Elliptic Curves over Finite Fields
نویسنده
چکیده
In this chapter, we study elliptic curves defined over finite fields. Our discussion will include the Weil conjectures for elliptic curves, criteria for supersingularity and a description of the possible groups arising as E(Fq). We shall use basic algebraic geometry of elliptic curves. Specifically, we shall need the notion and properties of isogenies of elliptic curves and of the Weil pairing. In later chapters, the theories of elliptic curves over C, R and algebraic number fields will be studied. In contrast to this chapter, the basic tools to be used in the later chapters will be elliptic functions and algebraic number theory. The standard reference is Silverman’s book [S].
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