Abstract and 1. Introduction 2 Related Work and 2. 1 Technology Convergence Approaches 2. 2 Technology Convergence Measurements 2. 3 Technology Convergence Models 3 Data 4 Method and 4. 1 Proximity Indices 4. 2 Interpolation and Fitting Data 4. 3 Clustering 4. 4 Forecasting 5 Results and Discussion and 5. 1 Overall Results 5. 2 Case Study 5. 3 Limitations and Future Works 6 Conclusion and References Appendix 5. 2 Case Study To demonstrate the practical significance of our results, we analyze the evolution of proximity indices between "Public-key cryptography" and "Blockchain, " as shown in Figure 4. An interpolation rate of 46% stands out. This stems from the limited interactions between these two technologies from 2002 to 2012, reflecting the nascent stages of blockchain development within the cybersecurity field. As a result, during this period, the indices remained mostly unchanged. It is important to emphasize that, although this interpolation rate is relatively high, it does not cause significant bias in our indices for "Public-key cryptography" and "Blockchain"; rather, it authentically represents the non-interaction phase between these technologies. From 2017 onward, there is a marked increase in the proximity indices, especially those related to common keywords and collaboration measured by incremental h-indices. This indicates a strong correlation between "common keywords" and "collaboration, " implying a considerable number of researchers engaging simultaneously with both public-key cryptography and blockchain technologies.

Additionally, there is a slight rise in mutual citations between the two areas. While citation-based indices show moderate growth, this might be due more to their structural characteristics than to an absence of interaction between these technologies. From this evidence, we propose that a significant technological convergence occurred between blockchain and public-key cryptography between 2017 and 2021. This convergence is underscored by the growing application of public-key cryptography in blockchain platforms during that timeframe. Techniques such as digital signatures, which rely on public-key cryptography, became essential for validating blockchain transactions. Moreover, the adoption of zero-knowledge proofs—also based on public-key cryptography—increased within blockchain frameworks to enable validation of claims without disclosing underlying data. In summary, our findings reveal a crucial phase of technological convergence linking blockchain and public-key cryptography from 2017 through 2021.