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Reduced Elliptic Curve Group - E23(1,4)
This section provides an example of a reduced Elliptic Curve group E23(1,4). A detailed calculation of reduced point doubling operation on (0,2) is also provided. 2022-10-01, ∼328🔥, 0💬

Niels Henrik Abel and Abelian Group
Abelian Groups are named after early 19th century mathematician Niels Henrik Abel. 2022-10-01, ∼326🔥, 0💬

Scalar Multiplication on Elliptic Curve as Trapdoor Function
This section confirms that Scalar Multiplication on Elliptic Curve is a good Trapdoor Function by the comparing difficulty level against its reverse operation, which is the DLP. 2022-10-01, ∼324🔥, 0💬

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, ∼324🔥, 0💬

What Is Discrete Logarithm Problem (DLP)
This section describes what is Discrete Logarithm Problem (DLP), which is the reverse operation of an exponentiation (or scalar multiplication) operation in an Abelian group. 2022-10-01, ∼323🔥, 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, ∼321🔥, 0💬

Associativity of Elliptic Curve Operations
This section describes the associativity of the addition operation on an elliptic curve. P + (Q + S) = (P + Q) + S is true. 2022-10-01, ∼319🔥, 0💬

Scalar Multiplication or Exponentiation
This section describes what is Scalar Multiplication or Exponentiation in Abelian Groups. They are used represent the process of performing Abelian Group operations consecutively n times with the same element. 2022-10-01, ∼310🔥, 0💬

References
List of reference materials used in this book. 2022-10-01, ∼309🔥, 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, ∼306🔥, 0💬

Set Subgroup Order to Higher Value
This section provides a tutorial example on how to set the subgroup order a value greater than the order of the entire group, like 2 times of the modulo, to ensure correct result of scalar multiplications. 2022-10-01, ∼306🔥, 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, ∼304🔥, 0💬

Terminology
List of terms used in this book. 2022-10-01, ∼302🔥, 0💬

What Is Subgroup in Abelian Group
This section describes Subgroups in a Abelian Group. A subgroup in a Abelian Group is a subset of the Abelian Group that itself is an Abelian Group. The subgroup and its parent group are using the same operation. 2022-10-01, ∼298🔥, 0💬

Modular Multiplication of 11 - Abelian Group
This section provides an Abelian Group using the modular arithmetic multiplication of 11 (integer multiplication operation followed by a modular reduction of 11). 2022-10-01, ∼293🔥, 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, ∼291🔥, 0💬

Elliptic Curve Operation Summary
This section provides a summary of elliptic curve operations and their properties discussed in this chapter. 2022-10-01, ∼289🔥, 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, ∼288🔥, 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, ∼279🔥, 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, ∼274🔥, 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, ∼271🔥, 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, ∼270🔥, 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, ∼269🔥, 0💬

Elliptic Curves Reduced by Modular Arithmetic
This section describes elliptic curves reduced by modular arithmetic of prime numbers. We can find lots of more integer points on those reduced elliptic curves. 2022-10-01, ∼265🔥, 0💬

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Android ASP Astrology Big5 Bitcoin Blowfish Built-in C# Calendar CD-DVD Cheminformatics Chinese Cryptography DES Email Encoding Ethereum Flash GB2312 General H Herong History HTML Java JavaScript JDBC JSP JVM Linux Molecule Movie Music MySQL Neural Network Perl PHP Physics PKI Publication Python REST SOAP Sorting Swing TV Series UML Unicode VBScript Web Web-Services Windows WSDL XML XMLPad XSD XSL-FO