| Summary: | 博士 === 國立成功大學 === 電腦與通信工程研究所 === 100 === The ubiquitous cryptographic concept, Public Key Infrastructure (PKI), is facing a slew of severe risks. A particular issue is long-term security, which can be classified into long-term authenticity and long-term confidentiality. The issue of authenticity has been widely discussed in the last decade while the confidentiality issue has been neglected. As the factorization of RSA is advancing, there is increased urgency to refresh confidentiality of existing instances of PKI with longer validity terms. Unfortunately, among these discussions, there is no realistic, low cost and efficient solution to the problem. Long-term confidentiality is the most challenging unaddressed open problem from previous works. In this dissertation, we formalize this problem by defining Privacy-Free Window (PFW). By taking advantage of a PKI special property called asymmetric secrecy property, we give a specific solution addressing PFW. This method can be further developed to extend the originally defined security interval of some PKIs and other cryptographic tools. We also furnish an algorithm to verify existing protocols and provide suggested actions for reacting to a PFW occurrence. Furthermore, pending the possible realization of quantum computers, the RSA public key cryptosystems which PKI relies on is facing critical challenges because of weaknesses under quantum cryptanalysis. We research a possible replacement, knapsack cryptosystems, which do not yield any weaknesses to quantum computation in this dissertation. Building on experimental results, we develop an empirically secure knapsack cryptosystem which explores possible directions for improving a candidate for public key cryptosystem which can survives in the quantum era.
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