A new reduction shows k-sparse LWE and LPN in dimension n inherit nearly the full hardness of dense LWE and LPN in a much smaller dimension.
Mult i-party Homomorphic Secret Sharing and Sublinear MPC from Sparse LPN
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Near-Optimal Time-Sparsity Trade-Offs for Solving Noisy Linear Equations
A new reduction shows k-sparse LWE and LPN in dimension n inherit nearly the full hardness of dense LWE and LPN in a much smaller dimension.