Post-Quantum Signatures and KEMs from Unstructured Noisy Linear Algebra

Instantiate public-key encryption, KEM, and signature schemes from unstructured noisy linear algebraic assumptions introduced by Ghosal, Jain, Lou, Sahai, and Vafa (2025). Develop trapdoors and hashing-to-instance techniques analogous to SIS/LWE but without relying on ring or cyclotomic structures. Explore aggregate signatures and tight QROM proofs exploiting the unstructured noise model. This approach avoids known algebraic attack vectors that exploit ring structures common in PQC schemes like NewHope, NTRU, and Dilithium, offering a qualitatively different hardness substrate. By closing the performance gap with careful parameterization and new trapdoor gadgets, the research aims to produce primitives with fewer structural attack surfaces. Aggregation-friendly signatures over these assumptions could benefit blockchains and IoT by reducing key and certificate bloat. The impact is the emergence of a second major family of PQ primitives beyond LWE/LPN/rings, expanding the design space for long-term standardization.

References:

1. Applications of Ring Theory in Post-Quantum Cryptography. Dr. Muhammed Basheer (2025). International Journal for Research in Applied Science and Engineering Technology.
2. Post-quantum PKE from Unstructured Noisy Linear Algebraic Assumptions: Beyond LWE and Alekhnovich's LPN. Riddhi Ghosal, Aayush Jain, P. Lou, Amit Sahai, Neekon Vafa (2025). International Conference on the Theory and Application of Cryptographic Techniques.