BA-02 · LESSON 02

Hash functions and SHA-256

KEY DEFINITIONS

Terms used in this lesson

SHA-256: A cryptographic hash function used throughout Bitcoin to produce fixed-size 256-bit digests.
Preimage: The original secret data whose hash equals a previously committed value.
ASCII: A standard mapping between common text characters and byte values.

A hash turns any message into a fixed-size fingerprint. Bitcoin commonly uses the Secure Hash Algorithm 256, called SHA-256, to detect changes and make commitments.

45 min Difficulty 1/5 Not started

VISUAL MODEL

See the whole mechanism before going step by step

Use the diagrams to orient yourself. Then the guided explanation below teaches every part in depth.

4 explanatory views

CONCEPT-SPECIFIC MAP · sha256 roundsOne changed input produces a different 256-bit digestSelect any state to inspect its exact role.

RELATIONSHIP MAPOrdered mechanism flow

01
MESSAGEBitcoin = 7 bytes
Text is first encoded as bytes. Adding one byte changes the padded block.
02
PAD426974636f696e8000...0038
A 1 bit, zero fill, and the original bit length produce a multiple of 512 bits.
03
SCHEDULEW0=42697463, W1=6f696e80
The first 16 words come from the block; rotations and shifts derive W16 through W63.
04
64 ROUNDSa..h + Kt + Wt
Each round mixes the schedule word, a fixed constant, and the eight working state words modulo 2^32.
05
DIGESTB4056df6...4eb63aa4
The 32-byte result changes unpredictably when the input changes.

Rule shown: SHA-256 pads the exact message bytes, expands 16 words into 64, and updates eight 32-bit state words for every round.

STAGE 1 OF 5MESSAGE: Bitcoin = 7 bytes

Text is first encoded as bytes. Adding one byte changes the padded block.

Governing relationship: SHA-256 pads the exact message bytes, expands 16 words into 64, and updates eight 32-bit state words for every round. Complete path: 1. MESSAGE, Bitcoin = 7 bytes. Text is first encoded as bytes. Adding one byte changes the padded block. 2. PAD, 426974636f696e8000...0038. A 1 bit, zero fill, and the original bit length produce a multiple of 512 bits. 3. SCHEDULE, W0=42697463, W1=6f696e80. The first 16 words come from the block; rotations and shifts derive W16 through W63. 4. 64 ROUNDS, a..h + Kt + Wt. Each round mixes the schedule word, a fixed constant, and the eight working state words modulo 2^32. 5. DIGEST, B4056df6...4eb63aa4. The 32-byte result changes unpredictably when the input changes.

1. State transitionWhat exists, what changes, and what results

BEFORE

Hash the ASCII strings abc and abd.

MECHANISM

A hash receives bytes, not an abstract sentence or number. Encoding, length, and field order must be fixed before hashing.

AFTER

Hashes are deterministic public commitments to exact bytes, not secrecy or identity proofs.

Text equivalent: Starting from Hash the ASCII strings abc and abd. The mechanism begins when A hash receives bytes, not an abstract sentence or number. Encoding, length, and field order must be fixed before hashing. The resulting lesson is Hashes are deterministic public commitments to exact bytes, not secrecy or identity proofs.

2. Mechanism pathSelect a stage to inspect its job

STAGE 1 OF 5

Serialize exact bytes

A hash receives bytes, not an abstract sentence or number. Encoding, length, and field order must be fixed before hashing.

Complete path: 1. Serialize exact bytes: A hash receives bytes, not an abstract sentence or number. Encoding, length, and field order must be fixed before hashing. 2. Process the complete message: SHA-256 pads the message and runs a compression function over 512-bit blocks, carrying an internal state from one block to the next. 3. Produce one 32-byte digest: The same bytes always produce the same digest. The fixed output can identify or commit to much larger data. 4. Verify by recomputation: Anyone with the bytes can run SHA-256 and compare digests without trusting the original publisher. 5. Use the right guarantee: A digest does not encrypt its input and does not prove who created it. Authentication requires a key-based construction or signature.

3. Rule and failure boundaryWhat accepts the result and where it can stop

ACCEPTED PATH

Verification hashes the exact serialized bytes and compares the entire 32-byte digest.

CHANGED CONDITION

Changing encoding or one byte produces a different digest; the mismatch proves only different committed bytes, not who authored either input.

Important distinction: SHA-256 encrypts data so only the intended recipient can read it. Hashing is one-way and has no decryption key. Encryption is reversible for a key holder; hashing supports comparison and commitment.

Text equivalent: The accepted path is enforced by Verification hashes the exact serialized bytes and compares the entire 32-byte digest. If the required condition changes, Changing encoding or one byte produces a different digest; the mismatch proves only different committed bytes, not who authored either input.

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Learn the idea

A cryptographic hash function maps any byte string to a fixed-size digest. SHA-256 produces 256 bits, or 32 bytes. Preimage resistance makes it impractical to recover an input from a digest, collision resistance makes it impractical to find two inputs with the same digest, and the avalanche effect means a small input change usually changes many output bits.

GUIDED EXPLANATION1/5 ideas inspected

Serialize exact bytes

A hash receives bytes, not an abstract sentence or number. Encoding, length, and field order must be fixed before hashing.

The worked example follows the explanation

Inspect every idea above to open it.

Important distinction“SHA-256 encrypts data so only the intended recipient can read it.”

Hashing is one-way and has no decryption key. Encryption is reversible for a key holder; hashing supports comparison and commitment.

FINISH LEARNING FIRST

The questions unlock after every required learning activity

Inspect every guided idea, open the worked example, rebuild its mechanism, and complete the deterministic lesson tool. Your progress is saved automatically.