Provide the citation for the study here.
NEJATOLLAHI, H., DUTT, N., RAY, S., REGAZZONI, F., BANERJEE, I., & CAMMAROTA, R. (2018). Post-Quantum Lattice-Based Cryptography Implementations: A Survey. ACM Computing Surveys, 51(6), 1–41. https://doi.org/10.1145/3292548
Post-Quantum Lattice-Based Cryptography
 
What is the abstract of the article?
The advent of quantum computing threatens to break many classical cryptographic schemes, leading to innovations in public key cryptography that focus on post-quantum cryptography primitives and protocols resistant to quantum computing threats. Lattice-based cryptography is a promising post-quantum cryptography family, both in terms of foundational properties as well as in its application to both traditional and emerging security problems such as encryption, digital signature, key exchange, and homomorphic encryption. While such techniques provide guarantees, in theory, their realization on contemporary computing platforms requires careful design choices and tradeoffs to manage both the diversity of computing platforms (e.g., high-performance to resource constrained), as well as the agility for deployment in the face of emerging and changing standards. In this work, we survey trends in lattice-based cryptographic schemes, some recent fundamental proposals for the use of lattices in computer security, challenges for their implementation in software and hardware, and emerging needs for their adoption. The survey means to be informative about the math to allow the reader to focus on the mechanics of the computation ultimately needed for mapping schemes on existing hardware or synthesizing part or all of a scheme on special-purpose har dware. NEJATOLLAHI, H., DUTT, N., RAY, S., REGAZZONI, F., BANERJEE, I., & CAMMAROTA, R. (2018).
Was the study experimental or non-experimental? Explain.
This research was non-experimental.  No algorithms were tested, all information about the algorithms was already available.
Was the research qualitative or quantitative? Explain.
The research was qualitative.  The properties of different algorithms, their advantages and disadvantages were compared to each other.  While this type of research can use numbers to compare properties of each algorithm, it was far from a direct numerical comparison.
What was the population studied?
Different types of lattice based post quantum cryptography that could be used for public key encryption, digital signatures and key exchanges were compared, as well as different software implementations of this encryption.
What sample was used for this study?
22 Public Key Encryption algorithms, 19 Digital Signature algorithms and 31 Key Exchange algorithms
Method of measurement. (If the research was qualitative, what data was collected?)
Information about the key sizes of each algorithm, available software and hardware implementations of them and their performance.  The level of security they provide and how quantum resistant each algorithm is (future proof)
 Method of analysis. (If the research was qualitative, in what manner was the data analyzed?)
The entire document was assessed to determine the feasibility of lattice-based cryptography, it was assessed by skilled experts in the field.
What was the conclusion of the study?
The conclusion was that “LBC algorithms and protocols promise to tackle the challenges posed by deployment across diverse computing platforms, as well as for diverse use cases within reasonable security, performance, and energy efficiency guarantees.” NEJATOLLAHI, H., DUTT, N., RAY, S., REGAZZONI, F., BANERJEE, I., & CAMMAROTA, R. (2018).
Why is this study useful to you? Explain in detail.
This study is important to me because the computer systems I use all rely on cryptography to keep sensitive data secure.  The current RSA technology is secure against attacks by classical computers (transistor based), but weak against quantum computers.  In the coming decades we will need to move to more advanced algorithms that can resist attacks from quantum and classical computers, part of my job will be to stay up to date with technology and keep systems secure.
What would be the next logical step in extending this study?
The next logical step to extend this study would be comparing lattice algorithms to other competing post quantum algorithms.  These include Hash based cryptography, Code based, Multivariate and Supersingular elliptical curve isogeny cryptography.  In the coming years standardization of algorithms will occur, it’s important to pick a wide variety in the event a new development obsoletes one.
 
 
References
NEJATOLLAHI, H., DUTT, N., RAY, S., REGAZZONI, F., BANERJEE, I., & CAMMAROTA, R. (2018). Post-Quantum Lattice-Based Cryptography Implementations: A Survey. ACM Computing Surveys, 51(6), 1–41. Retrieved from http://web.a.ebscohost.com/ehost/pdfviewer/pdfviewer?vid=6&sid=3425c4b1-7098-4b37-a665-fbf6e8c756b1%40sessionmgr4007
Patten, M. L., & Newhart, M. (2018).Understanding research methods: an overview of the essentials. New York: Routledge.