Skip to main content

crypto

Introduction to Cryptography Concepts​

Cryptography is the backbone of modern security, enabling trust in digital systems. Below are foundational concepts every learner should understand, as they specifically relate to Terp Network:

Key-Pairs​

What: A key-pair consists of a public key (shared openly) and a private key (kept secret). These generally are either stored on hardware we own (phones, computer, cold-wallets), or on custodial hardware (companies server, "big-tech"). Keys are really the 'magicians secret' to cryptography.

The Magic of Asymmetric Cryptography​

This powerful tool enables secure communication and digital signatures. But what does that really mean?

  • Purpose: Allows two parties to communicate securely without ever sharing their secret key in the open.
  • How it Works:
    • 1. Encryption: Imagine you want to send a secret message to your friend Bob. You use Bob's public key (which he shares openly) to lock your message. Only Bob's private key (kept super secret) can unlock it!
    • 2. Signing: Like signing your name, but digitally! You use your private key to "sign" a message, and others use your public key to verify it's really from you.

Real-Life Example: Alice and Bob's Secret Message​

  1. Alice writes a message and locks it with Bob's public key.
  2. She sends the locked message to Bob.
  3. Bob uses his private key to unlock and read the message.

Elliptic Curves​

In cryptography, elliptic curves are defined by complex equations like:

$$ y^2 = x^3 + ax + b \quad \text{(mod } p\text{)} $$

Don't worry too much about the math; focus on what they do for us!

The Superpower of Elliptic Curves​

  • Provide Efficient Security: Through the Elliptic Curve Discrete Logarithm Problem (ECDLP), which is really hard for computers to reverse, even with massive power.
  • How Keys are Made:
    1. **Private Key**: Just a number.
    2. **Public Key**: Generated by "walking" the private key along the elliptic curve (via **scalar multiplication**).

Computationaly Hard​

Key-pairs and elliptic curves enable secure identities and transactions, without requiring custodial ownership of the private keys.​

Hashes​

Hash functions are like super-powerful, one-way mixers. You put in any input (text, image, etc.), and out comes a fixed-size, unique string (like a fingerprint).

The Awesome Properties of Hashes​

  1. Deterministic: Same input always gives the same output.
  2. One-way: Good luck reversing the output to find the original input!
  3. Collision-resistant: Finding two different inputs with the same output hash is extremely hard.

Hash in Action: "Hello" Transformed​

  • Input: "Hello"
  • SHA-256 Hash Output: 2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824

Why We Love Hashes​

  • Secure Password Storage: Stores hashes of passwords, not the passwords themselves.
  • Data Integrity Checks: Verify data hasn’t been tampered with by comparing hashes.
  • Blockchain Block Headers: Used to uniquely identify blocks in chains like Bitcoin.

Merkle Trees​

Imagine a family tree, but instead of names, it's filled with hashes! Merkle Trees are hierarchical structures that helps us verify data quickly.

Visual Example​

                  Root (Hash(A+B))
                     /          \
             Hash(A)       Hash(B+C)
             /   \             /   \
         Data A  Data B    Data C  Data D

The Trees Structure​

  • Leaves: The bottom layer, where each "leaf" is a hash of an individual piece of data (e.g., a message).
  • Branches: Each parent node is a hash of its two children, all the way up...
  • Root: The topmost hash, representing the entire dataset. This is the "summary" of your whole tree!

The Superpower of Merkle Trees​

  • Efficient Verification: Check a subset of data without downloading the entire dataset. How? By only verifying the path from the leaf to the root!
  • Real-World Use: Blockchains use Merkle Trees to summarize all transactions in a block, making verification faster and more efficient.

Blockchains​

A decentralized book (ledger) where once something is written, it can't be erased. It's a chain of "blocks," each linked via cryptographic hashes.

Blockchain Structure Decoded​

  • Blocks:
    • Transactions (e.g., sending cryptocurrency).
    • Timestamp.
    • Previous Block’s Hash (the "chain" link).
  • Consensus Mechanisms:
    • Proof of Work (PoW) - Bitcoin's energy-intensive puzzle-solving.
    • Proof of Stake (PoS) - Ethereum’s stake-based validation.

Key Properties of Blockchains​

  1. Immutability: Changing a block would require altering all subsequent blocks, making tampering practically impossible.
  2. Transparency: The entire ledger is open for all participants to audit.

Why These Concepts Matter Together​

  • Hashes and Merkle trees ensure data integrity and efficiency.
  • Blockchains combine these tools to create trustless, decentralized systems.

This foundation allows anyone to understand how modern crypto systems secure value, data, and trust in the digital world.

Let me know if you'd like deeper dives into any of these topics!