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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, ∼565🔥, 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, ∼531🔥, 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, ∼517🔥, 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, ∼502🔥, 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, ∼495🔥, 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, ∼491🔥, 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, ∼490🔥, 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, ∼473🔥, 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, ∼470🔥, 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, ∼457🔥, 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, ∼450🔥, 0💬

Elliptic Curves with Singularities
This section describes elliptic curves with singularities where curves are not smooth. 2022-10-01, ∼425🔥, 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, ∼424🔥, 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, ∼415🔥, 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, ∼410🔥, 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, ∼394🔥, 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, ∼376🔥, 0💬

Reduced Elliptic Curve Groups
This chapter provides notes and tutorials on reduced elliptic curve groups. Topics include elliptic curve on in integer space; elliptic curves and the addition operation reduced by modular arithmetic; elliptic curve groups and examples. 2022-10-01, ∼375🔥, 0💬

What Is Order of Element
This section describes the order of a given element in a finite Abelian Group, which is defined as the least positive integer n, such that the scalar multiplication of n and P is 0, where 0 is the identity element. 2022-10-01, ∼371🔥, 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, ∼366🔥, 0💬

What Is Subgroup Generator in Abelian Group
This section describes subgroup generator in a Abelian Group. A subgroup generator is an element in an Abelian Group that can be used to generator a subgroup using a series of scalar multiplication operations. 2022-10-01, ∼366🔥, 0💬

"Legacy SunEC curve disabled" Error
This section provides a tutorial example on how to resolve the 'Legacy SunEC curve disabled' error and get short and insecure EC private-public key pairs. 2022-10-01, ∼366🔥, 0💬

What Is Cyclic Group
This section describes Cyclic Group, which is a finite Abelian group that can be generated by a single element using the scalar multiplication operation in additive notation (or exponentiation operation in multiplicative notation). 2022-10-01, ∼364🔥, 0💬

Niels Henrik Abel and Abelian Group
Abelian Groups are named after early 19th century mathematician Niels Henrik Abel. 2022-10-01, ∼361🔥, 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