Tutorial Books:
Order of Subgroup and Lagrange Theorem
This section describes Lagrange Theorem which states that the order of any subgroup in an finite Abelian group divides the order of the parent group. 2022-10-01, 237🔥, 0💬
Algebraic Description of Elliptic Curve Addition
This section provides an algebraic description of the problem of calculating the addition operation defined on an elliptic curve. 2022-10-01, 226🔥, 0💬
What Are Standard Elliptic Curves
This section provides a list of standard elliptic curves selected and recommended by different organizations to generate secure EC private-pubic key pairs. 2022-10-01, 226🔥, 0💬
What Is Abelian Group
This section describes Abelian Group, which a set of elements with a binary operation satisfing 5 conditions. 2022-10-01, 220🔥, 0💬
Additive Notation of Abelian Group
This section describes the Additive notation of an Abelian Group. The addition sign, +, is used as the operator. Number 0 is used as the identity element. 2022-10-01, 216🔥, 0💬
Algebraic Solution for Point Doubling
This section provides an algebraic solution for calculating the addition operation of two points at the same location on an elliptic curve. 2022-10-01, 211🔥, 0💬
Reduced Elliptic Curve Group - E97(-1,1)
This section provides an example of a reduced Elliptic Curve group E97(-1,1). Some example points on the curve are is also provided. 2022-10-01, 201🔥, 0💬
Prove of Elliptic Curve Addition Operation
This section describes how to prove that the addition operation on an elliptic curve can be successfully performed geometrically. 2022-10-01, 197🔥, 0💬
Python Program for Reduced Elliptic Curves
This section provides a Python program that finds all points on a reduced elliptic curve group, Ep(a,b). 2022-10-01, 197🔥, 0💬
EC Curves Supported by Java
This section provides is a list of named curves that are supported or not supported by 'keytool' and Java default library. 2022-10-01, 197🔥, 0💬
Reduced Elliptic Curve Group - E127(-1,3)
This section provides an example of a reduced Elliptic Curve group E127(-1,3). An example of addition operation is also provided. 2022-10-01, 195🔥, 0💬
Elliptic Curves in Integer Space
This section describes the fact that elliptic equations in 2-dimensional integer space can not be used to construct Abelian groups. 2022-10-01, 194🔥, 0💬
Elliptic Curve Operation Summary
This section provides a summary of elliptic curve operations and their properties discussed in this chapter. 2022-10-01, 192🔥, 0💬
Terminology
List of terms used in this book. 2022-10-01, 192🔥, 0💬
Converting Elliptic Curve Groups
This section describes steps on how to convert real number elliptic curve groups to cyclic subgroups of integer elliptic curve groups. 2022-10-01, 182🔥, 0💬
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