Cryptography Primitives: The Building Blocks of Crypto

What you'll learn

• Why Cryptography Comes First
• The Birth of Public Key Cryptography
• Digital Signatures: ECDSA vs Schnorr
• Hash Functions Revisited
• Commitment Schemes
• Stealth Addresses: Privacy on Public Chains
• Putting It Together
• For Deeper Reading

Key terms

Symmetric cryptography

Cryptographic schemes where the same key is used for encryption and decryption. Requires both parties to share a secret in advance. AES is the most common modern symmetric cipher.

Asymmetric cryptography (public key cryptography)

Cryptographic schemes using two related keys: a public key for encryption or verification, and a private key for decryption or signing. Pioneered by Diffie and Hellman in 1976.

Diffie-Hellman key exchange

A protocol published in 1976 that allows two parties to derive a shared secret over a public channel. Foundational for modern internet security and stealth address constructions in crypto.

RSA

Rivest-Shamir-Adleman, the first practical public key cryptosystem (1977). Based on the difficulty of factoring large composite numbers. Still in widespread use but being replaced by ECC in many applications.

Elliptic curve cryptography (ECC)

A family of public key cryptosystems based on the mathematics of elliptic curves over finite fields. Provides strong security with much smaller keys than RSA. Used by Bitcoin (secp256k1), Ethereum, and many modern protocols.

ECDSA

Elliptic Curve Digital Signature Algorithm, the signature scheme used by Bitcoin pre-Taproot and by Ethereum externally-owned accounts. Standardized in 1992, adopted in NIST FIPS 186 (2000).

Schnorr signature

A digital signature scheme proposed by Claus-Peter Schnorr in 1989. Cryptographically simpler and more efficient than ECDSA. Activated in Bitcoin via Taproot (BIP-340) in November 2021.

Preimage resistance

A property of cryptographic hash functions: given an output, it should be infeasible to find any input that produces that output. Makes hash functions one-way.

Collision resistance

A property of cryptographic hash functions: it should be infeasible to find any two distinct inputs that hash to the same output. Critical for Merkle tree integrity.

Commitment scheme

A cryptographic primitive that lets a party commit to a value while keeping it hidden, with the ability to later reveal it. Hiding plus binding properties. Used in zero-knowledge proofs, sealed-bid auctions, HTLCs, and more.

Pedersen commitment

A specific commitment scheme that is additively homomorphic: commitments to two values can be added to produce a commitment to their sum. Used in Bulletproofs (Monero) and many privacy systems.

Stealth address

A privacy technique published by Vitalik Buterin in detail on January 20, 2023. Lets a recipient publish a single meta-address while every actual payment goes to a fresh unlinkable address. ERC-5564 standardizes this on Ethereum.