## The IMI Colloquium Report in June 8, 2022

2022.06.21

Title: Cryptography Implementation and Mathematics

Speaker: Shigeo Mitsunari (Cybozu Labs, Inc.)

Place: Live-streaming by Zoom

Attendance: 50 (Students: 16; Staffs: 33; Others: 1)

In this talk, the speaker told about the cryptographic technology and its efficient implementation. Public key cryptosystems (PKC), which are representatives of the cryptographic technology, are constructed based on hard computational problems in mathematics. For example, RSA and elliptic curve cryptosystem (ECC) are constructed based on integer factoring and discrete logarithm problems. For the actual uses of above cryptographic technology on the internet and so on, it is required to implement them efficiently. In this talk, the speaker described ECC and pairing-based cryptosystem constructed by using the theory of elliptic curves, and explained various mathematical techniques to realize efficient implementations for elliptic curves, such as binary method, window method and GLV method.