2024/08/07 by Madhura Pathegama, Alexander Barg, Pathegama, Madhura +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #94A60 #94B05 #Algorithms and Data Compression #Cryptography and Security (cs.CR) #DNA and Biological Computing #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2408.03742
openalex publication_date 2024/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The Learning Parity with Noise (LPN) problem underlines several classic cryptographic primitives. Researchers have attempted to demonstrate the algorithmic hardness of this problem by finding reductions from the decoding problem of linear codes, for which several hardness results exist. Earlier studies used code smoothing as a tool to achieve reductions for codes with vanishing rate. This has left open the question of attaining a reduction with positive-rate codes. Addressing this case, we characterize the efficiency of the reduction in terms of the parameters of the decoding and LPN problems. As a conclusion, we isolate the parameter regimes for which a meaningful reduction is possible and the regimes for which its existence is unlikely.