE which does not rely on pairings, and secure in therandom oracle model. It can be implemented efficiently with any traditional modular arithmetic.
Proxy re-encryption, introduced by Blaze et al. in 1998, allows a proxy to transform a ciphertext computed under Alice's public key into one that can be opened under Bob's decryption key. An open problem of constructing (bidirectional or unidirectional) IND-PRE-CCA2 secure proxy re-encryption scheme in the standard model yet without pairings was left until now. In this paper, based on Hanaoka's efficient chosen ciphertext secure public key encryption under the computational Diffie-Hellman assumption, we try to solve this open problem by presenting two new bidirectional proxy re-encryption schemes, which are restricted IND-PRE-CCA2 secure without pairing nor random oracle.
Proxy re-encryption (PRE) can be classified as single-hop PRE and multi-use PRE according to the times which the ciphertext is transformed. Finding a unidirectional, multi-use, and chosen ciphertext attack (CCA) secure PRE is presented as an open problem by Canetti et al. Wang claimed to resolve this problem by proposing the first multi-use CCAsecure unidirectional PRE scheme. But we found that different with single-hop PRE, multi-use PRE without randomize encrypt key in its re-encryption algorithm could be vulnerable to attack. A new type attack to multi-use CCA-secure PRE named proxy bypass attack is proposed with a concrete attacks on Wang-MultiUse-PRE scheme. This attack is also effective for other multi-use scheme. At last we propose an improvement for Multi-Use-PRE to resist proxy bypass attack by randomize re-encryption algorithm.