Survey of Lattice to Design Post Quantum Cryptographic Algorithm Using Lattice

  IJETT-book-cover  International Journal of Engineering Trends and Technology (IJETT)          
  
© 2021 by IJETT Journal
Volume-69 Issue-1
Year of Publication : 2021
Authors : Dr. Uma Pujeri, Dr. P. S. Aithal, Dr. Ramachandra Pujeri
DOI :  10.14445/22315381/IJETT-V69I1P214

Citation 

MLA Style: Dr. Uma Pujeri, Dr. P. S. Aithal, Dr. Ramachandra Pujeri. "Survey of Lattice to Design Post Quantum Cryptographic Algorithm Using Lattice" International Journal of Engineering Trends and Technology 69.1(2021):92-96. 

APA Style:Dr. Uma Pujeri, Dr. P. S. Aithal, Dr. Ramachandra Pujeri. Survey of Lattice to Design Post Quantum Cryptographic Algorithm Using Lattice  International Journal of Engineering Trends and Technology, 69(1), 92-96.

Abstract
Objective: Quantum algorithms are stronger and more secure than classical computers because they run on faster, harder ones and require fewer steps. With Quantum computers, the attackers have high computing power, and with a quantum, the algorithm can easily break the cryptographic system. Lattice is a regularly spaced grid of points stretching to infinity. Quantum safe security algorithms are resistant to both attacks caused by quantum computers and attacks caused by classical computers. Lattice-based cryptography is the post-quantum cryptographic standards resistant to the attacks from quantum computers, hence having the advantage of strong security and high efficiency. The paper`s main objective is to study Lattice, lattice properties, Lattice – based cryptographic algorithm to design new Lattice-based cryptographic algorithms that are quantum resistant in the future.

Methods: In this paper, lattice-based cryptography is discussed right from its seminal work to its efficient cryptographic schemes. Paper discusses Lattice, lattice properties, lattice problem, the algorithmic solution to lattice problem, and lattice-based cryptography.

Findings: After studying post-quantum cryptographic algorithms using Lattice, lattice-based post-quantum cryptographic algorithms are resistant to quantum computer attacks.

Novelty: The paper discusses Lattice, properties of Lattice in a simple way. Widely used cryptographic algorithms like RSA, Diffie-Hellman Key exchange, Elliptic Curve Cryptography are not resistant to quantum computer attacks. Paper discusses the importance of a post-quantum algorithm using Lattice that is resistant to quantum computer attacks.

Reference
[1] Arora, S., L. Babai, J. Stern, and E.Z. Sweedyk. The Hardness of Approximate Optima in Lattices, Codes, and Systems of Linear Equations. Journal of Computer and System Sciences.,54(2)(1997) 317–331.
[2] George Grätzer. Latice Theory. Springer Publication.,(2011).
[3] Mathematics | Partial Orders and Lattices. https://www.geeksforgeeks.org/mathematics-partial-orders-lattices/ (accessed: 15/12/2019).
[4] Jhon B. distributive lattice. https://ncatlab.org/nlab/show/distributive+lattice (accessed 1 April 2020).
[5] Lattice. https://www.euclideanspace.com/maths/discrete/structure/lattice/index.htm (accessed 2 April 2020).
[6] Birkhoff representation theorem https://en.wikipedia.org/wiki/Birkhoff%27s_representation_theorem#:~:text=In%20mathematics%2C%20Birkhoff%27s%20representation%20theorem,unions%20and%20intersections%20of%20sets (accessed 4 April 2020).
[7] Advance topic in cryptography https://people.csail.mit.edu/vinodv/6876-Fall2015/L3.pdf (accessed 14 April 2020).
[8] Lattice Cryptography http://cseweb.ucsd.edu/~daniele/LatticeLinks/SVP.html (accessed 1 May 2020).
[9] Babai L. On Lovasz` Lattice Reduction and the Nearest Lattice Point Problem. Combinatorica 1986; 6(1): 1-13.
[10] Daniele M. Closest Vector Problem. https://cseweb.ucsd.edu/~daniele/papers/CryptoEncyclopediaCVP.pdf (accessed 10-September-2020).
[11] Shortest Vector Problem https://web.eecs.umich.edu/~cpeikert/lic13/lec02.pdf (accessed 20-September-2020).
[12] Voulgaris, Panagiotis. Algorithms for the Closest and Shortest Vector Problems on General Lattices. https://escholarship.org/content/qt4zt7x45z/qt4zt7x45z.pdf?t=ml518a (accessed 25 September 2020).
[13] Lattice and Cryptography https://www.isical.ac.in/~shashank_r/lattice.pdf (accessed 25-September-2020).
[14] Micciancio D., Regev O.,Lattice-based Cryptography. In: Bernstein D.J., Buchmann J., Dahmen E. (eds) Post-Quantum Cryptography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88702-7_5., (2009).

Keywords
Cryptography, Quantum Computer, Post Quantum Cryptography, Lattice, Lattice-based cryptography.