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Elliptic Curves with Singularities
This section describes elliptic curves with singularities where curves are not smooth. 2022-10-01, 258🔥, 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, 249🔥, 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, 247🔥, 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, 245🔥, 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, 244🔥, 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, 244🔥, 0💬

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, 244🔥, 0💬

Niels Henrik Abel and Abelian Group
Abelian Groups are named after early 19th century mathematician Niels Henrik Abel. 2022-10-01, 242🔥, 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, 242🔥, 0💬

References
List of reference materials used in this book. 2022-10-01, 240🔥, 0💬

RsaKeyEncryption.java for RSA Encryption Operation
This section provides a tutorial example on how to implement RSA encryption operation using the java.math.BigInteger class. The important part of the implementation is to determine the cleartext block size, ciphertext block size, and the padding of the last block. 2022-12-15, 239🔥, 1💬

"keytool -genkeypair" Generating PrivateKeyEntry
This section provides a tutorial example on how to generate a private and public key pair using the 'keytool -genkeypair' command. It stores the key pair in a 'PrivateKeyEntry' in a 'keystore' file. 2022-10-04, 239🔥, 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, 237🔥, 0💬

"keytool -exportcert" Exporting PrivateKeyEntry
This section provides a tutorial example on how to export a 'PrivateKeyEntry' stored in a 'keystore' file using the 'keytool -exportcert' command. 2022-10-04, 236🔥, 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, 227🔥, 0💬

Summary - Migrating "keystore" Keys to "OpenSSL"
This section describes high level steps on how to migrate a private key generated in a JKS (Java KeyStore) file to an 'OpenSSL' key file. The key step is to convert a JKS file into a PKCS#12 file with 'keytool'. 2016-04-09, 227🔥, 1💬

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 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, 222🔥, 0💬

mcrypt Encryption Functions
This section describes mcrypt encryption functions and 4 DES ciphers (operation modes) - 8-byte ECB, 8-byte CBC, 1-byte CFB, and 1-byte OFB ciphers. 2023-02-28, 220🔥, 1💬

💬 2023-02-28 adry: password

AES Key Schedule Algorithm
A quick description of the AES key schedule algorithm is provided. AES key schedule expands the given cipher key into 11 round keys. It uses round constants, S-box lookups and byte rotations. 2022-10-04, 220🔥, 0💬

Importing CA Certificate into Firefox
This section provides a tutorial example on how to import a CA certificate into Firefox in the 'Authorities' category. 2022-10-04, 220🔥, 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💬

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, 220🔥, 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 Reference REST SOAP Sorting Swing TV Series UML Unicode VBScript Web Web-Services Windows WSDL XML XMLPad XSD XSL-FO