In this talk, I will introduce a new variant, MP-LWE, of the Learning With Errors problem (LWE) making use of the Middle Product between polynomials modulo an integer q. We exhibit a reduction from the Polynomial-LWE problem (PLWE) parametrized by a polynomial f, to MP-LWE, which is defined independently of any such f. We also explore some applications of different variants of MP-LWE into Titanium, a public-key encryption (PKE) scheme and MPSign, a digital signature scheme proven secure in the quantum random oracle model (QROM). If time allows, I will introduce FACCT, a fast, compact and constant-time implementation technique in lattice-based crypto with applications to well-established PKE and DS schemes.