In the modern information society, the value of information is increasing. Therefore, it is important to handle information safely. For example

• Communicating information securely
• Guaranteeing the validity of information
• Processing information safely

Cryptography is an indispensable technique to realize those topics above. My research topic contains the establishment of theories on finite algebraic systems (finite sets with operations) and their computational theory, and their application to cryptography. For example, number theory (prime factorization, etc.), algebraic geometry (sets of solution of equations, curves, etc.), and lattice theory.