How public-key cryptography and digital signatures laid the mathematical groundwork for trustless digital money.
In 1976, Whitfield Diffie and Martin Hellman published "New Directions in Cryptography," one of the most consequential papers in computer science history. Before this paper, cryptography was symmetric: both parties needed to share the same secret key, which meant you needed a secure channel just to set up a secure channel.
Diffie and Hellman proposed an entirely new paradigm: asymmetric cryptography. Two mathematically related keys — one public, one private — could solve the key distribution problem. Anyone could encrypt a message with your public key, but only your private key could decrypt it. This single idea would eventually make trustless digital ownership possible.
In 1977, Ron Rivest, Adi Shamir, and Leonard Adleman created RSA, the first practical public-key cryptosystem. RSA proved that Diffie and Hellman's theoretical framework could actually work at scale.
Critically, RSA introduced practical digital signatures: a way to prove that a message came from a specific person without revealing their private key. This is the core mechanism that Bitcoin uses to authorize transactions. When you send Bitcoin, your wallet signs the transaction with your private key. Anyone on the network can verify the signature using your public key, but no one can forge it.
While public-key cryptography gets the headlines, cryptographic hash functions are equally essential to Bitcoin. A hash function takes any input and produces a fixed-length output that appears random. Change one bit of the input, and the output changes completely.
SHA-256, published by the NSA in 2001, became Bitcoin's hash function of choice. It serves three roles: linking blocks into an immutable chain, creating the proof-of-work puzzle that miners solve, and deriving Bitcoin addresses from public keys. Without hash functions, there would be no blockchain.
The path from Diffie-Hellman to Bitcoin took three decades, but every step built on these foundations. Elliptic curve cryptography (proposed by Neal Koblitz and Victor Miller in 1985) made public-key operations faster and more compact — Bitcoin uses the secp256k1 curve for all key generation and signing.
Satoshi Nakamoto didn't invent new cryptography. Instead, Bitcoin's genius was in combining proven cryptographic primitives — public-key signatures, hash functions, and hash chains — into a system that solved the double-spending problem without a central authority. Every Bitcoin transaction is a direct descendant of that 1976 paper.
Two key breakthroughs enabled Bitcoin: Whitfield Diffie and Martin Hellman's public-key cryptography (1976), which allows two parties to communicate securely without a shared secret, and RSA (1977), which provided the first practical implementation of digital signatures. These made it possible to prove ownership of digital assets without trusting a central authority.
Bitcoin uses elliptic curve cryptography (a descendant of Diffie-Hellman) to generate key pairs. Your private key signs transactions to prove you authorized them, while your public key (compressed into a Bitcoin address) lets anyone verify the signature. This eliminates the need for a bank or intermediary to confirm your identity.
Hash functions like SHA-256 are used throughout Bitcoin: to link blocks together in the blockchain, to create the proof-of-work mining puzzle, and to generate addresses from public keys. Their one-way nature ensures that blocks cannot be tampered with without redoing all subsequent work.
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