Reproduce “Mathematics and Efficiency of Song's CVP Hardness Reduction” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Shuhong Gao
The reduction turns satisfying assignments into low-weight code witnesses and then lattice instances using affine constraints and polynomial moment tables. Shared recurrences and revised parameter schedules reduce feasible output dimensions. For fixed ε, the code length and lattice rank scale as n^{4/ε²+O(1/ε)}/(log n)^{r+1}, versus Song’s n^{8/ε²+O(1/ε)} schedule, while preserving CCP hardness N^{1−ε} and CVP hardness N^{(1−ε)/2}; the limiting exponents do not improve.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.