Lattice-based identity-based resplittable threshold public key encryption scheme

Abstract

Threshold public key encryption is a cryptographic primitive where a secret key of an organization is distributed among special members called decryption servers (insiders) and a certain threshold number of insiders must cooperate to decrypt any ciphertext. Threshold public key encryption with an additional randomized algorithm Tsplit is called resplittable threshold public key encryption (RTPKE). Cryptographic primitive RTPKE was introduced by Hanaoka et al. [Generic construction of chosen ciphertext secure proxy re-encryption, in CT-RSA, San Francisco, CA, USA, LNCS, O. Dunkelman, ed., Springer-Verlag, Heidelberg, 2012, pp. 349–364] in a generic construction of chosen ciphertext attack secure proxy re-encryption scheme. In MIST 2013 conference Singh et al. [Lattice based efficient threshold public key encryption scheme, J. Wirel. Mob. Netw. Ubiquitous Comput. Dependable Appl. (JoWUA) 4(4) (2013), pp. 93–107] presented lattice-based RTPKE scheme based on Regev's LWE [On lattices, learning with errors, random linear codes, and cryptography, in STOC, Baltimore, MD, USA, H.N. Gabow and R. Fagin, eds., ACM, University of Wales, Cardiff, 2005, pp. 84–93] assumption. In this paper, we propose lattice-based RTPKE scheme in the identity-based setting.

Keywords:

• lattice
• resplittable threshold public key encryption
• learning with error
• identity-based encryption

2000 AMS Subject Classifications:

• 94A60
• 94A62
• 68W20
• 06D50

Acknowledgements

We would like to thank anonymous reviewers of MIST 2013 for their useful comments.

Notes

[1] A function g(n) is in $\tilde{O}(f(n)$) if there exist constants a, c≥0 such that $g(n)\le af(n){\log }^{c}f(n)$ for all sufficiently large n.