### 活動內容：

主講人：楊策仲 教授(東吳大學財務工程與精算數學系)

題 目：Elliptic Curves Cryptosystem and post-quantum Diffie-Hellman

摘要Abstract:

The Diffie-Hellman key exchange protocol is the foundation in public key cryptosystem. The elliptic curve cryptosystem(ECC) is a standard example and widely used now. The ECC uses the algebraic group structure of an elliptic curve over a finite field. The security of this protocol depends on the hardness of solving discrete logarithm problem(DLP). In 1994, Shor presents a quantum algorithm which solves DLP (breaks ECC) and factorization problem (breaks RSA) in polynomial time using quantum computers. De Feo and Jao, in 2011, proposed supersingular isogeny Diffie-Hellman(SIDH) key exchange protocol which is quantum-resistant. In January 2019, SIKE (supersingular isogeny key encapsulation), which is an incarnation of SIDH, was chosen as one of the seventeen second-round contenders, to become a NIST(National Institute of Standards and Technology) standard for post quantum key establishment. However, it is broken due to Castryck-Decru attack in 2022. Recently, a commutative supersingular isogeny-based Diffie-Hellman scheme(CSIDH) with an efficient variant has been proposed. It is based on the action of the class group of an endomorphism ring on the isomorphism classes of elliptic curves over finite fields. In this talk, I will introduce ECC and SIDH CSIDH key exchange protocol. If time is permitted, I will talk about an extension of SIDH to genus-2 hyperelliptic curves over finite fields. That is, use the jacobians of superspecial genus-2 hyperelliptic curves and product of two supersingular elliptic curves together with Richelot isogenies to construct a genus-2 isogeny cryptosystem.

### 活動時間：

2023/05/30 14:10 ~ 2023/05/30 16:00

### 報名時間：

2023/05/19 15:30 ~ 2023/05/29 17:00

### 活動地點：

科學館 S433室

聯絡單位：數學學系

聯絡人：莊麗秋

聯絡電話：02-26215656#2501

傳真：

電子信箱：tsmx@oa.tku.edu.tw