Boosted Performances of NTRUencrypt Post-Quantum Cryptosystem

The bottleneck of all cryptosystems is the difficulty of the computational complexity of the polynomials multiplication, vectors multiplication, etc. Thus most of them use some algorithms to reduce the complexity of the multiplication like NTT, Montgomery, CRT, and Karatsuba algorithms, etc. We contribute by creating a new release of NTRUencrypt1024 with great improvement, by using our own polynomials multiplication algorithm operate in the ring of the form Rq=Zq[X]/(XN+1), combined to Montgomery algorithm rather than using the NTT algorithm as used by the original version. We obtained a good result, our implementation outperforms the original one by speed-up of a factor up to (X10) for encryption and a factor up to (X11) for decryption functions. We note that our improved implementation used the latest hash function standard SHA-3, and reduce the size of the public key, private key, and cipher-text from 4097 bytes to 2049 bytes with the same security level.

Short Principal Ideal Problem in multicubic fields

One family of candidates to build a post-quantum cryptosystem upon relies on euclidean lattices. In order to make such cryptosystems more efficient, one can consider special lattices with an additional algebraic structure such as ideal lattices. Ideal lattices can be seen as ideals in a number field. However recent progress in both quantum and classical computing showed that such cryptosystems can be cryptanalysed efficiently over some number fields. It is therefore important to study the security of such cryptosystems for other number fields in order to have a better understanding of the complexity of the underlying mathematical problems. We study in this paper the case of multicubic fields.