The Construction Of Quantum Block Cipher For Grover Algorithm
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Date
2018-01
Authors
Mishal Eid, Almazrooie
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Asymmetric and symmetric cryptography are believed to be secure against any attack using
classical computers. However, this view is no longer valid in the presence of quantum computing.
Asymmetric cryptographic algorithms which are based on integer factorization or discrete
logarithms problems are rendered unsecured against quantum attacks. In contrast, threats
posed by quantum computing to symmetric cryptography is not clear compared with asymmetric
cryptography. Similarly to classical computing, to conduct a quantum attack on a classical
block cipher, the block cipher must be designed and implemented as a quantum reversible circuit
in a quantum platform. There is no existing quantum design for any classical symmetric
cryptographic algorithm such that one could study and analyze in practice the possible threats
that might be posed by a quantum adversary to the security of the symmetric cryptographic
algorithms. In this study, quantum designs for Feistel structure and SPN block ciphers are presented.
First, the main building components that are used to provide diffusion and confusion
in block ciphers are designed as reversible circuits. The hand crafted S-Boxes such as in DES
cipher and the mathematically generated S-Boxes such as in AES are constructed as quantum
circuits. The finite fields F2[x]=(x4+x+1) and F2[x]=(x8+x4+x3+x+1) in SAES and AES
respectively, are considered in this study. Then, all the circuits are put together to form the
quantum version of the block cipher. By using a Quantum Simulator, quantum attacks are conducted
by using Grover’s algorithm to recover the secret key. The proposed quantum cipher
is used as a Black-box for the quantum search. The expected results of the proposed quantum
block ciphers have to match those ones of the classical block ciphers.
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Keywords
The construction of quantum block , cipher for grover algorithm