Adeline Langlois and Damien Stehlé. “Worst-case to average-case reductions for module lattices.” Designs, Codes and Cryptography, 75(3):565–599, 2015.

Introduced Module LWE (MLWE), which generalizes Ring LWE by considering rank-$k$ modules over a polynomial ring $R_q$. When $k=1$ this recovers Ring LWE; when $k=n$ this recovers plain LWE. The module structure interpolates between the two extremes, yielding a flexible parameter trade-off between efficiency and security assumptions. Kyber (ML-KEM) and Dilithium (ML-DSA), the NIST post-quantum standards, are based on Module LWE.

BibTeX

Copy

@Article{DCC:LanSte15,
  author = {Adeline Langlois and Damien Stehl{\'e}},
  title = {Worst-case to average-case reductions for module lattices},
  pages = {565--599},
  journal = {Designs, Codes and Cryptography},
  volume = {75},
  number = {3},
  publisher = {Springer},
  year = {2015},
  doi = {10.1007/s10623-014-9938-4},
}