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# System prepended metadata

title: ' CRYPTOGRAPHY MEANING AND MATHEMATICAL CALCULATIONS'

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# CRYPTOGRAPHY

Cryptography is the science of protecting information using codes so that only the right people can read it. In blockchain, it helps keep transactions secure, private, and tamper proof



# Types of Cryptography



There are three main types of cryptography:

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## 1. **Symmetric Key Cryptography**

### What it means:

One **single key** is used to **encrypt** and **decrypt** the data

### How it works:

* You use a secret key to lock (encrypt) a message
* You use the same key to unlock (decrypt) it

### Use case:

Used in private systems where both sender and receiver can safely share the secret key (e.g., AES encryption)


* If someone steals the key they can access everything

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## 2. **Asymmetric Key Cryptography** (Public-Key Cryptography)

### What it means:

Uses two keys**: a public key (shared) and a **private key** (kept secret)

### How it works:

* The **public key** is used to encrypt data
* Only the matching private key can decrypt it
* Also used for digital signatures

### Use case in blockchain:

Used in wallets:

* Your public key is your wallet address.
* Your private key proves that you own it and can send funds.

### Advantage:

More secure for communication no need to share your private key.

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## 3. **Hash Functions**

### What it means:

A hash function turns any input (text, number, file) into a fixed-length string of characters

### How it works:

* You input: data  it gives a unique output (called a hash)
* It's one way: you can’t reverse it back to the original input

### Use case in blockchain:

* Used in block creation mining (PoW) and data integrity
* Example: Bitcoin uses SHA-256 hashing

### Key Feature:

Even a small change in input gives a completely different hash

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# Keys and Addresses in Blockchain

In blockchain, keys and addresses are how users own, access, and transfer their crypto or data securely

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## 1. **Private Key**

* A secret code known only to you
* It's like your password or signature
* Used to sign transactions and prove ownership of crypto

If someone gets your private key, they can steal your crypto

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## 2. **Public Key**

* Generated from the private key
* Can be shared with anyone
* Used to create your wallet address and verify your signature

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## 3. **Wallet Address**

* A short version of your public key
* It’s like your account number on the blockchain
* People can send you crypto using your wallet address

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| Term        | Like in Real Life    |
| - | - |
| Private Key | Your password or PIN |
| Public Key  | Your identity        |
| Address     | Your account number  |

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### Example:

* Private key: `5Jv3kYfZ...` (never share this)
* Public key: `041a3b...`
* Address: `0xAb12Cd34Ef...` (share this to receive crypto)

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### Summary:

* **Private key** = proves ownership, stay secret
* **Public key** = created from private key
* **Address** = short version to receive crypto
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# What is VRS in Ethereum?
* When someone sends a transaction in Ethereum, it is digitally signed using their private key
* This signature is broken into three parts: V, R, and S. Together, they prove the transaction is authentic and was sent by the real owner.

## 1. R (Signature Component)
* A 256-bit value from the signature.
* It's part of the output from the ECDSA algorithm (the signing algorithm Ethereum uses).
* It helps identify the curve point used in the signature.

## 2. S (Signature Component)
* Also a 256-bit value.
* It works with R to prove the signature is valid.
* Helps ensure the transaction wasn’t tampered with.

## 3. V (Recovery ID / Chain ID Info)
* Originally used to help recover the public key
* Value is usually 27 or 28 (in older Ethereum) or chain-dependent in newer versions (EIP-155)
* Now also helps protect against replay attacks (when a signed tx is reused on another chain)


In Ethereum, the recipient of a payment is identified by an address, just like a bank account.
This address can belong to a user (EOA) created from a public key or to a smart contract, which doesn't have a private key.
