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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

On the Security of Luo et al.'s Fully Secure Hierarchical Identity Based Encryption Scheme

Kwangsu Lee, Jong Hwan Park, Dong Hoon Lee

Published Jan 1, 2012• 1 citation
Publisher

Abstract

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.

DOI
10.1587/transfun.e95.a.1631

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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.
Abstract We construct the first tightly secure hierarchical identity-based encryption (HIBE) scheme based on standard assumptions, which solves an open problem from Blazy, Kiltz, and Pan (CRYPTO 2014). At the core of our constructions is a novel randomization technique that enables us to randomize user secret keys for identities with flexible length. The security reductions of previous HIBEs lose at least a factor of Q, which is the number of user secret key queries. Different to that, the security loss of our schemes is only dependent on the security parameter. Our schemes are adaptively secure based on the Matrix Diffie-Hellman assumption, which is a generalization of standard Diffie-Hellman assumptions such as k-Linear. We have two tightly secure constructions, one with constant ciphertext size, and the other with tighter security at the cost of linear ciphertext size. Among other things, our schemes imply the first tightly secure identity-based signature scheme by a variant of the Naor transformation.
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.
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.
Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only ( dm 2 + mn ) log q bits and whose message-ciphertext expansion factor is only log q , where d is the maximum hierarchical depth and ( n , m , q ) are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2 d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2 dm 2 + mn + m ) log q . To reduce the message-ciphertext expansion factor of the proposed scheme to log q , the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m 2 bits of plaintext are encrypted into m 2 log q bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.