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Is EC Private Key Secure
This section discusses the question of: how secure is the EC (Elliptic Curve) key pair? Or how hard is it someone to figure out the private key from a given EC public key? 2025-09-06, ∼431🔥, 1💬

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, ∼428🔥, 0💬

Elliptic Curves with Singularities
This section describes elliptic curves with singularities where curves are not smooth. 2022-10-01, ∼426🔥, 0💬

AES, or Rijndael, Encryption Algorithm
A quick description of the AES (Advanced Encryption Standard) encryption algorithm is provided. This description only covers AES encryption for a single block of 128-bit plaintext with a 128-bit cipher key. 2022-10-04, ∼423🔥, 0💬

mcrypt Library for PHP
This section describes the mcrypt library - encryption extension for PHP. mcrypt supports DES and many other encryption algorithms. 2019-12-19, ∼419🔥, 1💬

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, ∼418🔥, 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, ∼412🔥, 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, ∼396🔥, 0💬

Archived Tutorials
This chapter contains some outdated tutorial notes and example codes from previous versions of this book. 2022-10-06, ∼392🔥, 0💬

OpenSSL Validating Certificate Path
This chapter provides tutorial notes and example codes on certificate path validation with OpenSSL. Topics include introduction of certificate path; certificate path validation rules; generating and validating a certificate path. 2022-10-04, ∼378🔥, 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, ∼376🔥, 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, ∼373🔥, 0💬

"keytool" Generating Maria's Private Key
This section provides a tutorial example on how to use 'keytool' to generate a pair of private key and public key. 2019-05-08, ∼373🔥, 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, ∼369🔥, 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, ∼369🔥, 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, ∼368🔥, 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, ∼368🔥, 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, ∼365🔥, 0💬

Niels Henrik Abel and Abelian Group
Abelian Groups are named after early 19th century mathematician Niels Henrik Abel. 2022-10-01, ∼364🔥, 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, ∼362🔥, 1💬

Viewing Certificate Details
This section provides a tutorial example on how to view certificate details when visiting an 'https' Web site in Firefox. 2022-10-04, ∼358🔥, 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, ∼358🔥, 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, ∼356🔥, 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