High-performance Dual-field High-radix Montgomery Modular Multiplier

• Main Authors: Guan-Ying Chen, 陳冠穎
• Other Authors: Shiann-Rong Kuang
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/eu856e

碩士 === 國立中山大學 === 資訊工程學系研究所 === 106 === With the advancement of technology and the flourishing development of the Internet world, the amount of data circulating on the Internet has become very large. Therefore, the security and privacy of data transmission and reception are very important. In order to achieve security and confidentiality, we can encrypt and decrypt data to protect data, so cryptography plays an important role in ensuring data security. RSA cryptosystem is one of the most widely used public key cryptosystems. According to the mathematical theory of prime number and factorization, RSA cryptosystem has a high level security. Due to the increase in security levels, the bit length of key required for encryption and decryption in the RSA cryptosystem is also increasing to meet the needs of information security. If software is used to perform operations, it will not meet the real-time requirement. To solve this problem, we will use hardware implementation to increase the speed of operation. In addition to the RSA cryptosystem, the ECC cryptosystem is also one of the widely used public cryptographic key systems. The characteristic of the ECC cryptosystem is that it requires only a short key length, and can achieve or even exceed the security of the symmetric cryptosystem and the RSA cryptosystem. Therefore, the ECC cryptosystem has been adopted by many Internet of Things devices to ensure security. Since ECC has two kinds of operation fields: prime field and binary field, in order to select the operation field according to the demand, we will design a circuit with two kinds of operation fields.   This thesis proposes the hardware architecture of a dual-field high-radix Montgomery modular multiplier to perform the encryption and decryption operations of RSA cryptosystem and ECC cryptosystem. To avoid the excessive expansion of the cell area, the high-radix hardware architecture is designed to meet the needs of high-performance. In addition, the dual field is also added facilitate the operation of the ECC cryptography system in different fields.