Miyaji Laboratory

Lattice-based cryptography has attracted attention year by year due to the standardization of Post- Quantum Cryptography by the National Institute of Standards and Technology (NIST). Ring-Learning with Errors (Ring-LWE) problem is one of the mathematical problems that constitute such lattice cryp- tosystems. The Ring-LWE problem has many algebraic properties because it is considered in the ring of integers R of a number field K. When modulus q is unramified in K, it is known that the Ring-LWE problem, to determine the secret information s ∈ Rq, can be solved by determining s (mod q) ∈ Fqf for the prime ideal q lying over q. χ2-attack determines s (mod q) by brute force and using χ2-tests, which is improved where the residue degree f is even number. In this paper, we propose an improved χ2-attack that efficiently works for any residue degree. Furthermore, we perform security analyses of the Ring-LWE problem for number fields.