@inbook{4d46ec9fa6c24cf4800bf5ab2948ef8b,

title = "Arithmetic of special curves",

abstract = "In this chapter we present the arithmetic for special choices of curves that offer advantages in the computation of scalar multiples. The first example is given by Koblitz curves. There the improvement results from a clever use of the Frobenius endomorphism. The use of endomorphisms on special curves over prime fields is the topic of the following section. An approach similar to Koblitz curves but for large characteristic is the key to trace zero varieties, which we present in the last section.",

keywords = "Koblitz curves, scalar multiples, endomorphism, special curves, trace zero varieties",

author = "Christophe Doche and Tanja Lange",

year = "2006",

language = "English",

isbn = "9781584885184",

series = "Discrete mathematics and its applications",

publisher = "CRC Press, Taylor & Francis Group",

pages = "355--387",

booktitle = "Handbook of elliptic and hyperelliptic curve cryptography",

address = "United States",

}