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Performance analysis of elliptic curve multiplication algorithms for elliptic curve cryptography

Özcan, Ayça Bahar
Elliptic curve cryptography (ECC) has been introduced as a public-key cryptosystem, which offers smaller key sizes than the other known public-key systems at equivalent security level. The key size advantage of ECC provides faster computations, less memory consumption, less processing power and efficient bandwidth usage. These properties make ECC attractive especially for the next generation public-key cryptosystems. The implementation of ECC involves so many arithmetic operations; one of them is the elliptic curve point multiplication operation, which has a great influence on the performance of ECC protocols. In this thesis work, we have studied on elliptic curve point multiplication methods which are proposed by many researchers. The software implementations of these methods are developed in C programming language on Pentium 4 at 3 GHz. We have used NIST-recommended elliptic curves over prime and binary fields, by using efficient finite field arithmetic. We have then applied our elliptic curve point multiplication implementations to Elliptic Curve Digital Signature Algorithm (ECDSA), and compared different methods. The timing results are presented and comparisons with recent studies have been done.