This project aims to develop the cryptographic foundations for secure communication in the post-quantum era. Most current public-key cryptographic systems, which underpin the security of modern digital infrastructure, rely on the hardness of problems such as integer factorization and the discrete logarithm problem. These problems can be solved efficiently by quantum algorithms (using Shor’s algorithm), making today’s cryptographic systems vulnerable to future large-scale quantum computers. Post-quantum cryptography seeks to replace these vulnerable systems with new cryptographic primitives based on mathematical problems believed to remain hard even against quantum adversaries. While recent standardization efforts have primarily focused on basic primitives such as encryption and digital signatures, many emerging applications, including decentralized systems and privacy-preserving protocols, require more advanced cryptographic functionalities. This project addresses this gap by designing and analyzing post-quantum cryptographic protocols with advanced features. The research focuses on algebraic structures arising from lattices, error-correcting codes, and group actions, including isogeny-based cryptography. Key objectives include the construction of protocols supporting advanced functionalities such as blind signatures, threshold signatures, multisignatures, and verifiable random functions, together with rigorous security proofs based on well-defined computational assumptions. The central methodological tools include zero-knowledge proofs and group action frameworks. The project will also investigate improvements in efficiency, security, and scalability of the protocols. Expected outcomes include new provably secure cryptographic schemes, conceptual advances in the use of algebraic methods for post-quantum cryptography, and contributions to the training of students through research mentoring and outreach activities. This award reflects NSF's statutory mission an