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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, ∼355🔥, 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, ∼355🔥, 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, ∼351🔥, 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, ∼350🔥, 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, ∼349🔥, 0💬

PKCS#8 and X.509 Key Encoding Classes
This section describes 2 JDK classes: PKCS8EncodedKeySpec representing the PKCS#8 encoding standard and the X.509 encoding standard.
2022-10-05, ∼348🔥, 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, ∼348🔥, 0💬

Introduction of RSA Algorithm
This chapter provides tutorial notes and example codes on RSA public key encryption algorithm. Topics include illustration of public key algorithm; proof of RSA encryption algorithm; security of public key; efficient way of calculating exponentiation and modulus; generating large prime numbers.
2022-10-13, ∼341🔥, 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, ∼341🔥, 0💬

Additive Notation of Abelian Group
This section describes the Additive notation of an Abelian Group. The addition sign, +, is used as the operator. Number 0 is used as the identity element.
2022-10-01, ∼338🔥, 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, ∼336🔥, 0💬

What Is a Certification Path?
This section describes what is a certificate path or certificate chain - An ordered list of certificates where the subject entity of one certificate is identical to the issuing entity of the next certificate.
2022-10-05, ∼335🔥, 0💬

Algebraic Solution for Point Doubling
This section provides an algebraic solution for calculating the addition operation of two points at the same location on an elliptic curve.
2022-10-01, ∼334🔥, 0💬

Terminology
List of terms used in this book.
2022-10-01, ∼334🔥, 0💬

References
List of reference materials used in this book.
2022-10-01, ∼334🔥, 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, ∼331🔥, 0💬

What Is Key Encoding?
This section describes private and public key encoding standards: PKCS#8 is used for encoding private keys and X.509 is used for encoding public keys.
2022-10-06, ∼330🔥, 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, ∼330🔥, 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, ∼329🔥, 1💬

💬 2025-02-21 bz: good for helping me

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, ∼328🔥, 1💬

💬 2023-02-28 adry: password

"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, ∼325🔥, 0💬

Elliptic Curve Operation Summary
This section provides a summary of elliptic curve operations and their properties discussed in this chapter.
2022-10-01, ∼324🔥, 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, ∼323🔥, 1💬

What is CBC (Cipher Block Chaining) Operation Mode?
This section describes what is CBC (Cipher Block Chaining) Operation Mode - each plaintext block is XORed with the ciphertext of the previous block before encryption.
2022-10-08, ∼320🔥, 0💬

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