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International Conference on Computational Intelligence and Security (CIS)

New CCA-Secure Proxy Re-encryption Scheme without Random Oracles

Xu An Wang, Ping Wei, Minqing Zhang

Published Dec 1, 2010• 2 citations
Publisher

Abstract

Proxy re-encryption (PRE) allows a ciphertext computed under Alice's public key to be transformed to those which can be decrypted by Bob. In PKC'08, Libert and Vergnaud proposed the first unidirectional RCCA-secure PRE scheme in the standard model. They left the open problem of constructing unidirectional CCA-secure PRE scheme in the standard model open. Until recently, this open problem was solved by Weng et al. and Shao et al. independently. In this paper, based on Shao et al.'s proposal, we give a new efficient CCA-secure PRE scheme without random oracles and prove its security.

DOI
10.1109/cis.2010.87

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•Jan 1, 2011•21 citations
Proxy re-encryption (PRE) allows a ciphertext computed under Alice's public key to be transformed to those which can be decrypted by Bob. In PKC'08, Libert and Vergnaud proposed the first unidirectional RCCA-secure PRE scheme in the standard model. They left the open problem of constructing unidirectional CCA-secure PRE scheme in the standard model open. Until recently, this open problem was solved by Weng et al. and Shao et al. independently. In this paper, based on Shao et al.'s proposal, we give a new efficient CCA-secure PRE scheme without random oracles and prove its security.
Proxy re-encryption allows a proxy to transform a ciphertext computed under Alice's public key into one that can be opened under Bob's decryption key. In CANS'08, Deng et al. proposed the first bidirectional IND-PRE-CCA2 secure proxy re-encryption without parings. Later, in PKC'09, Shao et al. proposed the first unidirectional IND-PRE-CCA2 secure proxy re-encryption without parings. But both of these schemes prove their security in the random oracle. They left an open problem of constructing (bidirectional or unidirectional) IND-PRE-CCA2 secure proxy re-encryption scheme in the standard model yet without pairings. In this paper, we try to solve this open problem by proposing two new restricted IND-PRE-CCA2 secure bidirectional proxy re-encryption schemes without pairing nor random oracle.
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.
Blaze et al. in 1998 introduced the concept of proxy re-encryption, which allows a proxy to transform a ciphertext computed under Alice's public key into one that can be opened under Bob's decryption key. In CCS'07, Canetti et al. proposed an IND-PRE-CCA2 bidirectional proxy re-encryption scheme, and later, Libert et al. proposed another IND-PRE-CCA2 secure unidirectional proxy re-encryption. However, both schemes rely on the costly bilinear pairings. In CANS'08, Deng et al. proposed the first IND-PRE-CCA2 secure proxy re-encryption without parings. Later, in PKC'09, Shao et al. proposed another IND-PRE-CCA2 secure proxy re-encryption without parings. But both of these schemes prove their security in the random oracle. In this paper, based on Hanaoka's efficient chosen ciphertext secure public key encryption under the computational Diffie-Hellman assumption, we present two new interesting bidirectional proxy re-encryption schemes, which are restricted IND-PRE-CCA2 secure without pairing nor random oracle.
Up to now, it is still an open question of how to construct a chosen-ciphertext secure unidirectional proxy re-encryption scheme in the adaptive corruption model. To address this problem, we propose a new unidirectional proxy re-encryption scheme, and prove its chosen-ciphertext security in the adaptive corruption model without random oracles. Compared with the best known unidirectional proxy re-encryption scheme proposed by Libert and Vergnaud in PKC’08, our scheme enjoys the advantages of both higher efficiency and stronger security.
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.