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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, ∼412🔥, 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, ∼411🔥, 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, ∼410🔥, 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, ∼410🔥, 1💬

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, ∼408🔥, 0💬

"DumpKey.java" Dumping Private Keys Out of "keystore"
This section provides a tutorial example on how to dump private key and public key pair output of a 'PrivateKeyEntry' in a 'keystore' file using a Java program, DumpKey.java.
2022-10-05, ∼407🔥, 0💬

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, ∼405🔥, 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, ∼404🔥, 0💬

Java Default Implementation of DSA
This chapter provides tutorial notes and example codes on the Java default implementation of DSA (Digital Signature Algorithm). Generating DSA key pair in Java; Examples of public key and private key pairs; Checking DSA key parameter; Generating DSA digital signature in Java using SHA1withDSA; Verif...
2022-10-13, ∼397🔥, 0💬

Archived: Visiting an "https" Web Site with Firefox 18
This section describes how Firefox 18 shows a lock icon when you visit an 'https' Web site to provide you more security related information.
2022-10-11, ∼396🔥, 0💬

OFB (Output FeedBack) as a Stream Cipher
This section describes how DES OFB (Output FeedBack) operation mode can be modified as a 1-bit stream cipher or a 1-byte stream cipher.
2022-10-04, ∼395🔥, 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, ∼393🔥, 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, ∼392🔥, 0💬

Elliptic Curve Operation Summary
This section provides a summary of elliptic curve operations and their properties discussed in this chapter.
2022-10-01, ∼388🔥, 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, ∼387🔥, 0💬

Finite Elliptic Curve Group, Eq(a,b), q = p^n
This section describes finite elliptic curve groups constructed with modular arithmetic reduction of prime power numbers, p^n.
2022-10-01, ∼386🔥, 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, ∼384🔥, 0💬

Terminology
List of terms used in this book.
2022-10-01, ∼384🔥, 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, ∼383🔥, 0💬

Modular Multiplication of 10 - Not Abelian Group
This section demonstrates that the modular arithmetic multiplication of 10 (integer multiplication operation followed by a modular reduction of 10) can not define an Abelian Group.
2022-10-01, ∼381🔥, 0💬

OpenSSL Generating and Managing RSA Keys
This chapter provides tutorial notes and example codes on managing RSA keys with OpenSSL. Topics include generating new RSA keys; viewing existing RSA keys; encrypting RSA keys with DES algorithm to protect them with passwords.
2025-02-21, ∼379🔥, 1💬

💬 2025-02-21 bz: good for helping me

Finding Large Prime Numbers
This section describes different ways to generate large prime numbers to be used to generate public key and private key. Today most RSA tools are using probable prime numbers.
2022-10-05, ∼379🔥, 0💬

"openssl dsa" Viewing Private and Public Key Pair
This section provides a tutorial example on how to view a private and public key pair stored in PEM format using the 'openssl dsa' command. The key pair was originally generated by the 'keytool -genkeypair' command.
2022-10-04, ∼379🔥, 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, ∼379🔥, 0💬

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