Explore advanced concepts in permutation-based cryptography through this 21-minute conference talk, the second in a three-part series presented at FSE 2025 and chaired by Yaobin Shen. Delve into cutting-edge research and methodologies in cryptographic systems that utilize permutation functions as their foundational building blocks. Gain insights into the latest developments in this specialized area of cryptography, examining theoretical frameworks, practical implementations, and security considerations. Access comprehensive supporting materials including research papers and presentation slides to deepen your understanding of permutation-based cryptographic techniques and their applications in modern security systems.