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Computer Science and Engineering Department NIT Trichy, Tiruchirappalli, India [email protected] Computer Science and Engineering Department IIT, Madras [email protected] 3 Mathematics Department NIT Trichy, Tiruchirappalli, India [email protected]

Abstract. The concept of identity-based cryptosystem was introduced by Adi Shamir in 1984. In this new paradigm users’ public key can be any string which uniquely identifies the user. The task of Public Key Generator (PKG) in IBE is to authenticate identity of the entity, generate the private key corresponding to the identity of the entity and finally transmit the private key securely to the entity. In large network PKG has a burdensome job. So the notion of Hierarchical IBE (HIBE) was introduced in [11,12] to distribute the workload by delegating the capability of private key generation and identity authentication to lower-level PKGs. In Eurocrypt 2010 Agrawal et al [1] presented an efficient lattice based secure HIBE scheme in the standard model in weaker security notion i.e. selective-ID. Based on [1], Singh et al [18] constructed adaptive-ID secure HIBE with short public parameters and still the public parameters is very large (total l  × h + 2 matrices). In this paper, we have reduced the size of the public parameters from l  × h + 2 matrices to l  + 2 matrices using Chatterjee and Sarkar’s [8] and blocking technique [7], where h is the number of levels in HIBE. Keywords: Lattice, Hierarchical Identity Base Encryption (HIBE), Learning With Error (LWE).

1 Introduction The concept of identity-based cryptosystem was introduced by Adi Shamir in 1984 [16]. In this new paradigm, users’ public key can be any string which uniquely identifies the user. For example, users’ identifier information such as email, phone number and IP address can be public key. As a result, it significantly reduces cost and complexity of establishing public key infrastructure (PKI). Although Shamir constructed an identitybased signature scheme using RSA function but was not able to construct an identitybased encryption scheme and this remained open problem until 2001, when this open problem was independently solved by Boneh-Franklin [5] and Cocks [9]. The task of Public Key Generator (PKG) in IBE is to authenticate identity of the entity, generate the private key corresponding to identity of the entity and finally transmit the private key securely to the entity. In large network PKG has a burdensome job. Linawati et al. (Eds.): ICT-EurAsia 2014, LNCS 8407, pp. 542–553, 2014. c IFIP International Federation for Information Processing 2014 

Efficient Lattice HIBE in the Standard Model with Shorter PP

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So the notion of Hierarchical IBE (HIBE) was introduced in [11,12] to distribute the workload by delegating the capability of private key generation and identity authentication to lower-level PKGs. However, lower level PKGs do not have their own public parameters. Only root PKG has some set of public parameters. In 1994, Peter Shor in his seminal paper showed that prime factorizati

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