Better Bias-Dimension Trade-offs---Some Results on Solving Hard Learning Problems Using Coding Theory

Hard learning problems (e.g., LPN, LWE and their variants) are attractive topics recently in the cryptographic community due to the numerous cryptosystems (symmetric or public-key) based on them. Normally these systems employ an instantiation of the underlying problem with a large dimension and relatively small noise to ensure the security and the high decryption success probability, respectively. In the famous BKW algorithm, Blum et al. first pointed out that balancing these two parameters plays a key role in solving these hard instances. Along their path, I will present a new idea to form better dimension-bias trade-offs by using coding theory, thereby resulting in better solutions. Lattice codes are used for solving LWE, and covering codes for LPN. Moreover, I will also present an improved method if additional algebraic structures are provided (e.g., in the reducible Ring-LPN case).