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Ring Theory
Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022
In this chapter, we will consider an area of mathematics, called ring theory, and discuss its applications to cryptography at an introductory level. We will focus on a public-key cryptosystem called the N-th Degree Truncated Polynomial Ring (NTRU), which was first introduced by Hoffstein et al. (1998). The major advantages of the NTRU (pronounced en-tr u¯) cryptosystem are that it is based on certain lattice problems, and it is thought to be resistant to all quantum-based computer attacks (Hoffstein et al., 2010). Additionally, it is considerably faster than other public-key cryptosystems like RSA (Rivest-Shamir-Adleman) and ECC (elliptic-curve cryptography), which are susceptible to quantum-based computer attacks (Hoffstein et al., 1998). The application of the NTRU cryptosystem requires some basic ring theory, and thus we proceed with the mathematical content about rings that will be required for this cryptosystem.
Post-Quantum Cryptography
Published in Khaleel Ahmad, M. N. Doja, Nur Izura Udzir, Manu Pratap Singh, Emerging Security Algorithms and Techniques, 2019
Amandeep Singh Bhatia, Ajay Kumar
NTRU cryptosystem is secure and efficient on comparing with the best-known public-key cryptosystems such as RSA and ECC. There exist several attacks against NTRU scheme: brute force, multiple transmission attacks, and alternate private keys are used to decrypt the message m and lattice-based attacks. (Mersin, 2007) compared the NTRU cryptosystem with RSA and ECC cryptosystems. It has been shown that the performance of NTRU cryptosystem is far better than other algorithms. Thus, the key generation, encryption, and decryption processes of NTRU take less time. But, on comparing with the McEliece public-key cryptosystem, it has been investigated that the encryption and decryption processes of NTRU cryptosystem take more time.
Iris-based privacy-preserving biometric authentication using NTRU homomorphic encryption
Published in Brij B. Gupta, Nadia Nedjah, Safety, Security, and Reliability of Robotic Systems, 2020
NTRU [13] is a lattice-based cryptosystem which involves lattices in construction of algorithm. NTRU is a post-quantum cryptography based on a shortest-vector problem in a lattice. Since NTRU is described over convolutional polynomial rings which support two operations, it can be extended to FHE. Hoffstein, Pipher, and Silverman proposed an NTRU scheme. This algorithm is standardized in IEEE 1363.1 and it is highly safe as it is immune to the attacks by quantum computers.
Security in Internet of Drones: A Comprehensive Review
Published in Cogent Engineering, 2022
Snehal Samanth, Prema K V, Mamatha Balachandra
Lv et al. have proposed a privacy protection scheme for UAV big data, by using blockchain technology. The proposed scheme uses concepts of blockchain and N-th degree Truncated polynomial Ring Units (NTRU) cryptography algorithm. The system model of the proposed scheme consists of four layers: blockchain layer, cloud layer, data layer, and user layer. The proposed scheme is executed in four stages: user data encryption stage, files upload and download stage, data recording in blockchain and user data reading from blockchain stage, and data exchange stage. Protection of data privacy and user private key privacy is preserved, due to encryption of exchanged data between users and blockchain center, and because of the NTRU password protection mechanism in the blockchain system. Considering the different NTRU parameters compatible with the X9.98 protocol, a key is selected to provide good performance without compromise in security. Results show that NTRU key generation takes the highest time, NTRU encryption consumes lower time, and NTRU decryption consumes the lowest time. Decryption time increases by hardly a ms when the key size is increased from 557-Bytes to 821-Bytes. NTRU cryptosystem shows the high efficiency of encryption and decryption. It has been observed that when the key size of NTRU is increased from 557-Bytes to 821-Bytes, the homomorphic encryption time of NTRU increases by around 6–8 ms. Multiplicative homomorphic encryption time is less than that of additive homomorphic encryption time, hence the proposed privacy protection scheme provides high security (Lv etal., 2021).