BA-02 · LESSON 09

The Bitcoin cryptography map

KEY DEFINITIONS

Terms used in this lesson

SHA-256: A cryptographic hash function used throughout Bitcoin to produce fixed-size 256-bit digests.
HASH256: Bitcoin's name for applying SHA-256 twice to the same byte sequence.
Hash160: SHA-256 followed by RIPEMD-160, producing the 20-byte hash used by several Bitcoin spending conditions.
HMAC: Hash-based message authentication code: a keyed hash construction used to authenticate data or derive deterministic secret material.
HMAC-SHA512: HMAC using SHA-512; BIP32 uses it to derive a master key and chain code from seed material.
PBKDF2: A password-based key-derivation function used by BIP39 to turn mnemonic words and an optional passphrase into a seed.
ECDSA: Elliptic Curve Digital Signature Algorithm, the signature scheme used by pre-Taproot Bitcoin outputs.
Schnorr signature: Bitcoin’s Taproot signature scheme, whose algebra supports compact verification and advanced multi-party signing.
RIPEMD-160: A 160-bit cryptographic hash function used in Bitcoin’s HASH160 construction.
BIP32: The Bitcoin standard for deriving a tree of child keys from one extended root key.
BIP39: A standard that converts entropy into mnemonic words and derives a seed using an optional passphrase.
BIP340: The Bitcoin Improvement Proposal specifying Schnorr signatures for the secp256k1 curve.
Taproot: A Bitcoin output and spending design that can combine a public-key path with privately committed alternative scripts.
SegWit: Segregated Witness: a Bitcoin upgrade that separates authorization data from the transaction identifier and introduces versioned witness programs.
Witness: Signatures, scripts, or other data supplied to satisfy a Bitcoin output’s spending condition.
BIP143: The Bitcoin Improvement Proposal that defines the version-zero SegWit transaction signature digest used by native P2WPKH and P2WSH spends.
Sighash: The exact transaction digest and signature mode that determine which fields a Bitcoin signature authorizes.

Connect SHA-256, HASH256, HASH160, HMAC-SHA512, PBKDF2, secp256k1, ECDSA, Schnorr, tagged hashes, and Merkle commitments to the exact job each performs.

35 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 · cryptography mapDifferent Bitcoin primitives perform different jobsSelect any state to inspect its exact role.

RELATIONSHIP MAPOrdered mechanism flow

01
SEEDPBKDF2 then HMAC-SHA512
BIP39 stretches mnemonic and passphrase; BIP32 derives child material with a keyed hash.
02
KEYd then P=dG
secp256k1 maps a valid secret scalar to a public point.
03
DESTINATIONHASH160(public key)
The exact serialized public key determines the 20-byte commitment.
04
AUTHORIZEECDSA or Schnorr
A signature proves authorization for one committed message under one public key.
05
AGGREGATEMerkle or tagged hash
Structured hashes commit many items or separate protocol purposes.

Rule shown: Each primitive has exact input bytes, output size, secrecy, domain, and a later verifier that consumes it.

STAGE 1 OF 5SEED: PBKDF2 then HMAC-SHA512

BIP39 stretches mnemonic and passphrase; BIP32 derives child material with a keyed hash.

Governing relationship: Each primitive has exact input bytes, output size, secrecy, domain, and a later verifier that consumes it. Complete path: 1. SEED, PBKDF2 then HMAC-SHA512. BIP39 stretches mnemonic and passphrase; BIP32 derives child material with a keyed hash. 2. KEY, d then P=dG. secp256k1 maps a valid secret scalar to a public point. 3. DESTINATION, HASH160(public key). The exact serialized public key determines the 20-byte commitment. 4. AUTHORIZE, ECDSA or Schnorr. A signature proves authorization for one committed message under one public key. 5. AGGREGATE, Merkle or tagged hash. Structured hashes commit many items or separate protocol purposes.

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

BEFORE

A wallet starts with BIP39 words and later signs a native SegWit transaction.

MECHANISM

SHA-256 produces one 32-byte digest. HASH256 applies SHA-256 twice for transaction and block identifiers and checksums. HASH160 applies SHA-256 then RIPEMD-160 for 20-byte ke…

AFTER

Cryptography becomes understandable when each primitive is assigned one concrete input, output, security boundary, and Bitcoin consumer.

Text equivalent: Starting from A wallet starts with BIP39 words and later signs a native SegWit transaction. The mechanism begins when SHA-256 produces one 32-byte digest. HASH256 applies SHA-256 twice for transaction and block identifiers and checksums. HASH160 applies SHA-256 then RIPEMD-160 for 20-byte key and script commitments. The resulting lesson is Cryptography becomes understandable when each primitive is assigned one concrete input, output, security boundary, and Bitcoin consumer.

2. Mechanism pathSelect a stage to inspect its job

STAGE 1 OF 5

Map the hash families

SHA-256 produces one 32-byte digest. HASH256 applies SHA-256 twice for transaction and block identifiers and checksums. HASH160 applies SHA-256 then RIPEMD-160 for 20-byte key and script commitments.

Complete path: 1. Map the hash families: SHA-256 produces one 32-byte digest. HASH256 applies SHA-256 twice for transaction and block identifiers and checksums. HASH160 applies SHA-256 then RIPEMD-160 for 20-byte key and script commitments. 2. Map key derivation functions: HMAC-SHA512 combines a key and message for BIP32 child derivation. PBKDF2-HMAC-SHA512 runs 2,048 rounds in BIP39 to derive a 64-byte seed from the normalized mnemonic and passphrase. 3. Map curve keys and signatures: secp256k1 scalar multiplication maps a valid private scalar to a public point. ECDSA and BIP340 Schnorr use different equations and encodings to prove authorization for a message digest. 4. Map domain separation: Tagged hashing commits a purpose label before data so bytes used for a TapLeaf, TapBranch, TapTweak, BIP340 challenge, or other role cannot be silently substituted across domains. 5. Map aggregate commitments: Merkle trees repeatedly hash ordered pairs so a short sibling path proves inclusion under one root. Bitcoin then commits that root in another structure such as a block header or Taproot output key.

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

ACCEPTED PATH

Every edge states exact input bytes, output length, domain, public or secret status, and the verifier that consumes the result.

CHANGED CONDITION

Replacing HASH160 with SHA-256, using an untagged Taproot hash, signing a different sighash, or treating a public hash as encryption changes the protocol result and must fail its intended check.

Important distinction: Bitcoin hashes or encrypts everything with SHA-256. Bitcoin combines hashes, keyed derivation, curve operations, signatures, and structured commitments. None of the named hash functions encrypts data.

Text equivalent: The accepted path is enforced by Every edge states exact input bytes, output length, domain, public or secret status, and the verifier that consumes the result. If the required condition changes, Replacing HASH160 with SHA-256, using an untagged Taproot hash, signing a different sighash, or treating a public hash as encryption changes the protocol result and must fail its intended check.

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Learn the idea

Bitcoin uses several cryptographic functions because each solves a different problem. Hashes commit and identify, keyed hashes derive secret-dependent material, password stretching derives a seed from a mnemonic, curve multiplication creates public keys, signatures authorize messages, and Merkle trees compress many commitments into one root. The primitives are related by exact byte flows rather than by a general idea of encryption.

GUIDED EXPLANATION1/5 ideas inspected

Map the hash families

SHA-256 produces one 32-byte digest. HASH256 applies SHA-256 twice for transaction and block identifiers and checksums. HASH160 applies SHA-256 then RIPEMD-160 for 20-byte key and script commitments.

The worked example follows the explanation

Inspect every idea above to open it.

Important distinction“Bitcoin hashes or encrypts everything with SHA-256.”

Bitcoin combines hashes, keyed derivation, curve operations, signatures, and structured commitments. None of the named hash functions encrypts data.

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