In the context of quantum computing, cryptographic primitives are
about to change to ensure security against quantum adversaries. To han-
dle this problem, the National Institute of Standards and Technology
(NIST) began a standardization campaign for post-quantum cryptosys-
tems. From that, new primitives are arising, and particularly lattices
problems computationally hard to solve like the Learning With Error
(LWE) problem [Regev05]. The decisional LWE problem asks to dis-
tinguish a sample (A, As + e (mod q)) from the uniform (A, b) where

A and s are uniforms over Zq and e is a gaussian error.
The search version of this problem asks to find s. However, in the precipitation of the standardization

process, some aspects of cryptanalysis are not well studied. Especially,

physical attacks (using electric consumption, magnetic field, ...), namely
Side Channels Analysis, permits to recover additional information on the
secret. To handle this problem, masking with random computation seems
to be a good alternative, but at what cost ? To optimize the masking of
post-quantum lattice-based schemes, we need to ensure the security of the
underlying primitive in knowledge of additional information on the secret
coming from sides channels analysis. To do it so, we study the most real-
istic model of information obtained with sides channels Analysis such as
the noisy Hamming Weight. So then, the adversary obtains the Hamming
weight of the element implied in the current operation. We present a new
variant Noisy Hamming Weight LWE (NHW-LWE) consisting in an LWE
sample with additional material such as the noisy Hamming weight of As:
(A, As + e (mod q), HW(As)+η), and prove its hardness under the LWE
assumption. Finally, we conclude on the hardness of the Learning With
Physical Rounding and Noise (LWPRN) which gives (A, HW(As) + η)
using the previous security reduction.

Collaboration avec Clément Hoffmann, Adeline Roux-Langlois et François-Xavier Standaert