The Novel Efficient Dual-field FIPS Modular Multiplication

• Tingting Zhang,
• Junru Zhu,
• Yang Liu,
• Fulong Chen,

Vol. 14, No. 2, February 29, 2020
10.3837/tiis.2020.02.015, Download Paper (Free):

• Montgomery algorithm
• FIPS
• Modular multiplication
• Modular Square
• Dual-field

Abstract

The modular multiplication is the key module of public-key cryptosystems such as RSA (Rivest-Shamir-Adleman) and ECC (Elliptic Curve Cryptography). However, the efficiency of the modular multiplication, especially the modular square, is very low. In order to reduce their operation cycles and power consumption, and improve the efficiency of the public-key cryptosystems, a dual-field efficient FIPS (Finely Integrated Product Scanning) modular multiplication algorithm is proposed. The algorithm makes a full use of the correlation of the data in the case of equal operands so as to avoid some redundant operations. The experimental results show that the operation speed of the modular square is increased by 23.8% compared to the traditional algorithm after the multiplication and addition operations are reduced about 2()/2ss−, and the read operations are reduced about 2ss−, where 32s=n/ for n-bit operands. In addition, since the algorithm supports the length scalable and dual-field modular multiplication, distinct applications focused on performance or cost could be satisfied by adjusting the relevant parameters.

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