Finite Field Definition: a "finite field" is defined as a finite set of numbers and two operations (addition) and (multiplication) that satisfy the following: 1. If a and b are in the set, a + b and a * b are in the set. We call this property closed. 2. 0 exists and has the property a + 0 = a. We call this additive identity. 3. 1 exists and has the property a * 1 = a. We call this multiplicative identity. 4. If a is in the set, -a is in the set, which is defined as the value that makes a + (-a) = 0. This is what we call the additive inverse. 5. If a is in the set and is not 0, a^-1 is in the set, which is defined as the value that makes a * a^-1 = 1. This is what we call the multiplicative inverse. We have a set of numbers that finite. The set is finite so we can designate a number p, which is how big the set is. This is what we call the order of the set. Fp = { 0, 1, 2, .... p-1 } Field of p Modulo Arithmetic 7 % 3 = 1, 1747 % 241 = 60 a, b ∈ F 19 ∈...
Digital signature prove knowledge of a secret without revealing it. Account address are derived directly from private keys. Public key cryptography also known as asymmetric cryptography. Public key can be derived from private keys. A digital signature is code that is produced with private key and the transaction details (the message). A private key is a number between 1 and 2^256 The public key is on a point on an elliptic curve, with an X and Y value. PubK = PrivKey * G a constant generator point Ethereum cryptographic Hash function: Keccak-256 (not the finalized SHA-3 different output) Addresses are hex numbers dervied from the last 20 bytes of the public key. Inter exchange client address protocol (ICAP) checksum prevent wrongly input address. Wallet: serves as the primary user interface for the user to access money, managing keys, address, creating and signing transaction. But at it's core it's a data structure that acts as a container to store the private ke...