Work-in-Progress: Security of Public-Key Schemes in the Quantum Computing Era – A Literature Review

Quantum computers, although still in the theoretical stage, conceptually have the power to break many current cryptosystems, including public-key schemes., for example, RSA (Rivest, Shamir., Adleman), elliptic-curve cryptography (ECC), and ElGamal. NIST specialists and national governments believe that existing cryptography algorithms will become vulnerable to brute force analysis by the end of the decade and agree that measures should be taken before then to ensure the secrecy of current and future algorithms. In this context, information security, including confidentiality and integrity, must be considered. This paper provides a systematic literature review on whether existing public-key schemes have the necessary complexity and solution space to resist a quantum computer. The discussion will focus on a quantum computer's negative “real-world” impact and examine existing post-quantum algorithms, then provide analysis across two selected dimensions. Finally, we summarise the latest trends and gaps in post-quantum cryptography and provide the security analysis of NIST's last round finalists.