Lossless Data Hiding in NTRU Cryptosystem by Polynomial Encoding and Modulation

Lossless data hiding in ciphertexts (LDH-CT) is to perform data embedding without changing their plaintexts, which can be used to transmit extra data in the applications of homomorphic encryption at little cost. In this paper, two LDH-CT algorithms named Polynomial Encoding (PE) and Polynomial Modulation (PM) are proposed for the “N-th Degree Truncated Polynomial Ring Unit” (NTRU) scheme, respectively. In the PE algorithm, a polynomial is encoded according to a string of bit values and further used to encrypt a plain-text polynomial. After decrypting the ciphertext, the encoded polynomial can be retrieved so that dozens of bit values can be extracted from it. Moreover, the PE algorithm can be combined with a polynomial partitioning strategy to achieve data extraction before decryption as well. In applying the PM algorithm, no parameter setting of an NTRU cryptosystem is changed while a cipher-text polynomial is generated by selectively sampling a polynomial to match the to-be-hidden value. Furthermore, the data hidden with the PM algorithm can be pre-chosen to be extracted without decryption or after decryption, and in each case up to 10 bit values can be hidden into one cipher-text polynomial. The proposed algorithms and schemes are implemented and compared with several schemes developed for NTRU, BGN, LWE and Paillier encryption. Experimental results and performance evaluations demonstrate the efficacy and superiority of the proposed algorithms and schemes.