Quantum cryptography

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ABSTRACT

The aim of this paper is to elucidate the implications of quantum computing  in  present  cryptography  andto introduce the reader to basic post-quantum algorithms. In particular the reader candel vein to the following subjects:present cryptographic schemes (symmetric and asymmetric), differences between quantum and classical computing, challenges in quantum computing,quantum al gorithms(Shor’sandGrover’s),public key encryption schemes affected, symmetric schemes affected, the impact on hash functions, and post quantum cryptography. Specifically, the section of Post-Quantum Cryptography deals with different quantum key distribution methods and mathematical- based solutions, such as the BB84 protocol, lattice-based cryptography, multivariate-based cryptography, hash-based signatures and code-based cryptography

INTRODUCTION

Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution to the key exchange problem. The advantage of quantum cryptography lies in the fact that it allows the completion of various cryptographic tasks that are proven or conjectured to be impossible using only classical (i.e. non-quantum) communication. For example, it is impossible to copy data encoded in a quantum state. If one attempts to read the encoded data, the quantum state will be changed (no-cloning theorem). This could be used to detect eavesdropping in quantum key distribution.

There is no doubt that advancements in technology and particularly electronic communications have become one of the main technological pillars of the modern age. The need for confidentiality, integrity, authenticity, and non-repudiation in data transmission and data storage makes the science of cryptography one of the most important disciplines in informationtechnology.Cryptography,etymologicallyderivedfrom the Greek words hidden and writing, is the process of securing data in transit or stored by third party adversaries. There are twokindsofcryptosystems;symmetricandasymmetric.

Quantum computing theory firstly introduced as a concept in 1982 by Richard Feynman, has been researched extensively and is considered the destructor of the present modern asymmetric cryptography. In addition, it is a fact that symmetric cryptography can also be affected by specific quantum algorithms; however, its security can be increased with the use     of larger key spaces. Furthermore, algorithms that can break the present asymmetric cryptoschemes whose security is based on the difficulty of factorizing large prime numbers and the discrete logarithm problem have been introduced. It appears that even elliptic curve cryptography which is considered presently the most secure and efficient scheme is weak against quantum computers. Consequently, a need for cryptographic algorithmsrobusttoquantumcomputationsarose.

The rest of the paper deals initially with the analysis of symmetric cryptography, asymmetric cryptography and hash functions. Specifically, an emphasis is given on algorithms that take advantage of the difficulty to factorize large prime numbers, as well as the discrete logarithm problem. We move on by giving an introduction to quantum mechanics and the challenge of building a true quantum computer.Furthermore,we introduce two important quantum algorithms that can have a huge impact in asymmetric cryptography and less in symmetric, namely, Shor’s algorithm and Grover’s algorithm respectively. Finally, post-quantum cryptography is presented. Particularly, an emphasis is given on the analysis of quantum key distribution and some mathematical based solutions such as lattice-based cryptography, multivariate-based cryptography, hash-based signatures, and code-based cryptography.

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