Lattice Based Efficient Threshold Public Key Encryption Scheme

Kunwar Singh¹⁺, C. Pandu Rangan², and A.K.Banerjee¹

¹National Institute of Technology Tiruchirappalli, India
{kunwar, banerjee}@nitt.edu

²Indian Institute of Technology Madras Chennai, Tamil Nadu, India
rangan@cse.iitm.ac.in

Abstract

Recent A (t,u)- threshold public key encryption (TPKE) is a public key encryption where a private key is splitted among u decryption servers (insiders) and at least t decryption servers (insiders) are required to decrypt the ciphertext but no group of t-1 or less malicious insiders can decrypt the message. Bendlin and Damgard [1] presented first lattice based threshold public key encryption scheme based on Regev’s LWE based encryption system [2]. We propose efficient lattice based threshold public key encryption scheme based on [3]. We have reduced size of the public key from (n²+1)log n ×||Zq|| to (n²+1)×||Zq|| with the same ciphertext size where ||Zq|| is the number of bits required to represent an element of Zq. Resplittable threshold public key encryption (RTPKE) was introduced by Hanaoka et al [4] in a generic construction of CCA secure uni-directional proxy re-encryption scheme. RTPKE is a threshold public key encryption with an additional randomized algorithm Tsplit. Based on our efficient threshold scheme, we have constructed efficient resplittable threshold public key encryption scheme.

Keywords: Lattice, Resplittable Threshold Public Key Encryption, Learning With Error (LWE)

+: Corresponding author: Kunwar Singh
Computer Science and Engineering Department, National Institute of Technology, Trichy,
Tiruchirappalli-15, Tamilnadu, India, Tel: +91-43125013212,
Web: http://www.nitt.edu/home/academics/departments/cse/faculty/kunwar/

Journal of Wireless Mobile Networks, Ubiquitous Computing, and Dependable Applications (JoWUA),

Vol. 4, No. 4, pp. 93-107, December 2013 [pdf]