International Association for Cryptologic Research

International Association
for Cryptologic Research


Rui Zhang


Formal Security Treatments for IBE-to-Signature Transformation: Relations among Security Notions
In a seminal paper of identity based encryption (IBE), Boneh and Franklin [BF01] mentioned an interesting transform from an IBE scheme to a signature scheme, which was observed by Moni Naor. In this paper, we give formal security treatments for this transform and discover several implications and separations among security notions of IBE and transformed signature. For example, we show for such a successful transform, one-wayness of IBE is an essential condition. Additionally, we give a sufficient and necessary condition for converting a semantically secure IBE scheme into an existentially unforgeable signature scheme. Our results help establish strategies on design and automatic security proof of signature schemes from (possibly weak) IBE schemes. We also show some separation results which strongly support that one-wayness, rather than semantic security, of IBE captures an essential condition to achieve secure signature.
Relations Among Notions of Security for Identity Based Encryption Schemes
Identity based encryption (IBE) schemes have been flourishing since the very beginning of this century. In IBE it is widely believed that proving the security of a scheme in the sense of IND-ID-CCA2 is sufficient to claim the scheme is also secure in the senses of both SS-ID-CCA2 and NM-ID-CCA2. The justification for this belief is the relations among indistinguishability (IND), semantic security (SS) and non-malleability (NM). But these relations are proved only for conventional public key encryption (PKE) schemes in historical works. The fact is that between IBE and PKE, there exists a difference of special importance, i.e. only in IBE the adversaries can perform a particular attack, namely the chosen identity attack. This paper shows that security proved in the sense of IND-ID-CCA2 is validly sufficient for implying security in any other sense in IBE. This is to say the security notion, IND-ID-CCA2, captures the essence of security for all IBE schemes. To achieve this intention, we first describe formal definitions of the notions of security for IBE, and then present the relations among IND, SS and NM in IBE, along with rigorous proofs. All of these results are proposed with the consideration of the chosen identity attack.
Efficient Identity-Based Encryption with Tight Security Reduction
In a famous paper of Crypto'01, Boneh and Franklin proposed the first identity-based encryption scheme (IBE), around fifteen years after the concept was introduced by Shamir. Their scheme security (more precisely, the notion of resistance against an IND-ID-CCA attacker) relies in the random oracle model. However, the reduction is far from being tight, and notably depends on the number of extractions queries. In this paper, we present an efficient modification to the Boneh-Franklin scheme that provides a tight reduction. Our scheme is basically an IBE under two keys, one of which is (randomly) detained by the recipient. It can be viewed as a continuation of an idea introduced by Katz and Wang; we will however show how our construction improves this last scheme. Our scheme features a tight reduction to the list bilinear Diffie-Hellman (LBDH) problem, which can be itself reduced tightly either to the gap bilinear Diffie-Hellman (GBDH) or the decisional bilinear Diffie-Hellman (DBDH) problems. Furthermore, for a relaxed notion of tightness (called weak-tightness) that we introduce and discuss in our paper, we show that there is a weakly tight reduction from our scheme to the computational bilinear Diffie-Hellman (CBDH) problem. Our scheme is very efficient, as one can precompute most of the quantity involved in the encryption process. Furthermore, the ciphertext size is very short: for proposed parameters, they are |M|+330 bits long.
On the Security of Multiple Encryption or CCA-security+CCA-security=CCA-security?
In a practical system, a message is often encrypted more than once by different encryptions, here called multiple encryption, to enhance its security. Additionally, new features may be achieved by multiple encrypting a message for a scheme, such as the key-insulated cryptosystems \cite{DKXY02} and anonymous channels \cite{Cha81}. Intuitively, a multiple encryption should remain ``secure'', whenever there is one component cipher unbreakable in it. In NESSIE's latest Portfolio of recommended cryptographic primitives (Feb. 2003), it is suggested to use multiple encryption with component ciphers based on different assumptions to acquire long term security. However, in this paper we show this needs careful discussion. Especially, this may \emph{not} be true according to (adaptive) chosen ciphertext attack ({\sf CCA}), even with all component ciphers {\sf CCA} secure. We define an extended version of {\sf CCA} called \emph{chosen ciphertext attack for multiple encryption} ({\sf ME-CCA}) to emulate real world partial breaking of assumptions, and give constructions of multiple encryption satisfying {\sf ME-CCA} security. Since {\sf CCA} security seems so stringent, we further relax it by introducing \emph{weak} {\sf ME-CCA} ({\sf ME-wCCA}), and prove {\sf IND-ME-wCCA} secure multiple encryption can be acquired from {\sf IND-gCCA} secure component ciphers. We also study the relation of various security notions for multiple encryption. We then apply these results to key-insulated cryptosystem. It is only previously known in \cite{DKXY02} that a generic construction exists provably secure against {\sf CPA} attack, however, we prove that this generic construction is in fact secure against {\sf ME-wCCA} by choosing all components {\sf IND-CCA} secure. We also give an efficient generic construction of key-insulated cryptosystem, which is so far the \emph{first} generic construction provably secure against {\sf CCA} (in the random oracle model).