In order to guarantee secure transactions through the Internet and to generate strong evidence that could be used in case of future legal disputes, several countries around the world have promoted and regulated the use of digital signatures based on Public Key Infrastructure (PKI). However, despite the high expectations, its implementation has achieved neither the desired results nor its globalization. Many of the reasons were discovered years ago, but they are still open problems for the scientific community nowadays. In order to consider the case of the national PKI of the Peruvian state as empirical evidence for studies that address the open problems, this article describes the details about a new certification hierarchy which is expected to overcome some of its predecessors' limitations. It is also expected that the information disclosed in this article could be useful to other countries for making a preliminary assessment for possible cross-border recognition of Peruvian digital signatures.