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Informatica

Cryptanalysis of a Fuzzy Identity Based Encryption Scheme in the Standard Model

Xu An Wang, Xiaoyuan Yang, Minqing Zhang, Yong Hong Yu

Published Jan 1, 2012• 6 citations
Publisher

Abstract

Fuzzy identity based encryption (FIBE), proposed by Sahai and Waters, is a new kind of identity based encryption. It allows users with identity w can decrypt ciphertext for w' if and only if w is close enough to w'. Recently, Ren et al. proposed a new FIBE scheme and claimed it is fully CCA2 secure in the standard model with a tight reduction. However, in this paper we will show that their scheme is not correct. Furthermore, the key generation process of their scheme cannot resist the collusion attack, which is a basic security requirement for FIBE. At last, we propose a new fully secure FIBE scheme based on the Sahai–Waters FIBE scheme and prove its security by using the “dual system encryption” technique.

DOI
10.15388/informatica.2012.361

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Fuzzy identity based encryption (FIBE), proposed by Sahai and Waters, is a new kind of identity based encryption. It allows users with identity w can decrypt ciphertext for w' if and only if w is close enough to w'. Recently, Ren et al. proposed a new FIBE scheme and claimed it is fully CCA2 secure in the standard model with a tight reduction. However, in this paper we will show that their scheme is not correct. Furthermore, the key generation process of their scheme cannot resist the collusion attack, which is a basic security requirement for FIBE. At last, we propose a new fully secure FIBE scheme based on the Sahai–Waters FIBE scheme and prove its security by using the “dual system encryption” technique.
Abstract—Sahai and Waters introduced a fuzzy id-based encryption (FIBE) scheme in which an identity was viewed as a set of descriptive attributes, and any user with a private key for an identity ID was allowed to decrypt a ciphertext encrypted with an identity ID ′ , if and only if the identity ID and ID ′ were close to each other as measured by the “set overlap ” distance metric. After that, Shweta Agrawal, Xavier Boyen, Vinod Vaikuntanathan, Panagiotis Voulgaris and Hoeteck Weeto constructed a fuzzy id-based encryption scheme from the hardness of the Learning With Errors ( LWE) problem. The two schemes both had more longer public and private keys, and it was not very efficient. This paper gives more efficient fuzzy id-based encryption scheme from lattice, in which the public keys are greatly reduced, and there are two vectors corresponding to each bit of the identity by using of the algorithm Sampleleft introduced by Shweta Agrawal, Dan Boneh and Xavier Boyen, and only a trapdoor basis is the secret key. Furthermore, the scheme is dealing with N bit − information and is also secure from the hardness of the Learning With Errors ( LWE) problem, and all these greatly raise efficiency.
Abstract. We use hybrid encryption with Fuzzy Identity-Based Encryption (Fuzzy-IBE) schemes, and present the first and efficient fuzzy identity-based key encapsulation mechanism (Fuzzy-IB-KEM) schemes which are chosen-ciphertext secure (CCA) without random oracle in the selective-ID model. To achieve these goals, we consider Fuzzy-IBE schemes as consisting of separate key and data encapsulation mechanisms (KEM-DEM), and then give the definition of Fuzzy-IB-KEM. Our main idea is to enhance Sahai and Waters ' "large universe " construction, chosen-plaintext secure (CPA) Fuzzy-IBE, by adding some redundant information to the ciphertext to make it CCA-secure.
This chapter provides the details of the Waters’ Identity-Based Encryption (IBE) scheme. It provides the preliminaries including the security model and hardness assumptions for the IBE scheme. The chapter gives the dual system encryption followed by the Waters’ IBE. In 2009, Waters proposed a new methodology called dual system encryption that allows us to prove that an IBE scheme is fully (adaptively) secure based on static assumptions without random oracle. The crux of Waters’ strategy is to move to a security game where both the challenge ciphertext and secret keys are semi-functional. At this point, any keys the challenger gives out are not useful in decrypting the ciphertext.
—In order to provide access control on encrypted data, Attribute-based encryption (ABE) defines each user using a set of attributes. Fuzzy identity-based encryption (FIBE) is a variant of ABE that allows for a threshold access structure for users. To address the potential threat posed by future quantum computers, this paper presents a postquantum fuzzy IBE scheme based on lattices. However, current lattice-based ABE schemes face challenges related to computational complexity and the length of ciphertext and keys. This paper aims to improve the performance of an existing fuzzy IBE scheme by reducing key length and computational complexity during the encryption phase. While negative attributes are not utilized in our scheme, we prove its security under the learning with error (LWE) hard problem assumption in the selective security model. These improvements have significant implications for the field of ABE.
Recently, Luo et al. proposed an efficient hierarchical identity based encryption (HIBE) scheme with constant size of ciphertexts, and proved its full security under standard assumptions. To construct the scheme, they used the dual system encryption technique of Waters, and devised a method that compresses the tag values of dual system encryption. In this paper, we show that the security proof of Luo et al. is wrong since there exists an algorithm that distinguishes whether it is a simulation or not.