Most traditional public key cryptosystems are constructed upon algebraically rich structures, which makes their key pairs combinable, i.e., the combination of some private keys and their corresponding public keys could form a new key pair. Exploring such combinable property, this paper proposes a novel Identity-Based Encryption (IBE) scheme based on the Diffie-Hellman Integrated Encryption Scheme (DHIES) with quadratic key combination structure from bilinear maps. The new scheme has a number of advantages over other IBE schemes. First, it uses DHIES to fulfill encryption, thus naturally obtains the security against adaptive chosen ciphertext attack from DHIES. Second, it is interoperable with existing security systems based on DHIES. Third, compared to many pairing-based IBE schemes, it only requires pairing computation during public key generation and there is no need for special hash function. We prove that our scheme is selective identity chosen ciphertext secure in the random oracle model assuming DHIES is chosen ciphertext secure. Additionally, the extract algorithm of our scheme also implies an identity-based short signature scheme.
Abstract. When using pairing-friendly ordinary elliptic curves over prime fields to implement identity-based protocols, there is often a need to hash identities to points on one or both of the two elliptic curve groups of prime order r involved in the pairing. Of these G1 is a group of points on the base field E(F p ) and G 2 is instantiated as a group of points with coordinates on some extension field, over a twisted curve E (F p d ), where d divides the embedding degree k. While hashing to G 1 is relatively easy, hashing to G 2 has been less considered, and is regarded as likely to be more expensive as it appears to require a multiplication by a large cofactor. In this paper we introduce a fast method for this cofactor multiplication on G2 which exploits an efficiently computable homomorphism.
Lossy Trapdoor Functions (LTFs) was introduced by Peikertand Waters in 2008. The importance of the LTFs was justified by their numerous cryptographic applications, like the construction of injective one-way trapdoor functions, CCAsecure public-key encryption, etc. However, little research on application of LTFs to key-leakage resilient public-key encryption was done. In this article we introduce a new variant of LTFs featuring leakage-resilience, namely lrLTFs and give a realization of lrLTFs with leakage rate 1/Θ(κ) (where κ is the security parameter) under the Decisional Diffie-Hellman (DDH) assumption. We further improve the leakage rate to 1 − o(1) over a composite-order group in which the Decisional Composite Residuosity (DCR) assumption holds. We also introduce a new notion of key-leakage attacks, which we call weak key-leakage attacks, for bridging the adaptive and non-adaptive key-leakage attacks in the setting of public-key cryptosystem. In this model, the leakage adversary only gets a part of public key before accessing to a leakage oracle. We show that lrLTFs imply public-key encryption schemes secure against chosen-ciphertext weak key-leakage attacks in a black-box sense.
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