Simple countermeasure to cryptanalysis against unified ECC codes

• Published in: Journal of communications and networks Vol. 12; no. 1; pp. 1 - 4
• Main Author: Baek, Yoo-Jin
• Format: Journal Article
• Language: English
• Published: Séoul Editorial Department of Journal of Communications and Networks 01.02.2010; Korean Institute of Communication Sciences; 한국통신학회
• Subjects: Applied sciences; Arrays; Correlation; Countermeasure; Cryptography; Elliptic curve cryptography; elliptic curve cryptosystem (ECC); Elliptic curves; Exact sciences and technology; Information, signal and communications theory; Power demand; Signal and communications theory; simple power attack (SPA); Telecommunications and information theory; Timing; unified code.16; 전자/정보통신공학; Finite field; elliptic curve cryptosystem (ECC); Multiplication; simple power attack (SPA); Security of data; Cryptanalysis; Countermeasure; Elliptic curve; Timing; Cryptography; unified code.16
• ISSN: 1229-2370; 1976-5541
• DOI: 10.1109/JCN.2010.6388428

As a countermeasure to simple power attack, the unified point addition codes for the elliptic curve cryptosystem were introduced. However, some authors proposed a different kind of power attacks to the codes. This power attack uses the observation that some internal operations in the codes behave differently for addition and doubling. In this paper, we propose a new counter-measure against such an attack. The basic idea of the new countermeasure is that, if one of the input points of the codes is transformed to an equivalent point over the underlying finite field, then the code will behave in the same manner for addition and doubling. The new countermeasure is highly efficient in that it only requires 27(n−1)/3 extra ordinary integer subtractions (in average) for the whole n-bit scalar multiplication. The timing analysis of the proposed countermeasure is also presented to confirm its SPA resistance.