RSA and Elliptic Curve Cryptosystems (ECC), which support modern information security, are constructed based on the hardness of integer factorization problem and discrete logarithm problem. However, if a large-scale quantum computer is built, then these problems can be solved in polynomial time by Shor’s algorithm and its variant, it means RSA and ECC will be vulnerable any longer.

Post-Quantum Cryptosystem (PQC), which resists against quantum computer attacks, is being researched all over the world because of the above-mentioned reason. PQC requires research to deal with various mathematical problems different from integer factorization and discrete logarithm problems. It is necessary to use various mathematical theories beyond elementary number theory.

My research interest is on PQC, especially, Multivariate Public Key Cryptosystem (MPKC), constructed based on the (MQ) problem of finding a solution to Multivariate Quadratic equations over a finite field. Since it is proven to be NPcomplete, it is expected that MPKC is resistant to quantum computer.

The virtues of MPKC are high-speed performance and its small signature size among other candidates. Therefore, MPKC is suitable for smart cards and IoT devices. There is also an interesting trial of creating crypto currency from an MPKC signature scheme, Rainbow, in recent.

I mainly study security analysis on MPKC. Mathematical arguments with respect to Gröbner basis or algebraic geometry are necessary. However, the complexity analysis against Gröbner basis algorithm, especially, F4/F5 algorithm is still not theoretically clear. Its complexity analysis depends on experimental results. For EFC MPKC encryption scheme, I am curre-ntly working on, I experimentally found that its security is weaker against hybrid attack than original estimation (Fig.1). However, its theoretical explanation is not yet established and remained as an open problem.

I also study other PQC, as lattice and isogeny cryptosystems. I am interest-ed in constructing a new cryptosystem by combining them.