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A Fast Inversion for Low-Complexity System over GF(2 $^{m}$)  

Kim, So-Sun (Center for Information and Security Technologies (CIST), Korea Univ.)
Chang, Nam-Su (Center for Information and Security Technologies (CIST), Korea Univ.)
Kim, Chang-Han (Dept. of Information and Security, Semyumg Univ.)
Publication Information
Journal of the Institute of Electronics Engineers of Korea SD / v.42, no.9, 2005 , pp. 51-60 More about this Journal
Abstract
The design of efficient cryptosystems is mainly appointed by the efficiency of the underlying finite field arithmetic. Especially, among the basic arithmetic over finite field, the rnultiplicative inversion is the most time consuming operation. In this paper, a fast inversion algerian in finite field $GF(2^m)$ with the standard basis representation is proposed. It is based on the Extended binary gcd algorithm (EBGA). The proposed algorithm executes about $18.8\%\;or\;45.9\%$ less iterations than EBGA or Montgomery inverse algorithm (MIA), respectively. In practical applications where the dimension of the field is large or may vary, systolic array sDucture becomes area-complexity and time-complexity costly or even impractical in previous algorithms. It is not suitable for low-weight and low-power systems, i.e., smartcard, the mobile phone. In this paper, we propose a new hardware architecture to apply an area-efficient and a synchronized inverter on low-complexity systems. It requires the number of addition and reduction operation less than previous architectures for computing the inverses in $GF(2^m)$ furthermore, the proposed inversion is applied over either prime or binary extension fields, more specially $GF(2^m)$ and GF(P) .
Keywords
Finite field arithmetic; Inversion; Extended binary red algorithm; Cryptography;
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