The field of quantum cryptography and coding theory is rapidly advancing, with a focus on developing secure and efficient protocols for quantum key distribution and storage. Researchers are exploring new techniques, such as the use of universal Gröbner bases and Burnside rings, to create quantum-resistant cryptosystems. Additionally, there is a growing interest in distributed quantum storage and the development of coding schemes that can ensure the security and reliability of quantum information. Notably, recent works have made significant progress in improving the performance of digital signature schemes and establishing tight quantum time-space tradeoffs for permutation inversion.

Some noteworthy papers in this area include: Quantum-Resistant Cryptography via Universal Gröbner Bases, which proposes a key establishment protocol resistant to quantum attacks. On the Capacity of Distributed Quantum Storage, which characterizes the capacity of distributed quantum storage for various graphs. MPCitH-based Signatures from Restricted Decoding Problems, which achieves competitive signature sizes by instantiating the restricted decoding problem within the MPCitH framework. Tight Quantum Time-Space Tradeoffs for Permutation Inversion, which proves a lower bound for permutation inversion with even quantum advice, matching the best known attacks.