(New) Understand How Bitcoin Works - A Visual Tech Guide

This lecture introduces the Paired-Pattern-Pitfall:

• Every input letter is directly paired one-to-one to an output (an encrypted letter).

• Both inputs and outputs are inextricably related to the patterns of human language.

Now enter the Feistel Function! This was the first modern electric computer application, and it solves the Paired-Pattern-Pitfall. The Feistel Function is at the heart of all modern cryptographic developments and the field of cryptography as a whole.

Hexadecimal or "Hex" representation makes long binary strings of 0s and 1s much easier to read and work with.

An important notion in cryptography is the term "Computationally infeasible." The lecture includes a binomial random walk (coin flip tree) to highlight the immense magnitude of potential outputs with a large number of coin flips in a row. Random numbers are not predictable, and they have no pattern.

DES represents the new era of modern cryptography. It is similar to the Enigma machine in that it can both encrypt and decrypt.

DES applied the "Feistel Process" to encrypt messages. DES is a major milestone in modern cryptography. It was not only the first modern cryptographic protocol at scale, it also paved the way for other critical tools: Hash Functions and Public Key Technology.

A simple and useful starting analogy for hash functions. A series of six coin flips has 64 potential and unique outputs (HHHHHH, HHHHHT, etc.) If you conduct 64 trials of six-coin-flip sessions, you would be close to "landing" on each unique output. This is like “spreading the peanut butter” evenly across all possible outputs.

The insides of a hash function. We draw in material from the prior lessons on the Feistel Function and the DES encryption and decryption protocol. Hash Functions start with data of any size, and produce a fixed-size output. (SHA 256 for example, produces a 256 bit output.)

Here we review a key Feistel concept that every input bit is tied to every output bit (and vice versa.) We show the avalanche effect in action with an example using a website that processes hash outputs.

How the three properties within hash functions work together to produce an unforgeable value; a digital fingerprint.

You can detect -changes- in a hash output. No change? No Problem. Data has not been altered. What happens if your hash value does not match the expected value.... Your data has been tampered!

Historical context, locations where used in Bitcoin, and the mechanics of how this function operates. Provides a 160 bit unique ID for data/documents.

One of the world's most popular hash functions. A look at how it works and where it's used in Bitcoin. Provides a 256 bit unique ID for data/documents.

Historically, to communicate securely, Alice had to create a secret key, travel to Bob with this key under her protection, and physically hand it to Bob. (She could use a trusted courier, but the workload and expense remained.)  As the internet began its scale to millions of users, physical exchange was not feasible.

One-way functions use select math combined with very large numbers to create public values (public keys) that are derived from secret inputs (secret keys). It is impossible to reverse-engineer the input (secret) from the output (public).

There are two One-way functions: the Integer Factorization Problem, and the Discrete Log Problem.

Secure shared key exchange comes from the combination of one-way functions, creative protocol designs, and a few (super) interesting math properties of prime numbers and modular arithmetic.

The rest of this Section covers the RSA Key Exchange which is rooted in the Integer Factorization Problem.

Basics of addition and subtraction over modulo "12 hour clock"

A beginner introduction to Multiplicative groups, multiplicative groups with Prime Numbers, Coprime numbers, Exponents, and a few more details regarding prime numbers. Math rocks!

• The inverse of addition is subtraction

• The inverse of multiplication is division

This lecture covers the inverse process within a modulo group. Given one number in the group, you can determine it's inverse.

Like the rest of mathematics and numbers .... modulo groups and different modulo groups are abound with patterns.

A look at the clever design to overlap prime numbers, special math (modulo), and the one-way function of the Integer Factorization Problem. The result: a digital Key Exchange solution!

Alice and Bob establish a shared secret key - instantly, digitally, and using only public channels. This is the first solution to the Key Distribution Problem!

Outputs from the DLP are non-linear, scattered, and essentially random. Similar to the Integer Factorization Problem, the DLP leverages numbers so large that it is impossible to reverse-engineer the input (secret key) if you are given the output (public key).

DH protocol is relatively simple compared to RSA. Alice and Bob again establish a shared secret key in an instant, digitally, and by only using public forums to exchange their public keys.

Given a prime number p, and the Discrete Log Problem, there exist special values called base generators (variable b, or sometimes labeled as g) that produce an output group that includes every number from 1 to p-1 and is seemingly random.

The DH Key Exchange seems too easy to be true. The power of this protocol stems from the base generator, which can relate any number - no matter how large - back to a number in the output group (which is from 1 to p-1).

Elliptical Curves are (fortunately) very similar to DH and the DLP.

EC 101: Base generator (a point on the curve), Elliptical curves plus a prime group, Tangent and Chord point addition, and the Point of Infinity.

The easiest part! All curves are predefined and publicly available. Bitcoin uses the secp256k1 Elliptical Curve standard.

The math within Elliptical Curves might be fancy and tricky, but it provides huge gains in compute efficiencies, and affords us much smaller Public Key bit-sizes.

Alice and Bob establish a shared secret key in an instant, digitally, and by only using public forums to exchange their public keys.

Hash results and public keys are not inherently tied to the creator/owner's identity.

Trusted certificate authorities centrally manage public keys, ensuring secure links between keys and the identity of the key's owner.

Wide public dissemination across diverse forums exponentially strengthens data protection.

It is possible to secure public values WITHOUT a central trusted third party. This lecture looks at the first decentralized database, which set the foundation for blockchain security.

Applying publicly known standards to data formats is an easy and clever way to protect data.

This section takes a crawl-walk-run approach through the evolution of digital signatures. RSA to El Gamal to DSA to Elliptical Curve DSA.

Alice can generate a signature, and Bob can check that it indeed originated from Alice. This lecture covers the mathematics involved in signature verification.

The basic functions of digital signatures are remarkably comparable to handwritten signatures.

Modern signatures make use of two private keys. One is an enduring or long-term private key, the other is a one-time key.

Upgraded capabilities from RSA, and a stepping stone towards Elliptical Curve signatures. El Gamal makes use of a one-time key. This lecture covers the math involved for signature production and verification.

There is one more critical reason that signatures require a One-time private keys. If one-time keys are not used, an attacker could compare two different signed documents and determine the long-term secret key, a.

A simple example to showcase the enhanced capability of El Gamal. The protocol "bundles" the signature and data, thus El Gamal ensures signed data has not been altered. Alice uses a one-time private key.

This lecture builds on what we already have learned about the Discrete Log Problem and public keys, and presents one critical additional detail in order to provide the full picture of DLP security and protocols.

The DSA signature protocol provides public r and s values that are 10x smaller than El Gamal.

This lecture covers the math for signature production and verification.

ECDSA is only a small step away from DSA. This lecture shows how an Elliptical Curve signature is created and verified.

Private - Public Key Pairs and Digital Signatures are integral to bitcoin ownership. Private Keys are the physical connection between the real-world and the digital blockchain.

A long time ago... the electronic age was new, and people didn't trust data that was stored electronically! A new breed of companies emerged that offered Data Authenticity. Surety LLC was one such company, and created a novel concept to link - or chain - blocks of data together in a highly public fashion.

Stuart Haber along with Scott Stornetta invented the first blockchain in 1995, based on a paper the two published in 1991.  Stuart Haber is three of the eight references in the Bitcoin White Paper.

A small yet relevant fact. In many places, Bitcoin hashes data by running it through SHA-256, then taking the output of that hash and running it through SHA-256 again.

Just like Surety LCC did in 1991, Bitcoin combines Hash Functions and Public Decentralization to create a world-wide database (the bitcoin public blockchain) that cannot be forged, tampered, altered, etc.

• Who makes new blocks?

• What/how are new blocks created (with SHA-256)? What is inside a new block?

• When are new blocks added?

• Where do new blocks go?

• Why is this critical for Bitcoin?

The long-term viability and survivability of Bitcoin's public blockchain is in unique category. It cannot be killed or banned or destroyed.

Think of holding an asset such as a gold or silver coin. You own this coin by holding it. You can transfer ownership of this coin by simply handing it over to someone else. And lastly, you must not lose the coin! Same goes for your bitcoin.

Note this course will use the Pay to Public Key Hash (P2PKH) Transaction format for all examples. While there are several transaction formats possible in Bitcoin, P2PKH represents all of the important learning points in an accessible fashion. It is the best starting point to learn how transactions work. 

Every transaction has a unique transaction identifier, called a TXID.

This lecture covers the steps and components of a Bitcoin transaction.

Users create, sign, and broadcast transactions.

All bitcoin nodes receive all broadcast transactions. Nodes check and validate the digital signature. Valid transactions are approved and enter the queue to be added in a new block.

Digital signatures provide a complete record of all bitcoin ownership. This is a primary ingredient of Bitcoin's holistic security.

Humans are fallible. Our management of private keys is the weak link.

Bitcoin combines three tools of cryptography (hash functions, public key solutions, digital signatures) with public decentralization.  Therein the security of bitcoin is comparable to security of Cryptography itself.

There are common practices with Cryptography that account for this threat. One is routine protocol upgrades as compute power increases. Another is to weave together multiple layers of defense.

Free resources for further study.