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Guide to Elliptic Curve Cryptography Darrel Hankerson, Alfred Menezes, Scott Vanstone Springer 2004 Introduction and Overview Cryptography basics Public-key cryptography RSA systems Discrete logarithm systems Elliptic curve systems Finite field arithmetic Prime field arithmetic Binary field arithmetic Optimal extension field arithmetic Elliptic curve arithmetic Elliptic curves Point representation and the group law Point multiplication Koblitz curves Curves with efficiently computable endomorphisms Point multiplication using halving Point multiplication costs Cryptographic protocols The elliptic curve discrete logarithm problem Domain parameters Key pairs Signature schemes ECDSA EC-KCDSA Public-key encryption ECIES PSEC Key extablishment Station-to-station ECMQV Implementation issues Software implementation Hardware implementation Secure implementation Simple parameters ECC Standards Software tools