Fully homomorphic encryption (FHE) supports arbitrary computations on ciphertexts without decryption to protect users’ privacy. However, currently, there are still some shortcomings in research studies FHE. For example, the NTRU-based FHE scheme constructed using approximate eigenvector method requires complex matrix multiplications, and power-of-two cyclotomic ring cannot prevent subfield atta...

In this paper, we propose a new unified architecture that utilizes the Montgomery Multiplication algorithm to perform a modular multiplication for both integers and binary polynomials and NTRU’s polynomial multiplications. The unified design is capable of supporting a majority of public-key cryptosystems such as NTRU, RSA, Diffie-Hellman key exchange, and Elliptic Curve schemes, among others. F...

We present a private information retrieval (PIR) scheme based on somewhat homomorphic encryption (SWHE). In particular, we customize an NTRU-based SWHE scheme in order to evaluate a specific class of fixed depth circuits relevant for PIR implementation, thus achieving a more practical implementation. In practice, a SWHE that can evaluate a depth 5 circuit is sufficient to construct a PIR capabl...

The subfield attack exploits the presence of a subfield to solve overstretched versions of the NTRU assumption: norming the public key h down to a subfield may lead to an easier lattice problem and any sufficiently good solution may be lifted to a short vector in the full NTRU-lattice. This approach was originally sketched in a paper of Gentry and Szydlo at Eurocrypt’02 and there also attribute...