Abstract
This chapter covers the essentials of elliptic curves as used in cryptography. The first section of the chapter gives the basics concepts of elliptic curves: the main defining equations for the curves of interest and an explanation of the arithmetic operations of “addition” and “multiplication” in the context of elliptic curves. We shall follow standard practice and first define elliptic curves over the field of real numbers, with geometric and algebraic interpretations of the arithmetic operations in relation to points on a curve.
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