Let $G$ be a finite abelian group and let $g_1,...,g_n \in G$. Define the relation lattice $L = { (x_1,...,x_n) \in Z^n : \sum_{i=1}^n x_i g_i = 0 }$. Ducas and Pierrot (Designs, Codes and Cryptography, 2019) showed how relation lattices can provide families of dense lattices with a polynomial-time bounded distance decoding algorithm. Li, Ling, Xing and Yeo (IEEE Transactions on Information Theory 2020) proposed using a relation lattice for a version of the McEliece code-based post-quantum encryption scheme. I will survey these results and discuss some improvements to the cryptosystem of Li, Ling, Xing and Yeo.
Also: Bush House (SE) 1.06
Professor Galbraith is a researcher in mathematics of public key cryptography at the University of Auckland in New Zealand. He has held positions at Royal Holloway, Bristol, Institute of Experimental Mathematics (Essen), and Waterloo.