4.6.3 Quantum Cryptography
Modern cryptography algorithms are based on the most important method of factorization against giant integers into their primes, which is tough to be solved. But modern cryptography is at risk of each technical growth of computing power in arithmetic to quickly reverse one-way functions like that of factorization massive numbers. So, quantum computing is introduced into cryptography, which ends up in the analysis of quantum cryptography. Quantum cryptography is the science that applies quantum mechanics to carry out cryptographic tasks. Quantum cryptography is one among the emerging topics within the sector of computer industry. Quantum cryptography brings quantum key generation, quantum key distribution, quantum public key encryption, and quantum random number generation. Quantum cryptography covers the weaknesses of recent digital cryptosystems, and eventually toward the longer term direction.
Figure 4.6 Visualization of a qubit state.
A classical machine device for quantum computing has a two-state system: 0 ↔ 1. The state of a quantum bit known as qubit is generally represented by the expression: α|0〉 + β|1〉, in which α and β are complex numbers which agree with |α|2 + |β|2 = 1. Thus, a qubit state is represented as a unit vector in a set of complex numbers which is known as the two-dimensional complex vector space shown in Figure 4.6. The vector
Quantum computing is totally different from most different branches of science therein it uses complex numbers in an elementary way. Quantum computing is driven through the language of complex vector space which is the set of vectors of a fixed length with complex entries. These vectors describe the states of quantum systems and quantum computers. The important role of complex vector spaces in quantum computing is described in the references [14–16].
4.7 Conclusion
This chapter discussed modular arithmetic, complex number arithmetic, matrix algebra, and elliptic curve arithmetic to create non-linear cryptographic transformations by using the integration of their mathematical properties. The intelligent computing on the complex plane based on the integration of complex number arithmetic with modular arithmetic is beneficial to the cryptographic applications. The proposed techniques need double the memory areas to store the keys however their security levels are generally squared. The complex plane supports the non-linear cryptographic transformations not only for traditional ciphers and elliptic curve cryptography but also for quantum cryptography in order to get more secure for sustainable development. This chapter points to the importance of complex plane in the modern cryptography.
References
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1 *Corresponding author: [email protected]
2 †Corresponding author: [email protected]
5
Application of Machine Learning Framework for Next-Generation Wireless Networks: Challenges and Case Studies
Satyendra Singh Yadav1, Shrishail Hiremath2*, Pravallika Surisetti2, Vijay Kumar3 and Sarat Kumar Patra4
1Department of ECE, National Institute of Technology Meghalaya, Meghalaya, India
2Department of ECE, National Institute of Technology Rourkela, Odisha, India
