A Lattice-Based Public Key Encryption with Equality Test in Standard Model

Abstract. Public key encryption with equality test (PKEET) allows

testing whether two ciphertexts are generated by the same message or

not. PKEET is a potential candidate for many practical applications

like efficient data management on encrypted databases. Potential applicability of PKEET leads to intensive research from its first instantiation

by Yang et al. (CT-RSA 2010). Most of the followup constructions are

secure in the random oracle model. Moreover, the security of all the

concrete constructions is based on number-theoretic hardness assumptions which are vulnerable in the post-quantum era. Recently, Lee et al.

(ePrint 2016) proposed a generic construction of PKEET schemes in the

standard model and hence it is possible to yield the first instantiation

of PKEET schemes based on lattices. Their method is to use a 2-level

hierarchical identity-based encryption (HIBE) scheme together with a

one-time signature scheme. In this paper, we propose, for the first time,

a direct construction of a PKEET scheme based on the hardness assumption of lattices in the standard model. More specifically, the security of

the proposed scheme is reduces to the hardness of the Learning With

Errors problem. We have used the idea of the full identity-based encryption scheme by Agrawal et al. (EUROCRYPT 2010) to construct the

proposed PKEET