A rank 3 lattice made with Blender.

A cryptosystem is a technique allowing someone to write and use secrets, for example, secret messages that are unreadable to web pirates. I'm interested into cryptosystems using euclidean lattices, which are mathematical objects from geometry of numbers.

The main question that prevents me from sleeping is : "How does one efficiently generate a random lattice that can't be broken by pirates ?".

The average hardness of SIVP in the case of lattices over a big number field has just been proved by my advisors and colleagues, see it here on HAL. I had the opportunity to help correcting the paper.

I currently work on the same subject but for lattices of arbitrary dimension. We will need to use deeper number theoretical tools, including Langlands's theory on automorphic representations, with an effective approach.