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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
The construction of lattice-based cryptosystems holds strong security proofs on the basis of worst-case resistance of lattice problems which offers efficient execution and simplicity. Moreover, such cryptosystems are reliable and secure against the attacks of quantum computers. Basically, a lattice representing arbitrary basis is given as an input and expected the output to be the shortest nonzero vector. The concept of lattice-based cryptosystem for the shortest vector problems is proposed by (Lenstra and Lenstra, 1993). It runs in polynomial time. It is the most extensively studied algorithm for lattice problems, but later on, its various extensions have been introduced. We described the main lattice-based cryptosystems that have been introduced so far. We start with the NTRU cryptosystem, which is the most well-known, practically implemented, lattice-based encryption scheme till now.
Quantum-Safe Asymmetric Cryptosystems
Published in Shashi Bhushan, Manoj Kumar, Pramod Kumar, Renjith V. Ravi, Anuj Kumar Singh, Holistic Approach to Quantum Cryptography in Cyber Security, 2023
Sagarika Ghosh, Marzia Zaman, Srinivas Sampalli
Lattice-based cryptography has been proven to be strongly resistant to subexponential as well as quantum threats. They are based on the concept of lattices, sets of points within an n-size periodic structured space as shown in Figure 6.1 [13]. In simple terms, lattice can be considered as any regularly spaced grid of points. The security of the lattice-based cryptography depends on the complexity of lattice problems, mainly the shortest vector problem (SVP), the closest vector problem (CVP), or the shortest independent vector problem (SIVP) [7,13]. The SVP is deriving the minimum nonzero vector in the current lattice and is an NP-hard problem, unsolvable by the present quantum algorithm [7].
Ring Theory
Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022
Although the NTRU cryptosystem does possess parameter choices for which decryption can fail without the receiver's knowledge, it offers many advantages. In particular, it is thought to be resistant to all quantum based computer attacks (Hoffstein et al., 2010). Moreover, the NTRU cryptosystem is faster than other public-key cryptosystems, and its security is built on the difficulty of certain lattice problems.
Systematic Survey: Secure and Privacy-Preserving Big Data Analytics in Cloud
Published in Journal of Computer Information Systems, 2023
Arun Amaithi Rajan, Vetriselvi V
The majority of authentication mechanisms in classical cryptosystems are based on cryptographic primitives. For instance, RSA and ElGamal are cryptosystems built on factorization or discrete logarithm hard problems. It is widely assumed that such primitives are vulnerable to quantum algorithms. Shor’s algorithm32 is a quantum algorithm that solves discrete logarithm and factorization problems in sub-exponential time complexity. So, if we continue to have the same cryptosystem, there is a chance that quantum computers will attack secure applications within polynomial time in the future. So, with a longer vision, more works are being done in quantum cryptography.33 As we have hard problems in traditional systems, such as discrete logarithm, there are some hard problems in the quantum environment also such as lattice problems which prompted scientists to develop quantum cryptography algorithms. A survey on lattice-based cryptography implementations in software and hardware by Nejatollahi et al.34 gives an overview of existing algorithms in post-quantum cryptography based on lattice problems. The authors worked on implementations which tackles different issues such as memory footprint, energy, security and, given some proposals for lattices in information security
A secure lattice-based anonymous authentication scheme for VANETs
Published in Journal of the Chinese Institute of Engineers, 2019
Hui Liu, Yining Sun, Yan Xu, Rui Xu, Zhuo Wei
We can conclude from Table 1 that the proposed scheme needs no TPD which can not resist against side-channel attacks. In addition, this scheme is constructed using lattice-based cryptography. This scheme is secure against forgery attack assuming SIS-problem is hard. The security of lattice-based cryptography is based on the worst-case hardness of lattice problems which is conjectured to be hard even for quantum computers (Regev 2006). Therefore, the proposed scheme can achieve postquantum security.