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With the emergence of quantum computers, classical cryptography is facing significant challenges. Address this compelling problem, it is the need of hour to develop Post Quantum cryptography (PQC), or quantum-resistant cryptography. PQC is a rapidly evolving field in computer science. The National Institute of Standards and Technology (NIST) posted a call for inviting new generation of PQC algorithms. This paper aims to explore the significance and relevance of PQC in the future. Performing bibliometric analysis is important for gathering the necessary information about this discipline. Performance analysis and science mapping are done to extract valuable insights from the dataset. The dataset includes 14,230 records extracted from the Scopus database. The analysis is done using qualitative as well as quantitative approaches. The quantity approach focuses on the number of publications and document type analysis of the publications, while the quality approach includes the citation analysis of research publications. Bibliographic coupling is also carried out to understand the relationship in a visualisation format between authors, documents, sources, and countries. After performing the analysis, it has been observed that China has made the most significant contribution to the field of PQC. Additionally, the most highly cited author identified is Nicolas Gisin from the University of Geneva. This study provides valuable insights into prominent keywords, emerging trends and key research areas within the PQC domain, offering a comprehensive overview of the current research landscape.
Introduction
In this digital world, where the security of data is of prime importance, the imminent arrival of quantum computers poses both an opportunity and a threat. Quantum computers will be the real challenge that jeopardize the integrity of current cryptography algorithms [1]. As Quantum computers are very close to the real-world application implementation, the base of the cryptography infrastructure that is umbrella for the digital communication, banking transactions and personal communication will be endangered. The vulnerability of classical cryptography, which relies upon the difficulty of mathematical problems, is increased by the exponential processing offered by quantum computing [2, 3]. The PQC is becoming the promising area of research because of the increasing quantum threats [4, 5]. A broad range of cryptographic protocols and primitives are encompassing in PQC so that the system can withstand the quantum system’s computational capacity. PQC researchers are investigating alternative techniques to the conventional cryptography, which mostly involves factorising huge numbers that ought to be prime numbers or computing discrete logarithms [6, 7]. The PQC cryptography mainly working in the domains of lattice based, code based, hash based, multivariate polynomial based problems [5, 8, 9, 10–11].
To standardize the PQC algorithm to the worldwide, National Institute of Standards and Technology (NIST) initiated a thorough effort in 2016 to solicit, access and systematized security algorithms to resist the quantum computing [12]. Cryptographers, Worldwide government agencies, business stakeholders, and researchers have collaborated on this endeavour, which is called the NIST Post-Quantum Cryptography Standardisation process. To meet the rigorous criteria for quantum security, multiple phases are performed in NIST standardization process, where each phase is meticulously crafted with stringent decision of cryptographic primitives. Proposals for public key cryptography, key management and establishment, and digital signature are called from all over the world. Diverse kind of mathematical frameworks and techniques based on quantum phenomena are received. Report on the first round selected algorithm is published in year 2019, where NIST qualified 26 candidates of asymmetric key cryptography algorithms, digital signatures, and key establishment algorithms [13]. Progressively lowering down the pool of promise algorithms based on their implementation overhead, security guarantees, and applicability to circumstances NIST continuously restricting its selection criteria and in year 2020, NIST publish the list of candidates who have passed the second round of standardization where four public key cryptography or Key Encapsulation Mechanism (KEM) [14, 15] and three Digital Signature algorithms were qualified [3, 16, 17]. Subsequently, the NIST disclosed the candidate’s third-round results and declared that Cryptographic Suite for Algebraic Lattices (CRYSTAL) Kyber is a standardised methodology for key establishment, with three digital signatures selected: CRYSTALS-Dilithium, FALCON, and SPHINCS+. NIST also states that several significant PQCs that may be taken into consideration for future standardisation will be included in the fourth round of testing [18]. Replace the RSA and ECC cryptosystems, NTRU was presented in 1998. Adopting NTRU has the benefit of having O(N2) complexity as compared to O(N3) complexity for other asymmetric cryptography algorithms. It is a lattice-based encryption technique used for key exchange and public key cryptography. The security and hardness of this algorithm relies on the challenge of short vector problem in lattices [11, 19]. Key creation of the NTRU algorithm takes 300 times faster than Rivest-Shamir-Adleman (RSA) key generation and it is 1.5 times quicker than Elliptic Curve Cryptography (ECC) technique [20, 21]. Kyber is a KEM that is founded on the implementation of difficult module lattice problems [22]. Because keys are the foundation of cryptography systems, KEM are algorithms that are employed only for the purpose of protecting keys. Both the Kyber Chosen Cipher Text Attack (CCA) and Kyber Chosen Plain Text Attack (CPA) are Kyber variants. The CPA is used for safe encryptions, while the CCA is used for secure key exchange procedures [23, 24].
As it is apparent from the explanation above, PQC algorithms are the standard of the future in the digital world as they provide essential security to financial transactions and private communications [25]. To study the scope, relationships, and recent trends of the PQC algorithms, bibliometric analysis on PQC will provide a way to understanding the trends, advancements, and impact of research in this field [26]. It provides researchers and practitioners with useful insights into the rise and progress of PQC research. However, one of the main reasons to conduct bibliometric in PQC is to determine emerging trends and future research directions [27, 28]. By monitoring the publication volume during the years and investigating keyword co-occurrences, it will become clear what is happening in the PQC landscape and how new cryptographic primitives, protocols, and implementation methods are evolving. Furthermore, bibliometric analysis will show interdisciplinary cooperation and the role of integration of different research communities, including cryptography, mathematics, computer science, and quantum physics [29]. In addition, bibliometric analysis and science mapping helps in finding out the influence of research contributions [30, 31]. It helps in identifying papers with a good number of citations, and it also helps in finding out influential authors and seminal works that have heavily influenced the field [32, 33]. Furthermore, bibliometric analysis can also aid in finding out the dissemination channels and publication venues that are chosen by researchers of the PQC community. By analysing journal publication records and trends, conference publication records and trends, and preprint archives, it can provide a clear understanding to researchers with visibility and impact of the publication outlet within the field [34]. It can be used by researchers for publishing their papers and can also be used by academic institutions and funding agencies for finding out the impact of the PQC research contributions.
The purpose of the paper is to conduct a bibliometric analysis of post quantum cryptography and identify the research dynamics and scholarly contributions of the emerging field. In sum, the work contributes to shedding “a light on the topic” as it relates to the scholarly understanding of post-quantum cryptography key areas and provides a direction for further research.
Review of bibliometric analysis in the domain of PQC
Bibliometric Analysis provides researchers and practitioners with useful insights into the rise and progress of domain research, as well as into the most successful contributors and works in the field, based on publication data, citation patterns, author collaborations, and journal preferences. Investigations are conducted to analyse the potential of the PQC research area. Donthu et al. [27] provided the step-by-step guidelines and methodology to perform bibliometric analysis in 2021. It should be objective in nature and must be massive. From massive, they want to say that the analysis data entities should be in thousands. Scholars will be empowered by bibliometric analysis because it (a) provides an overview of the field in a single step, (b) Provide novel ideas for investigation, (c) Assist in determining the gaps in that domain’s research [27]. To accurately measure experimental data, researcher needs technologies that facilitate data analysis and coupling of data across authors, journals, and nations to determine the impact of different researchers and publications. In an article published by Moral-Muñoz et al. in 2020 [35], the various tools employed in bibliometric analysis are reviewed. To do the analysis, database should be in the range of 500 to 50,000. The comparison of several bibliometric databases, performance analysis tools, Science Mapping Analysis (SMA) tools, and Python-related libraries that support analysis was carried out in their study. CiteSpace and VOSviewer are prominent SMA tools, while Web of Science and Scopus are reliable databases to get the right information, according to their study. Bibliometrix and its Shiny platform provide an intuitive user experience for data analysis. Linnenluecke et al. [36] have also covered in detail how to publish bibliometric analysis and what essential elements and parameters should be included while performing analysis. The COVID-19 pandemic highlighted the critical need for effective, non-invasive methods to continuously monitor people’s health and well-being, particularly in residential and communal settings [37]. In response to the COVID-19 epidemic, Sood et al. conducted bibliometric and scientometric analyses of intelligent control systems aided by information and communication technologies (ICT). They described the methods used to determine the insights in that field, including co-citation analysis, empirical techniques and various scientific mapping [38]. Further, to comprehend the analysis and findings, Sood et al. presented their work on a structured review of the ways in which technologies such as smart biomaterials, nanotechnology, and 3D bioprinting are promoting soft tissue regeneration. It identifies gaps for further interdisciplinary growth, highlights innovative contributions, and classifies research trends [39].
Baskaran has chosen the Web of Science (WoS) database for the years 2000–2011, which comprises 6610 records, for his paper on the Scientometric research of cryptography [40] in year 2013. He has found the relative growth rate of the publications and analyse the Countries distribution and Subject-wise papers of Cryptography. He has not examined the citation of publications or other elements like the author, journal, and publication coupling. Gosh et al., in year 2020 [30], has presented their contribution to find out the trends related to the performance of Indian Researcher in the field of cryptography. For the data collection, they used the time range of 1998 to 2018 from WoS. They have given the list of most prominent institutes in India and researchers who are working in the field of cryptography. In year 2023, Dewamuni et al. [41] published their bibliometric work, in the field of IoT Lightweight Cryptography. They analysis the research trends and pattern in IoT security by evaluating keywords, author, journals, and citations. They included the data of 2015 to 2023 year from WoS, Scopus and IEEE Xplore. They have found that India is leading country due to its contribution in IoT lightweight cryptography and given the names of the top researcher of that area and done the citation analysis where 118 articles are cited more than 1100 times. Author has done good work for analysing the future scope and directions in IoT cryptography [41], but they did not include the recent area of cryptography that is quantum resistant cryptography or PQC. There are a few publications in the PQC bibliometric analysis field [42]. Unlike earlier bibliometric research in the more general area of cryptography, this work looks at the new area of PQC, which has not been the core topic of previous studies. Through a systematic analysis of PQC-specific contributions in terms of authorship, journal sources, influential keywords, and international collaborations, our work bridges this gap and provides new insights into how the PQC research is changing in comparison to previous cryptography research domains.
Motivation
Although some work has been published in the bibliometric analysis of cryptography [30, 40], lightweight cryptography [41], authentication in IoT [43], and homomorphic encryption [44], it is clear from a review of recent research that little work has been done in the bibliometric and scientometric analysis of PQC. PQC is a popular research domain where many researchers are engaged, so precise analysis of keywords, researchers, publications, citations, journals, and correlation ships of countries and authors is required. It has led a motivation to accomplish the bibliometric analysis of the quantum resistant cryptography and PQC. This study is conducted to accomplish the goal to find the trends and future possibilities in this area. This study will analysis the research questions which are as follows:
Contribution of countries to the PQC development.
Top researchers who are contributing to the PQC.
Leading Journals who are publishing the papers of PQC.
Keyword analysis of the domain PQC.
Coupling of the authors, countries, and organizations.
To Conduct the analysis, appropriate research methodology is used. The rest of the paper presents the data collection, trend in research, query used to get the data from databases, analysis of keywords, impact of top authors and their affiliations, analysis based on research organizations and participating countries, citation analysis, top cited publications, top cited journals, coupling based on bibliography, co-occurrence relationship between authors, countries, and journals.
Research methodology
To conducting the bibliometric analysis on the PQC area, the approach used in this paper has been given in Fig. 1. To get started with the approach, the first thing that needs to be done is to collect the data from the research publications that are associated with the analytical domain. To get the research publications, there are various publications and academics databases such as Web of Science, IEEE Xplore, PubMed, and Google Scholar, each with its own advantages and limitations. Web of Science is a well-known high quality database where reputed journals are indexed with stronger historical reputation, but its coverage is comparatively narrow as it may exclude relevant emerging literature in PQC domain [45]. IEEE Xplore is primarily restricted to IEEE publications and lacks broader interdisciplinary representation. Despite of its wide range content, Google Scholar is not suitable as a primary dataset due to its inclusion of non-peer reviewed journals and sources, and unreliable citation metrices. PubMed, on the other hand, focuses mainly on biomedical and life sciences and is not relevant for cryptographic studies. Due to these constraints, Scopus is selected for this work because of its comprehensive interdisciplinary coverage, strong citation tracking capabilities, and interoperability with advanced bibliometric tools such as VOSviewer and Bibliometrix [46]. Its inclusion of peer-reviewed sources from a various set of publishers and journals ensures a reliable and comprehensive dataset for analysing trends and contributions in the PQC research landscape. The Scopus database is used for the purpose of data collecting, R packages are installed to carry out the analysis, and Biblioshiny, which is given by Bibliometrix, is utilised accordingly [47, 48]. Microsoft Excel and Microsoft Word have been used throughout the process of integrating the data and composing the article. All these tools have been used to conduct performance analysis. To do so, a keyword analysis is done, and the frequent keywords are tabulated. After that, Quantitative and qualitative analysis is carried out on the sources, authors, and documents. The scientometric mapping is carried out using VOSviewer. The following sections include a bibliographic coupling on four distinct criteria as well as a co-occurrence analysis of keywords depicted with pictographs.
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Fig. 1
Research methodology framework used for conducting the bibliometric analysis in PQC
Data collection
To begin the bibliometric analysis, the topic’s relevancy data must be gathered. Since Elsevier’s Scopus is the biggest archive and a standard for peer review in publishing, we gathered our data for this study from Scopus. Although WoS is also a well-known publishing database, Scopus contains almost twice as many articles as WoS [45]. It is also interdisciplinary databases and having almost papers from science and technology [46]. To extract the data from data base the query used is “(TITLE-ABS-KEY (“Quantum cryptography” OR “Post Quantum cryptography” OR “PQC” OR “Quantum Resistance Cryptography” OR “Types of PQC” OR “Polynomial based cryptography” OR “Lattice based cryptography” OR " Multivariate Based Cryptography” OR “Code Based Cryptography” OR “Hash Based Cryptography”))”. In this query, all the keywords have been used which incorporate the PQC algorithms, so that vast area of papers can be covered which are from PQC field. Key phrases pertinent to both general and specialised sections of PQC were used in the carefully constructed keyword search query to guarantee thorough coverage of the PQC research environment. The title, abstract, and keywords fields of the Scopus database were the focus of the query. Both general names like “Post Quantum Cryptography” and “PQC” are included in this formulation, along with the main algorithmic families that characterise the area, including hash-, lattice-, code-, multivariate-, and polynomial-based cryptography. Incorporating “Quantum cryptography” expands the scope to include comparative studies and basic literature. The number of records extracted using query from Scopus database is ‘18114’. From these records, data has been again separated from the year 2010 to 2023, which include ‘14230’ data items and bibliometric analysis is performed on these 14,230 records.
Preprocessing of the research data
Preprocessing is done on the resultant records after they have been gathered. First, data for the years 2010 through 2023 is separated. The number of publications from year 2010 to 2023 year is illustrated in Fig. 2. It is evident from figure that the number of publications in year 2023 is four times that of year 2010. The increasing trend is showing the importance of the field. On the extracted data, various results are obtained, including the number of authors who have published data in the PQC area, the number of publications each author has contributed to, the number of journals that have published papers in PQC, citation on each document, citations of each journal, the most popular keywords in this field, and many more.
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Fig. 2
Year wise number of publications in PQC
Analysis of the research trend through number of publications in the different aspects
In this section, the analysis is done based on the number of publications in different aspects that frequency of a keyword in whole publications, analysis based on the subject category, countries who have published a greater number of papers in given PQC field, authors and their number of publications showing impact to the research area.
Analysis of keywords
In bibliographic databases, keywords serve as the main resource for locating works within certain fields. Through keyword frequency analysis, researchers may get pertinent topics at that time [49]. The frequency and recurrence of the key words for the area in each time may be used to determine new research field expansion [50]. By demonstrating the relationships between multiple concepts and topics, keywords aid in mapping the knowledge networks within a certain area. Research domain knowledge structures may be revealed by examining co-occurring keywords or co-citation patterns [51]. During dataset examination, 153 unique keywords were found. The keyword list and frequency of that keywords are shown in Figs. 3 and 4. represents the tree map of PQC area’s top 25 keywords. Quantum Cryptography, Quantum Theory, Quantum Key Distribution, Network Security, and Cryptography are the most frequently appearing terms in that list, with occurrences of 2366, 2187, 2148, 1870, and 1811, respectively.
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Fig. 3
Keywords used by authors and their frequencies in PQC
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Fig. 4
Tree map of the top 25 keywords used by authors
Analysis of subject category
Interdisciplinary research is a modern trend in which many disciplines work together to maximize the potential of each subject in various application domains. The analysis based on subject category is essential to understand the influence of a specific research topic as it gives the effective application area of the research and promotes researcher collaborations to solve real-world problems [52, 53]. In this work, we have analysed the field PQC across different disciplines. Table 1 depicts the subject area with respect to the number of publications in that area. The most contribution of PQC is to computer science field and being quantum physics-based algorithms [54], PQC has made the greatest contribution to the area of Physics. Later, its contribution is in Mathematics and Engineering with number of publications more than 5000.
Table 1. Distribution of publications across subject areas in PQC research
Subject category | No. of Publication |
|---|---|
Computer Science | 9350 |
Physics and Astronomy | 8955 |
Engineering | 6863 |
Mathematics | 5406 |
Materials Science | 3839 |
Decision Sciences | 458 |
Chemistry | 420 |
Biochemistry, Genetics and Molecular Biology | 377 |
Social Sciences | 358 |
Multidisciplinary | 219 |
Energy | 218 |
Medicine | 193 |
Earth and Planetary Sciences | 97 |
Business, Management and Accounting | 93 |
Environmental Science | 89 |
Chemical Engineering | 87 |
Agricultural and Biological Sciences | 54 |
Neuroscience | 52 |
Pharmacology, Toxicology and Pharmaceutics | 29 |
Immunology and Microbiology | 24 |
Economics, Econometrics and Finance | 19 |
Arts and Humanities | 18 |
Analysis based on participated countries
The publication is examined to get the trend of the PQC fields in various nations. Figure 5 demonstrates how many research papers have been published in various nations. The data shows that, with 5403 articles overall, China has the strongest PQC trend. United States comes in second position with 2903 publications, followed by United Kingdom in third place with 1359 articles. With 1232 PQC submitted research papers, India is in fifth position, behind Germany in fourth place with 1243 publications. Figure 5 shows the broad summary of the highest contributing countries for the research domain “Quantum Resistance cryptography”.
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Fig. 5
Country-wise distribution of research articles on PQC
Analysis of number of authors per research publication
A representation of the total number of authors who contributed to each publication can be seen in Fig. 6. Figure 6 illustrates the proportion of publications that have several authors that range from one to seven. Based on the data shown in the figure, it can be deduced that 10.8% of the total publications have contributions from a single author, while 19.5% of publication is the work of two authors and 20.6% of the papers are written by three researchers working together. Regarding the articles with authors six and seven, the publishing percentage is low. It becomes obvious that a manuscript usually has two, three or four authors who collectively contributed to the research.
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Fig. 6
Number of authors contribution in publications
Year wise analysis of publications based on nature of document
It is a common practice for researchers to publish their findings in academic journals, at conferences, or in book chapters [55]. The analysis of publications is carried out in this section based on the document type of the publication, as well as the year-by-year publication count on that document type. This is done to gain a clear perspective on the types of documents in which researchers are publishing their work in. Figure 7 is a pie chart that illustrates the distribution of publications for the different types of documents. This figure can be used to understand that most researchers have published their work in journals, which account for 52.67% of the total publications. Subsequently, 39% of the papers are articles that are presented at various conferences. 4.8% of the publications fall into the category of book chapters, followed by 1% of the publications that are done as conference reviews, 2.12% of the publications that belong to the review articles, and at last 0.32% of the publications in this field have been published as books. After that the analysis is done year wise from 2015 to 2023 which is illustrated in Table 2. The year wise trend is showing that the publications are increasing year by year and journals has 6279 publications in last 9 years, whereas conferences have 4658 publications.
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Fig. 7
Distribution of PQC publications by document type
Table 2. Publication distribution in each document type
Document type | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | Document wise Total publications |
|---|---|---|---|---|---|---|---|---|---|---|
Conference paper | 859 | 715 | 680 | 553 | 547 | 460 | 354 | 290 | 200 | 4658 |
Journal Article | 1086 | 961 | 852 | 794 | 689 | 589 | 457 | 454 | 397 | 6279 |
Conference Review | 24 | 14 | 15 | 18 | 13 | 6 | 13 | 12 | 6 | 121 |
Book Chapter | 443 | 36 | 18 | 14 | 11 | 18 | 17 | 7 | 8 | 572 |
Book | 6 | 8 | 4 | 10 | 2 | 2 | 1 | 1 | 4 | 38 |
Review | 41 | 45 | 49 | 32 | 23 | 13 | 29 | 11 | 10 | 253 |
Year wise Total publication | 2459 | 1779 | 1618 | 1421 | 1285 | 1088 | 871 | 775 | 625 | 11,921 |
Validation of the research
Validation of the research is a word that is used to guarantee that the research is genuine, that the findings of the research are delivering benefit to the actual world, and that people are applying those findings and conclusions in their problems or applications, which increases the reliability and trustworthiness of the results of the research [33, 56]. It is possible to determine the validation of the work by looking at the citations of that research, The higher the number of citations, the greater the influence the research has had [57, 58]. Another term that is often used to get validation for research is “impact of the research.” Number of citations indicates the research’s impact. To understand the impact of the research and identify the journals and authors who are making significant contributions to society, we will examine the citations of publications, journals, authors, and organizations in this section. There is serval research metrics which are used to analyse the research impact in bibliometric analysis.
Normalized citation impact index (NCII)
NCII score is developed to determine the impact of a publication’s longevity. The duration of a publication’s active status and the number of citations it has received after it was published is indicated by its publication longevity [58]. The average number of citations per publication during a certain time period is calculated using the NCII. Equation 1 gives the formula for the NCII score.
1
Table 3 shows exciting pattern of NCII score to reveal the impact of the publication with respect to the publication longevity from year 2023 to 2015. The most impactful research per paper has mostly come from earlier years like 2017–2020, probably because it has longer time for citations to add up. This table shows both quantitative growth (calculated by publication count) and qualitative impact (calculated by average NCII). The NCII metric is a helpful tool for comparing the relative impact across publication years because it successfully normalises for longevity in this case.
Table 3. Average NCII score calculation per publication
Year | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 |
|---|---|---|---|---|---|---|---|---|---|
Number of publications | 2072 | 1791 | 1626 | 1432 | 1293 | 1094 | 883 | 782 | 633 |
Total Number of citations | 2539 | 8013 | 12,602 | 18,056 | 17,800 | 18,910 | 18,455 | 17,487 | 15,666 |
Longevity (in years) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Total NCII Score | 2539 | 4006.5 | 4200.66 | 4514 | 3560 | 3151.667 | 2636.429 | 2185.875 | 1740.667 |
Average NCII Score per publication | 1.2254 | 2.2370 | 2.5834 | 3.1522 | 2.7533 | 2.8809 | 2.9858 | 2.7952 | 2.7499 |
Insights from citation analysis: Exploring the impact scholarly research from the document wise and institution wise
This section analyses citations from 2015 to 2023 depending on the publishing year of the document to comprehend the impact of research publications according to the nature of the document. Table 4 illustrates how the year-wise proportion is computed for each category of document. 12% of the referenced articles in 2023 are conference papers, while 82.8% of the cited documents are journal research articles. Journal articles provide more citations than any other published document category, suggesting that they have a greater influence and originality than other types of publishing.
Table 4. Year-wise citation percentage by document type in PQC
Year → Document type ↓ | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 |
|---|---|---|---|---|---|---|---|---|---|
Journal Article | 82.867 | 78.672 | 74.496 | 76.961 | 68.663 | 74.273 | 71.493 | 71.442 | 81.291 |
Conference paper | 12.131 | 13.865 | 16.442 | 16.958 | 20.129 | 22.517 | 17.144 | 22.760 | 11.700 |
book | 0.000 | 0.175 | 0.246 | 0.244 | 0.028 | 0.021 | 0.022 | 0.120 | 0.421 |
book chapter | 0.276 | 0.562 | 0.246 | 0.255 | 0.326 | 0.333 | 0.672 | 0.114 | 0.064 |
Review | 4.647 | 6.302 | 7.515 | 5.356 | 9.197 | 2.475 | 9.764 | 4.964 | 5.100 |
Despite the nature of research document, the analysis of top institution who are cited more is also computed. Based on the examination of research organisation’s citations, the best institutions are identified as those that are doing excellent PQC research and contributing significantly to future security, and the results are shown in Fig. 8. The most cited affiliation is Shanghai Institute of Microsystem and Information Technology [59] with 1530 citations, after that State Key Laboratory of Cryptology [60], and University of Science and technology of China [60] takes place. Highly cited organisations will help to identify highly reputed researchers, and these institutes provide the immersive exploration of the ideal research environment.
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Fig. 8
Top research organizations by citation count in PQC
Insights from highly cited authors
Bibliometric analysis is performed on the data set to evaluate and examine the accomplishment and effectiveness of the authors [55, 61]. First, the list of authors who are most often referenced in PQC is gathered throughout the examination. Table 5 provides more details about these authors, including their Scopus ID, the number of articles they have published, and their H-index. With 16,062 citations in PQC articles, Nicolas Gisin [62, 63–64] is the most cited author from the University of Geneva. He belongs to Switzerland and having an H-index of 116. The second most referenced author is Hoi Kwong Lo [65, 66–67] from the University of Hong Kong, who accomplished excellent work in the PQC sector. The majority of highly referenced authors are from Poland [68, 69], Singapore [70], China [71], Switzerland [62], and the United Kingdom [72, 73]. These authors have a significant impact on the reputation of the organisations where they work, and they inspire other researchers to share their enthusiasm and commitment in order to collaborate on well-known projects in the same sector.
Table 5. Top cited authors in PQC and their research contributions
Sr. No. | Scopus ID | Author Name | Affiliation | Country | No. of Total Documents | No. of documents in PQC Field | H-index | Total Citation till date | Citation Count in PQC |
|---|---|---|---|---|---|---|---|---|---|
1 | 7102753380 | Gisin, Nicolas | University of Geneva | Switzerland | 664 | 59 | 116 | 58,076 | 16,062 |
2 | 7202085450 | Lo, Hoi Kwong | The University of Hong Kong | Hong Kong | 203 | 108 | 57 | 19,485 | 9611 |
3 | 7004921134 | Ekert, Artur K. | University of Oxford | United Kingdom | 120 | 5 | 50 | 25,726 | 9426 |
4 | 7003514984 | Zbinden, Hugo | University of Geneva | Switzerland | 281 | 43 | 72 | 25,174 | 9263 |
5 | 7404098450 | Pan, Jianwei | Hefei National Laboratory for Physical Sciences at the Microscale | China | 594 | 98 | 110 | 51,537 | 8871 |
6 | 6602825494 | Ribordy, Grègoire | ID Quantique SA | Switzerland | 40 | 9 | 22 | 11,363 | 7768 |
7 | 7003674257 | Scarani, Valerio | National University of Singapore | Singapore | 202 | 35 | 59 | 16,383 | 7679 |
8 | 6507877082 | Horodecki, Karol | University of Gdańsk | Poland | 53 | 13 | 18 | 8394 | 7529 |
9 | 7003764522 | Brassard, Gilles | University of Montreal | Canada | 155 | 30 | 43 | 28,858 | 7506 |
10 | 7004209558 | Horodecki, Michał Ł. | University of Gdańsk | Poland | 183 | 8 | 59 | 25,692 | 7476 |
11 | 57200185913 | Horodecki, Pawel | University of Gdańsk | Poland | 207 | 11 | 57 | 25,660 | 7268 |
12 | 7005709327 | Cerf, Nicolas J. | Université Libre de Bruxelles | Belgium | 203 | 21 | 56 | 17,169 | 7239 |
13 | 6701618041 | Lütkenhaus, Norbert | University of Waterloo | Canada | 203 | 77 | 50 | 13,364 | 7236 |
14 | 6701363699 | Tittel, Wolfgang | University of Geneva | Switzerland | 164 | 12 | 48 | 18,421 | 7180 |
15 | 55624488433 | Zhang, Qiang | Hefei National Laboratory for Physical Sciences at the Microscale | China | 222 | 70 | 54 | 13,067 | 5999 |
Citation analysis of journal and conference publications: unveiling trends and impact
In this section, a bibliometric analysis is performed to identify the journals with the highest publication counts and citation counts to determine which journals are publishing articles in PQC and which journals are demonstrating the influence of their publications via citation. To achieve this, a separate sheet is created from the dataset based on the title and source of each article. That sheet is then evaluated, and Table 6 displays the results of top journals with a high publication count. Additional analysis is conducted using the source’s citation. Table 7 shows the sources that are often cited. In Table 7, in addition to the citation, additional factors are provided to indicate the journal’s impact factor, the source’s h index, and the number of articles it has published. The highly cited journal is Physical Review Letters [74, 75] have 700 H-index and 9.185 impact factor. Lecture Notes in Computer Science is a series of conference proceedings which covers the wide range computer science related publication, and the publisher is springer. It is second highly cited source. Reviews of Modern Physics [62], Nature [76] and Nature Photonics [77] are also some highly cited journals.
Table 6. Journal having high publication count
Sr no. | Source | Publication Count |
|---|---|---|
1 | Proceedings of SPIE The International Society for Optical Engineering | 880 |
2 | Quantum Information Processing | 742 |
3 | Physical Review A: Atomic Molecular and Optical Physics | 602 |
4 | Optics Infobase Conference Papers | 500 |
5 | Physical Review A | 445 |
6 | Optics Express | 303 |
7 | Physical Review Letters | 290 |
8 | IEEE Access | 222 |
9 | New Journal of Physics | 201 |
10 | International Journal of Quantum Information | 186 |
11 | International Journal of Theoretical Physics | 183 |
12 | Leibniz International Proceedings In Informatics Lipics | 142 |
13 | Chinese Physics B | 140 |
14 | Physical Review Applied | 139 |
15 | Chinese Physics Letters | 128 |
Table 7. Top 20 journals by citation count in PQC
Sr. No. | Name of the Journal | Publication Count | Citations count for PQC | H-Index | Impact factor |
|---|---|---|---|---|---|
1 | Physical Review Letters | 290 | 59,080 | 700 | 9.185 |
2 | Lecture Notes in Computer Science (Including Subseries of Lecture Notes in Bioinformatics and Lecture Notes In Artificial Intelligence) | 1574 | 22,032 | 470 | - |
3 | Reviews of Modern Physics | 11 | 21,436 | 388 | 50.485 |
4 | Nature | 34 | 14,238 | 1381 | 69.504 |
5 | Nature Photonics | 42 | 13,174 | 385 | 39.728 |
6 | Quantum Information Processing | 742 | 11,275 | 74 | 1.965 |
7 | New Journal of Physics | 201 | 10,961 | 204 | 3.716 |
8 | Optics Express | 303 | 10,353 | 312 | 3.833 |
9 | Physical Review A | 445 | 9407 | 296 | 2.971 |
10 | Nature Physics | 23 | 5331 | 334 | 19.684 |
11 | IEEE Transactions on Information Theory | 75 | 5251 | 292 | 2.978 |
12 | Applied Physics Letters | 78 | 4405 | 478 | 3.971 |
13 | Physics Letters, Section A: General, Atomic and Solid-State Physics | 116 | 4279 | 189 | 2.58 |
14 | Quantum Information and Computation | 114 | 3921 | 75 | 3.379 |
15 | Optics Letters | 122 | 3840 | 299 | 2.707 |
16 | Journal of Modern Optics | 94 | 3424 | 99 | 1.293 |
17 | Chinese Physics Letters | 128 | 3228 | 76 | 2.293 |
18 | NPI Quantum Information | 82 | 3083 | 69 | 10.758 |
19 | Optics Communications | 113 | 2865 | 151 | 2.335 |
20 | Journal of Cryptology | 27 | 2713 | 84 | 1.691 |
Some of the international conferences who has published good work in PQC are detailed in Table 8. These conferences are well reputed conferences in their area and have published the genuine work showing the high impact.
Table 8. Most cited conferences in PQC research
Sr. no. | Conference Name | Citation |
|---|---|---|
1 | 40th Annual ACM Symposium on Theory of Computing, STOC 2008 | 1756 |
2 | 4th International Workshop on Post-Quantum Cryptography, PQCrypto 2011 | 763 |
3 | 3rd International Workshop on Post-Quantum Cryptography, PQCrypto 2010 | 545 |
4 | 25th USENIX Security Symposium | 538 |
5 | 50th Annual Symposium on Foundations of Computer Science, FOCS 2009 | 534 |
6 | 2nd International Workshop on Post-Quantum Cryptography, PQCrypto 2008 | 531 |
7 | 11th Cryptographers’ Track at the RSA Conference 2011: Topics in Cryptology, CT-RSA 2011 | 487 |
8 | 9th International Conference on Post-Quantum Cryptography, PQCrypto 2018 | 446 |
9 | 8th International Workshop on Post-Quantum Cryptography, PQCrypto 2017 | 428 |
10 | Second Theory of Cryptography Conference, TCC 2005 | 420 |
11 | 36th Annual International Cryptology Conference, CRYPTO 2016 | 411 |
12 | 29th Annual International Cryptology Conference, CRYPTO 2009 | 408 |
13 | 5th International Workshop on Post-Quantum Cryptography, PQCrypto 2013 | 404 |
14 | Proceedings of the 1998 39th Annual Symposium on Foundations of Computer Science | 396 |
15 | 7th International Workshop on Post-Quantum Cryptography, PQCrypto 2016 | 391 |
Top cited research articles
The work of the researchers is published in the article which influence the impact of journal, author, and organizations. In this section, the analysis of that publication is done who has shown significant research and are highly cited by the world. Table 9 depicts the highly cited research articles title published after 2015 year and the authors of that research along with the publishing year and number of citations.
Table 9. Top cited research publications in PQC
Sr. No. | Authors | Title | Year | Cited by |
|---|---|---|---|---|
1 | Pirandola S et al. [78] | Advances in quantum cryptography | 2020 | 824 |
2 | Xu F. et al. [79] | Secure quantum key distribution with realistic devices | 2020 | 739 |
3 | Yin H.-L. et al. [80] | Measurement-Device-Independent Quantum Key Distribution over a 404 km Optical Fiber | 2016 | 645 |
4 | Alkim E. et al. [81] | Post-quantum key exchange – A new hope | 2016 | 538 |
5 | Liao S.-K et al. [82] | Satellite-Relayed Intercontinental Quantum Network | 2018 | 511 |
6 | Diamanti E. et al. [83] | Practical challenges in quantum key distribution | 2016 | 502 |
7 | Mirhosseini M. et al. [84] | High-dimensional quantum cryptography with twisted light | 2015 | 495 |
8 | Zhang W. et al. [85] | Quantum Secure Direct Communication with Quantum Memory | 2017 | 470 |
9 | Boaron A. et al.[86] | Secure Quantum Key Distribution over 421 km of Optical Fiber | 2018 | 450 |
10 | Albrecht M.R. et al. [87] | On the concrete hardness of Learning with Errors | 2015 | 413 |
11 | Flamini F. et al. [88] | Photonic quantum information processing: A review | 2019 | 401 |
12 | Korzh B.et al. [89] | Provably secure and practical quantum key distribution over 307 km of optical fibre | 2015 | 390 |
13 | Bos J. et al. [23] | CRYSTALS - Kyber: A CCA-Secure Module-Lattice-Based KEM | 2018 | 388 |
14 | Coles P.J. et al. [90] | Entropic uncertainty relations and their applications | 2017 | 380 |
15 | Javidi B. et al. [91] | Roadmap on optical security | 2016 | 361 |
16 | Acín A.et al. [92] | The quantum technologies roadmap: A European community view | 2018 | 358 |
17 | Yin J.et al. [72] | Entanglement-based secure quantum cryptography over 1,120 km | 2020 | 355 |
18 | Pirandola S. et al. [77] | High-rate measurement-device-independent quantum cryptography | 2015 | 339 |
19 | Sit A. et al. [93] | High-dimensional intracity quantum cryptography with structured photons | 2017 | 334 |
20 | Hoang T.B. [94] | Ultrafast Room-Temperature Single Photon Emission from Quantum Dots Coupled to Plasmonic Nanocavities | 2016 | 328 |
Bibliometric coupling analysis
To measure the degree of the relationship or the similarity between the two documents, authors and sources, the term coupling is used [95]. The measurement of coupling is done thorough the citation analysis, if two documents, sources or authors cited together in third document then that documents, authors or sources are called to be coupled together [96]. This implies that even if the research paper has been written by different authors and published in different sources, they may have thematic or conceptual similarity. It uncovers the interdisciplinary connection, identify research area in a field, provide the insights into the structure of scientific mapping. A popular tool that is used to do the coupling analysis is VOSviewer. It provides the network structure based on the data fed to the tool [97]. VOSviewer create the visualization diagrams based on co-citation, co-authorship, cooccurrence, citation, or bibliographic coupling relationships. The analysis based on co-authorship, co-citation, and documentation coupling has been accomplished in this section.
Analysis of bibliographic coupling
The bibliographing coupling of documents, sources, countries, and author is done with the use of VOSviewer (1.6.20 version) tool and Table 10 depicts the detail of features that are shown in visualization coupling layout.
Table 10. Bibliographic coupling of different analysis unit
Sr. no. | Analysis unit | Number of samples | Threshold | Clusters |
|---|---|---|---|---|
1 | Analysis of Documents | 13,230 | Minimum number of citations of a document:1 | 5 |
2 | Analysis of Source | 404 | Minimum number of documents of a source: 5 | 8 |
Minimum number of citations of a source:5 | ||||
3 | Analysis of Countries | 90 | Minimum number of documents of a country: 3 | 2 |
Minimum number of citations of a country:3 | ||||
4 | Analysis of Authors | 5528 | Minimum number of documents of an author: 3 | 5 |
Minimum number of citations of an author:3 |
Bibliographic coupling analysis based on “Document”
Bibliographic coupling based on document analysis is shown in Fig. 9 as network visualization. Number of samples in document unit of analysis is 18,114. From these documents only those documents have been chosen for visualization who has at least one citation and 13,230 samples have passed the threshold. The number of clusters or the research sub-teams formed by the visualization is 5. Cluster 1(red colour) contains 419 items, whereas cluster 2(green colour) has 380 items, 192 items are there in cluster 3 (blue colour). Cluster 4 (yellow colour) and 5 (purple colour) have a smaller number of items respectively 5 and 4, these clusters are connected within their own clusters and has no interconnection with other clusters. Cluster 4 and 5 is not visible in the Fig. 9 due to the smaller number of items in the cluster. The documents having high density circles are most cited documents showing high link strength. According to a thematic interpretation of Fig. 9, Gisin’s publications are among the most centrally positioned and frequently cited papers, demonstrating their high bibliographic coupling strength and significant effect across several clusters.
Bibliographic coupling analysis based on “Source”
The bibliographic coupling is performed for the source unit of analysis, and the network visualization result for the same is shown in Fig. 10. It represents the sources and conference in which the papers are published, and it also represent the coupling behaviour between them. The sample size of the sources is 3294 and the threshold value set for the sources is 5 for minimum number of documents per source and the citation of each source should also be 5. After setting the threshold limit, the number of samples chosen for the visualization is 404. The network visualization has 8 clusters showing 8 subcategories. Each cluster is having 50 to 100 items. Most cited sources are shown as high-density circle, some of the highly reputed sources are quantum information processing, proceedings of Spie, Physical Review A, Lecture notes in Computer Science, International Journal of Quantum Information and many more. These sources have strong link strength. The sources are multidisciplinary and show high bibliographic linkage, according to the clustering. Notably, the cross-disciplinary traits of post-quantum cryptography research is highlighted by the close relationships between computer science journals and quantum information sources, which are then connected with sources related to physics.
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Fig. 9
Bibliographic coupling analysis based on “Documents”
Bibliographic coupling analysis based on “Country”
In the “country” unit of analysis, coupling is shown as a network visualisation in Fig. 11. From 204 number of samples, 90 samples are chosen for the visualization as these samples has passed the threshold criteria given in Table 10. Two clusters are there in visualization, and the items in these two clusters are respectively 59 and 39. The most cited countries and having strong link strength are China, United States, United Kingdom, Japan, India, Germany and Canada.
Bibliographic coupling analysis based on “Author”
In “author” analysis, coupling is shown as a network visualisation in Fig. 12. From 30,355 number of samples, 5528 samples are chosen for the visualization as these samples has passed the threshold criteria given in Table 10. There are five clusters in visualization. The authors having high density has a greater number of citations and higher link strength. Blue colour cluster has high density and high link strength as compared to the other clusters. According to Fig. 12, a significant number of the authors are connected to one another and show a high degree of bibliographic coupling between various clusters. This suggests that the topic has a high level of multidisciplinary collaboration, which reflects the convergence of several research authors who are advancing post-quantum cryptography.
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Fig. 10
Bibliographic coupling analysis based on “Sources”
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Fig. 11
Bibliographic coupling analysis based on “Countries”
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Fig. 12
Bibliographic coupling analysis based on “Authors”
Co-occurrence analysis
In this type of analysis, the co-occurrence of the keyword is verified for the keyword who has been repeated in publications has high link strength and density. This analysis is performed using VOSviewer. On the dataset file, preprocessing is performed to the keywords to clean and normalize them to enhance accuracy of clustering. Variants like “post quantum security” and “post quantum cryptography” were standardised to “post quantum cryptography.” Both singular and plural forms were combined, such as “signatures” and “signature”, “lattices” and “lattice.” The VOSviewer thesaurus file was used to implement these standardisations, enabling manual term mapping and the removal of irrelevant or too general terms [98]. After normalisation, to show the cooccurrence analysis, the threshold used, and the number of samples chosen are given in Table 11.
Table 11. Co-occurrence analysis based on keywords
Sr. No. | Unit of analysis | Number Of Samples | Threshold | Clusters |
|---|---|---|---|---|
1 | All Keywords | 6372 | The minimum number of repetitions a keyword appears: 5 | 5 |
2 | Index keywords | 5681 | The minimum number of repetitions a keyword appears: 5 | 5 |
The analysis of index keywords co-occurrence has been done in this section, and the network visualization and density visualization graphs are shown in Figs. 13 and 14. Total number of index keywords in datasets are 38,003 and to choose the sample keywords from this keyword set, threshold is applied, which ensure that each keyword must be repeated 5 times in publications, and after the refining the sample size for keyword analysis is 5681.
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Fig. 13
Network visualization co-occurrence graph of index keywords
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Fig. 14
Density visualization co-occurrence graph of index keywords
There are 5 clusters in visualization network. The network visualization of the index keyword in Fig. 13 shows the link strength of the keywords, while the density visualization shows how dense the keywords are, and high density is proportional to the high co-occurrence of that keyword. The co-occurred keywords in PQC field are Quantum cryptography, post quantum cryptography, quantum computers, quantum information, optical communication, authentication and many more.
Thematic map and trend topics
A thematic map is used in bibliometric analysis to show the thematic development and structure of the subject of study. Usually, this approach divides themes into four quadrants according to two parameters: density (the theme’s development) and centrality (its significance to the field) [99, 100]. Themes that are under the niche themes are highly developed themes but having low centrality. Motor themes are those themes which has high centrality and density. These themes are the driving force to the research and topics under motor themes are highly influential and highly cited topics. The third theme is emerging or declining themes, these themes have low density and low centrality. These themes are either emerging, means they are going to developed in future, or declining, means they have lost their significance. Basic themes have low density but having high centrality. The field’s structure is supported by basic themes, which provide essential ideas and techniques that are often basic subjects that all researchers must comprehend [101, 102]. Figure 15 illustrates the thematic map of the dataset, which depicts cryptography, security and quantum computing come into the categories of basic theme and motor theme, demonstrating their maturity and central relevance. Quantum cryptography, key distribution, and quantum communication are basic and may be emerging themes but not declining themes. In the context of secure communication in the quantum age, these are critical sectors that are becoming more relevant rather than diminishing. Their comparatively lesser density emphasises the continuous need for deeper advancement, especially in real-world applications and compatibility with conventional systems. These themes will be the future trend of the area. Post quantum cryptography, lattice-based cryptography and code-based cryptography are given under the niche theme showing the high density and low centrality. Theoretically advanced, post-quantum cryptography, lattice-based cryptography, and code-based cryptography are classified as niche themes because of their inadequate integration with broader interdisciplinary themes or issues with practical implementation. This could be a result of the present emphasis on theoretical constructs and algorithmic proofs in research, with less attention paid to issues like hardware restrictions, side-channel resistance, and migration techniques. These discrepancies point to the need for more applied research that tackles practical adoption obstacles such standardisation issues, hybrid deployment approaches, and performance overhead.
The trend topic of the dataset is shown on Fig. 16 based on a year-wise structure spanning from 2016 to 2024. Network security, authentication, post-quantum cryptography, and quantum cryptography are the most widely studied topics in the field with the most citations. These topics have been trending since 2015. Blockchain, computational methods, and secure aggregations are new developing topics. The trending subject is shown in Fig. 16 with a dense thick point that illustrates the topic’s citation trend, which ranges from 5000 to 10,000. But the limited coverage of some of these topics indicates that these areas need more research, especially in cross-domain applications and in the establishment of reliable, scalable PQC systems.
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Fig. 15
Thematic map
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Fig. 16
Trend topics according to the timeline in the field of PQC
Findings and future directions
The analysis’s objective is to provide a thorough impression of the field so that citation and mapping criteria may be used to evaluate it. The methods of coupling analysis, citation analysis, and co-occurrence keyword analysis are used in this bibliometric research. The sample data set includes 18,114 entries total from all years, of which 14,230 were selected from 2010 to 2023. Frequent keyword appearance, and co-occurrence of keywords are some of the indications that research in quantum cryptography and security is an emerging field of research. The opportunity to do study in quantum cryptography area is great for a researcher who is interested in the subject. From the country publication count analysis, it has been seen that China and United states are the topmost countries who has published maximum number of articles in this research area. This area is classified as a subfield of computer science, engineering, and physics. The significance of the journals is shown by the fact that respectable journals are responsible for publishing the greatest number of papers in this discipline. The NCII score per publication is high for the year 2020, which indicates that the subject topic began to gain popularity in the year 2020 and that high citations have begun to bring in around the same year and impact of the discipline is also increased all around the world.
Based on citation analysis, it is found that Shanghai Institute of Microsystem and Information Technology of China is highly cited institute with 1530 citation. The evaluation of the highly cited author is performed, and Nicolas Gisin is found to be highly cited author in the discipline having H-index of 116 from University of Geneva, which is showing how impactful work he has done in this discipline. Physical Review Letter is the highly cited journal, and the H-index of that journal is 700 and impact factor is 9.185. The publications of the given field have high impact as compared to the other journal’s publication. Researchers can focus to publish their articles in that kind of journal to prove the significance of their work. The research article authored by Pirandola S. et al. [78] having title “Advances in quantum cryptography” is highly cited article with citation count 824. The international conference “40th Annual ACM Symposium on Theory of Computing, STOC 2008” has published article related to quantum security field yields the high citation count of 1756. Researchers can refer the articles of these authors, journals, and conferences in their research work to know the quality of their work and to compare the results with these highly influential articles and journals.
For the science mapping of the data set, bibliometric coupling is performed, where visualization diagram of coupling is made on the analysis of documents, sources, countries, and authors. In these coupling diagrams the link strength and density are discussed. High dense and having more link strength documents and sources are influential than others. Co-occurrence analysis of keyword is also performed to know the renowned keywords and their density in the PQC discipline.
When examined considering current PQC research, these bibliometric results show that although some algorithmic domains, such as lattice-based and code-based cryptography, are well-developed (as evidenced by their inclusion in the niche quadrant in Sect. 8), they are still relatively isolated from more general interdisciplinary application and adoption discussions. This might be an indication of a gap between the advancement of theoretical cryptography and issues with real-world implementation, including hardware integration, side-channel resistance, or computing efficiency. The under-representation of real-world deployment research in the existing literature is highlighted by the lack or poor presence of themes like “migration strategies,” “hybrid cryptography,” or “implementation challenges.” Enhancing these interpretative links can direct future studies to solve important adoption hurdles in the shift to post-quantum security as well as towards algorithm design innovation. The findings also reveal potential for multidisciplinary collaboration, especially with hardware engineers to create quantum-safe, lightweight implementations for embedded systems and the Internet of Things. Additionally, integrating blockchain technology creates opportunities for developing decentralised platforms that are resistant to quantum attacks. Additionally, attack modelling, efficiency optimisation, and adaptive security models can be improved by collaboration with quantum physicists and AI researchers.
Answers to the research questions
In the Sect. ‘Motivation’ some research question had been set up which need to be concluded after the analysis of the dataset. The answers to that questions are given below.
a. Contribution of countries to the PQC development.
From the coupling analysis and citation analysis of the countries done in Subsection “Analysis based on participated Countries” and “Analysis of bibliographic coupling”, it is concluded that China’s contribution is very high to PQC development as compared to the other countries. The other highly contributed countries in this domain are United States, United Kingdom, Canada, Japan, India, and Germany.
b. Top researchers which are contributing to the PQC.
Form the citation analysis done in Subsection “Insights from highly Cited Authors”, Gisin N [63]. is highly cited author and top researcher in this domain and published high quality work. Pirandola S. et al. [78] are the authors whose published work “Advances in quantum cryptography” is highly cited from all the publications and the analysis of publications is performed in subsection “Top cited Research articles”.
c. Leading Journals who are publishing the papers of PQC.
The leading journals of PQC domain (refer Subsection “Citation Analysis of Journal and Conference Publications: Unveiling Trends and Impact” and Table 7) are Physical Review Letters, Lecture Notes in Computer Science, Reviews of Modern Physics, Nature, and Quantum Information Processing.
d. Keyword analysis of the domain PQC
Highly dense and frequent keywords (refer Subsection “Analysis of Keywords”, Subsection “Co-occurrence analysis” and Fig. 13) of the domain are Quantum Cryptography, Quantum theory, Quantum key Distribution, Quantum Communication and Quantum Computer and Photons.
e. Coupling of the authors, countries, and sources.
The coupling of the authors, countries and sources are performed to know the highly influential sources, countries, and authors in the PQC domain, which already has been explained in Sect. “Bibliometric coupling analysis”.
Future direction
Researchers in this emerging field have numerous opportunities with PQC, which is experiencing rapid growth. While significant progress has been made in the field of quantum cryptography, there is still more to be accomplished in the realm PQC to establish a universally accepted algorithm for quantum security. There is a great deal of potential in PQC for the new PQC algorithm. With the emergence of new algorithms, there is a vast opportunity for cryptanalysts to delve into the capabilities and limitations of these proposed algorithms by collaborating with the authors having high experience in this field and countries which are contributing more to PQC along with the institutes and sources who are providing research opportunities in this area. There is also the potential to combine classical and quantum cryptography to enhance security during the transition phase. Quantum resources can be optimized since they are costly in the initial phase of implementation. Legal and regulatory research is also an important aspect to consider in this field. Researchers can use the above analysis to generate valuable research that will impact the field of PQC in the future. Future directions also involve the interdisciplinary collaboration between hardware engineers and quantum engineers to develop IoT devices portable lightweight PQC. PQC researchers can collaborate effectively with blockchain experts for developing quantum secure decentralized systems. Collaborations with experts in artificial intelligence field and quantum physics might improve attack prediction and performance optimisation.
Conclusion
To determine the importance, patterns, and applicability of PQC, this research analyses the dataset of articles published in the PQC field using bibliometric and scientometric methods. A total of 14,230 entries has been collected from the Scopus dataset, covering the years 2010 to 2023, for analysis. There has been a significant rise in the number of publications on PQC since 2010, indicating a growing interest and research focus in this field. This manuscript analyses the highest cited countries, authors, sources, and titles. Additionally, it examines the coupling relationship network diagrams. This study highlights the significance of ongoing research and collaboration in PQC to guarantee the development of strong, quantum-resistant cryptographic solutions. With the standardization process underway at NIST, the findings from this bibliometric analysis can offer valuable insights for future research directions and policy decisions. This, in turn, will play a crucial role in advancing secure communication in the quantum era. This work benefits contributors and researcher by helping authors and researchers to understand research priorities and publications in the field of PQC by giving them insights about influential authors, key research trends, and impactful journals. Institutions will be influenced in identifying strategic partnerships and impactful research directions. This research analysis will support funding agencies in aligning resources with high-growth areas, so that funding agencies can allocate their resources toward impactful and emerging topics. The future work involves the collaboration of interdisciplinary fields and offers practical recommendations for research funders, and standardisation organisations for aligning their objectives with worldwide cryptographic trends by highlighting active and unexplored topics in PQC research. Concrete future bibliometric directions include Integrating advanced measures such as Field-Weighted Citation Impact (FWCI) and normalised H-index for a more thorough assessment of authors and documents. Databases like IEEE Xplore and Web of Science can be added to the research to provide more comprehensive coverage. Furthermore, examining the establishment of policies and their practical application might help bridge the gaps between research and practice.
Author contributions
Taniya Hasija conceptualized the research design and methodology. Ram Kumar performed the data extraction and analysis using bibliometric tools. Amanpreet Kaur wrote the initial manuscript draft. Malvinder Singh reviewed, edited, and finalized the manuscript. All authors contributed to the interpretation of results and approved the final manuscript.
Funding
Open access funding provided by Manipal University Jaipur.
Data availability
No datasets were generated or analysed during the current study.
Declarations
Ethical approval
All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee.
Competing interests
The authors declare no competing interests.
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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