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Negation Operation on an Elliptic Curve
This section describes the Negation operation on an elliptic curve. If the resulting point the negation operation of an given point P is R, then P + R is the infinity point. 2022-10-01, ∼659🔥, 0💬

What Is Trapdoor Function
This section describes what is Trapdoor Function - An operation that is much easier to perform than its reverse operation. 2022-10-01, ∼659🔥, 0💬

Modular Arithmetic Reduction on Rational Numbers
This section describes how to perform Modular Arithmetic Reduction on Rational Numbers, which is equivalent to perform modular multiplication of the numerator and the multiplicative inverse of the denominator. 2022-10-01, ∼658🔥, 0💬

"keytool -groupname ..." - Select Curve Name
This section provides a tutorial example on how to using 'keytool -groupname ...' option to select a different elliptic curve when generating EC private-public key pairs. 2022-10-01, ∼646🔥, 0💬

Subtraction Operation on an Elliptic Curve
This section describes the Subtraction operation on an elliptic curve. If the resulting point of the subtraction operation of point Q from P, then P - R = P + (-Q).. 2022-10-01, ∼630🔥, 0💬

Same Point Addition on an Elliptic Curve
This section describes how to perform the addition operation of a point P to the same point P on an elliptic curve. In this case, we will draw a straight line that passes P and tangent to the curve to find -R. 2022-10-01, ∼595🔥, 0💬

EC Key File with Curve Name
This section provides a tutorial example on the EC private key file with curve name only. Actuall domain parameters are not stored in the key file. 2022-10-01, ∼567🔥, 0💬

Is ECDH Key Exchange Secure
This section discusses the question of: how secure is the ECDH (Elliptic Curve Diffie-Hellman) key exchange protocol? 2022-10-01, ∼564🔥, 0💬

Find Subgroup with Point Addition
This section provides a tutorial example on how to find the subgroup of a given point on an elliptic curve using a loop of point additions with tinyec Python library. 2022-10-01, ∼562🔥, 0💬

Create EC Public Key File
This section provides a tutorial example on how to extract the public key out of an EC private key file with the 'openssl ec -pubout' command. 2022-10-01, ∼551🔥, 0💬

Commutativity 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, ∼546🔥, 0💬

Abelian Group and Elliptic Curves
This chapter provides an introduction to Abelian Group, which can be expressed in the multiplicative notation or the additive notation. An Abelian Group and be defined on an elliptic curve using the 'rule of chord' operation. 2022-10-01, ∼525🔥, 0💬

Finite Fields
This chapter provides an introduction to Finite Fields. Topics covered include definition of finite fields; examples of finite fields: prime fields GF(p), binary fields GF(2^n) and polynomial fields GF(p^n); field order as the number of elements; field characteristic p is the least positive integer ... 2022-10-01, ∼512🔥, 0💬

"sect283r1" - For 256-Bit ECC Keys
This section describes 'sect283r1' elliptic curve domain parameters for generating 256-Bit ECC Keys as specified by secg.org. 2022-10-01, ∼509🔥, 0💬

Addition Operation on an Elliptic Curve
This section describes the addition operation on an elliptic curve geometrically. The addition of points P and Q on an elliptic curve is a point R on the curve, which is the symmetrical point of -R, which is the third intersection of the curve and the straight line passing through P and Q. 2022-10-01, ∼508🔥, 0💬

Algebraic Introduction to Elliptic Curves
This chapter provides an algebraic introduction of addition operations on elliptic curves. Algebraic solutions are provided to calculate addition operations by dividing the problem into 4 cases: two symmetric points, one infinity point, two identical points, and two distinct points. 2022-10-01, ∼503🔥, 0💬

Examples of Discrete Logarithm Problem (DLP)
This section describes the Discrete Logarithm Problem (DLP) in several Abelian Group examples, including elliptic curve groups. 2022-10-01, ∼477🔥, 0💬

Elliptic Curves with Singularities
This section describes elliptic curves with singularities where curves are not smooth. 2022-10-01, ∼467🔥, 0💬

Discrete Logarithm Problem (DLP)
This chapter provides an introduction to the Discrete Logarithm Problem (DLP), which is the reverse operation of the exponentiation operation in Abelian Groups in multiplicative notation, or the scalar multiplication in additive notation. The DLP in many Abelian Groups is easy to solve. But the DLP ... 2022-10-01, ∼459🔥, 0💬

DLP and Trapdoor Function
This section exams the difficulty level of the Discrete Logarithm Problem (DLP) in several Abelian Group examples to see if them can be used to build trapdoor functions. 2022-10-01, ∼457🔥, 0💬

Elliptic Curve Subgroups
This chapter provides notes on subgroup generation from reduced elliptic curve groups, Ep(a,b). Python programs are provided to perform point addition, scalar multiplication, and subgroup generation. 2022-10-01, ∼444🔥, 0💬

Modular Addition of 10 - Abelian Group
This section provides an Abelian Group using the modular arithmetic addition of 10 (integer addition operation followed by a modular reduction of 10). 2022-10-01, ∼442🔥, 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, ∼431🔥, 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, ∼430🔥, 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