A New Cryptographic Frontier: Key-Independent Security and Post-Quantum Hardness Assumptions

With the rapid advancement of quantum computing, many classical encryption schemes are becoming increasingly vulnerable to quantum attacks, highlighting the urgent need for post-quantum cryptographic solutions that can withstand this emerging threat. In this context, this paper introduces the Q-Problem, a novel post-quantum hardness assumption specifically designed to resist quantum adversaries by presenting them with a vast and computationally infeasible preimage space. Building on this foundation, we propose Q-KIE (a post-quantum key-independent encryption scheme), which replaces persistent cryptographic keys with ephemeral, message-bound secret holders. Q-KIE features dynamic complexity tuning, offering flexible security levels and maintaining efficient performance across both classical and quantum computing environments. Detailed analysis and comprehensive evaluations demonstrate the scheme's strong potential in preserving confidentiality, integrity, and computational practicality, positioning it as a promising candidate for hybrid and post-quantum cryptographic frameworks.