June 7, 2021
Elena Kirshanova - Immanuel Kant Baltic Federal University
In two of the main areas of post-quantum cryptography, based on lattices and codes, nearest neighbor techniques have been used to speed up state-of-the-art cryptanalytic algorithms, and to obtain the lowest asymptotic cost estimates to date [May{Ozerov, Eurocrypt'15; Becker{Ducas{Gama{Laarhoven, SODA'16]. These upper bounds are useful for assessing the security of cryptosystems against known attacks, but to guarantee long-term security one would like to have closely matching lower bounds, showing that improvements on the algorithmic side will not drastically reduce the security in the future. As existing lower bounds from the nearest neighbor literature do not apply to the nearest neighbor problems appearing in this context, one might wonder whether further speedups to these cryptanalytic algorithms can still be found by only improving the nearest neighbor subroutines.