柴田 紗由美
The cryptography used in the current public key and some common key schemes are secure against conventional computers, but can be broken by quantum computers. The lattice-based cryptography is being studied as a candidate for post-quantum cryptography. Learning with Errors (LWE) problem is a mathematical problem that constitutes a lattice-based cryptography. Especially, the LWE problem over the ring of integers of a cyclotomic field is called the Ring-LWE problem, and cryptosystems and digital signatures have been proposed. Moreover, Function Field Decoding Problem (FF-DP), which is the Ring-LWE problem over function fields, was proposed by Bomber et al. for leads to another point of view strengthening the connection between lattice-based and code-based cryptography. Number fields and function fields have many similarities, and FF-DP also has many similarities with the Ring-LWE problem over number fields. However, FF-DP has only a definition and some simple applications, and it has not yet been discussed the security of FF-DP. In this paper, we examine the security of FF-DP, by applying Kannan's Embedding:, used in lattice attack.
