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On the Security of a Bidirectional Proxy Re-Encryption Scheme from PKC 2010.

Jian Weng, Yunlei Zhao

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

In PKC 2010, Matsuda, Nishimaki and Tanaka proposed a bidirectional proxy reencryption (PRE) scheme without bilinear maps, and claimed that their scheme is chosenciphertext secure in the standard model. However, by giving a concrete attack, in this paper we indicate that their PRE scheme fails to achieve the chosen-ciphertext security. The purpose of this paper is to clarify the fact that, it is still an open problem to come up with a chosen-ciphertext secure PRE scheme without bilinear maps in the standard model.

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In this work, we study (the direct constructions of) bidirectional proxy re-encryption (PRE) with alleviated trust in the proxy, specifically the master secret security (MSS) and the nontransitivity (NT) security, in the standard model, and achieve the following: • A multi-hop MSS-secure bidirectional PRE scheme with security against chosen plaintext attacks (CPA) in the standard model, where the ciphertext remains constant size regardless how many times it has been re-encrypted. To the best of our knowledge, there exists previously no MSS-secure multi-hop bidirectional PRE scheme with constant size of ciphertexts (whether in the random oracle model or not). • A single-hop MSS-secure and non-transitive bidirectional PRE scheme with security against chosen ciphertext attacks (CCA) in the standard model. The CCA-secure scheme is based on the CPA-secure scheme, and particularly employs a new re-encryption key (REK) generation mechanism to which each user makes equal contributions, where a single REK is used in both directions with the same computation so that the proxy needs not to distinguish the transform direction when it re-encrypts ciphertexts. Besides alleviated trust in proxy, single-hop non-transitive bidirectional PRE schemes also enjoy better fine-grained delegate right control (against malicious proxy). The security analysis uses Coron’s technique [Coron, Crypto 2000], which particularly allows adaptive secret-key corruption. Along the way, we also refine and clarify the security models for bidirectional PRE. 1

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Wireless Communications, Networking and Information Security•Jun 1, 2010•3 citations
In PKC 2010, Matsuda, Nishimaki and Tanaka proposed a bidirectional proxy reencryption (PRE) scheme without bilinear maps, and claimed that their scheme is chosenciphertext secure in the standard model. However, by giving a concrete attack, in this paper we indicate that their PRE scheme fails to achieve the chosen-ciphertext security. The purpose of this paper is to clarify the fact that, it is still an open problem to come up with a chosen-ciphertext secure PRE scheme without bilinear maps in the standard model.
In this work, we study (the direct constructions of) bidirectional proxy re-encryption (PRE) with alleviated trust in the proxy, specifically the master secret security (MSS) and the nontransitivity (NT) security, in the standard model, and achieve the following: • A multi-hop MSS-secure bidirectional PRE scheme with security against chosen plaintext attacks (CPA) in the standard model, where the ciphertext remains constant size regardless how many times it has been re-encrypted. To the best of our knowledge, there exists previously no MSS-secure multi-hop bidirectional PRE scheme with constant size of ciphertexts (whether in the random oracle model or not). • A single-hop MSS-secure and non-transitive bidirectional PRE scheme with security against chosen ciphertext attacks (CCA) in the standard model. The CCA-secure scheme is based on the CPA-secure scheme, and particularly employs a new re-encryption key (REK) generation mechanism to which each user makes equal contributions, where a single REK is used in both directions with the same computation so that the proxy needs not to distinguish the transform direction when it re-encrypts ciphertexts. Besides alleviated trust in proxy, single-hop non-transitive bidirectional PRE schemes also enjoy better fine-grained delegate right control (against malicious proxy). The security analysis uses Coron’s technique [Coron, Crypto 2000], which particularly allows adaptive secret-key corruption. Along the way, we also refine and clarify the security models for bidirectional PRE. 1
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.
The notion of proxy cryptography is very useful in cases when one user needs to perform sensitive operation without holding the necessary secret key. Recently, proxy reencryption scheme received much attention due to its application in information storing, secure email, etc. In this paper, we propose a proxy re-encryption used to divert ciphertext from one group to another. The scheme is bidirectional and any member can independently decrypt the ciphertexts encrypted to its group. We discuss the security of the proposed scheme and show that our scheme withstands chosen ciphertext attack in standard model.
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 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.