Euclidean lattices are among the most promising objects for building a post-quantum cryptography, i.e. constructions that would resist the power of large scale quantum computers. For efficiency reasons, most constructions use lattices enjoying a strong algebraic structure, and can be interpreted as constructions over polynomials with rational coefficients. However, it is still unknown to this date to what extent this additional structure can be used to attack those cryptosystems. Thus, studying more generic lattices is still an important challenge for future cryptography.
Plantard et al. (2016) submitted a scheme called DRS to the NIST process aiming at standardising post-quantum cryptography, based on diagonally dominant matrices. However, it suffered a different learning attack from Ducas and Yu (2017), lowering the security estimates by at least 30 bits.
In this talk, I will first give some background on Euclidean lattices and their use in cryptography. Then I will describe GGH-like schemes and statistical attacks known on these constructions. Finally I will present a recent joint work with T. Plantard and A. Sipasseuth submitted to PQCrypto 2024. We study diagonally dominant matrices (as in the DRS scheme) and study their use in cryptography. We propose an encryption scheme based on new algorithmic results on this type of matrices and study potential patches to the attack of Ducas and Yu.
