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.
The BB84 quantum key distribution (QKD) protocol is based on the no-cloning quantum physic property, so if an attacker measures a photon state, he disturbs that state. This protocol uses two channels: (1) A quantum channel for sending the quantum information (photons polarized). (2) And a classical channel for exchanging the polarization and the measurement information (base sets or filters). The BB84 supposes that the classical channel is secure, but it is not always right, because it depends on the methods used during the communication over this channel. If an eavesdropper gets the sender or the receiver filters or both of them, he can leak some or all bits of the constructed key. In this context, we contribute by creating a protocol that combines the BB84 protocol with an improved scheme of NTRU post-quantum cryptosystem, which will secure the transmitted information over the classical channel. NTRU is a structured lattice scheme, and it is based on the hardness to solve lattice problems in Rn. Actually, it is one of the most important candidates for the NIST post-quantum standardization project.
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