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http://dx.doi.org/10.13089/JKIISC.2019.29.3.515

Efficient Modular Multiplication for 224-bit Prime Field  

Chang, Nam Su (Department of Information Security, Sejong Cyber University)
Publication Information
Journal of the Korea Institute of Information Security & Cryptology / v.29, no.3, 2019 , pp. 515-518 More about this Journal
Abstract
The performance of Elliptic Curves Cryptosystem(ECC) is dominated by the modular multiplication since the elliptic curve scalar multiplication consists of the modular multiplication in projective coordinates. In this paper, we propose a new method that combines the Karatsuba-Ofman multiplication method and a new modular reduction algorithm in order to improve the performance of the modular multiplication for NIST p224 in the FIPS 186-4 standard. The proposed method leads to a running time improvement for computing the modular multiplication about 25% faster than the previous methods. The results also show that the method can reduce the arithmetic complexity by half when compared with traditional implementations on the standpoint of the modular reduction.
Keywords
Elliptic Curve Cryptosystem; Modular Multiplication; Finite Field Arithmetic;
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