 Hello everyone and thank you for watching this video abstract. My name is Joel Felderhoff, I am PhD student at the UNS de Lyon and I am going to present the article on module unique SVP and NTRU, which is a joint work with Alice Polynmarie and Damien Stélet. The NTRU Security Assumption asks, given a polynomial h, a modulus q and a power of 2n, to find f and g, small polynomials verifying that h est equal to f over g modulo q and x to the n plus 1, provided that such small polynomial exists. This can be seen as finding a small non-zero vector in a lattice l, which verifies that firstly every element of l are pairs of integral polynomials modulo x to the n plus 1 and secondly there exist some very short vectors in l. This problem of finding short non-zero vector in lattices with an exceptionally short vector is called the unique short vector problem. It has already been studied and it is known to be equivalent to some other classical problem in lattice-based cryptography, such as bounded-descense decoding or the short independent vector problem where the equivalence requires a quantum computer. In our paper we studied a structured version of usvp that we called module usvp in rank 2. It asks, given basis of a lattice l whose elements are pairs of polynomials modulo x to the n plus 1, to find a short non-zero vector in it, with the guarantee that the shortest element of l is a lot smaller than the lattice's root volume. As we said, entro is a particular case of module usvp in rank 2. Our first contribution consists in proving that it is indeed a generic case entro is equivalent to module usvp in rank 2. This is done by giving an algorithm transforming any module usvp in rank 2 instance into a related entro instance and a way to leave back entro solution to an initial module usvp solution. Next, we give a random self-reduction for module usvp in rank 2. We show that there exists a distribution over its instances, such that if someone can solve module usvp in rank 2 with non-negligible probability for an instance sampled from the distribution, then they can solve every state of module usvp in rank 2. This is done by giving an algorithm that randomizes in an invertible way any instance of module usp in rank 2. All our reductions are classical, but require calls to idealSvp oracle. Their outline will be given in the in-person talk. I hope this video made you want to assist to my presentation, and I hope to see you live in Taiwan soon. Bye.