What Is Cryptography

Cryptography is the science of securing information using mathematics. It’s been used for thousands of years — Caesar encoded military messages by shifting letters. World War II was partly decided by the ability to break encrypted communications. Today it secures every online banking transaction, every HTTPS website, and the entire Bitcoin network.

The version Bitcoin uses is called public key cryptography — or asymmetric cryptography. The asymmetry refers to the one-way relationship covered yesterday: easy to compute in one direction, practically impossible to reverse.

Here’s the underlying concept made simple.

Certain mathematical operations are trivially easy to perform but extraordinarily hard to undo. Multiplying two large prime numbers together takes a computer a fraction of a second. Factoring the result back into the original primes takes longer than the age of the universe with current technology.

Bitcoin’s cryptography exploits a similar mathematical property — elliptic curve multiplication. Given a starting point on a mathematical curve, multiplying it by a number is fast and deterministic. Working backwards from the result to find the original number is computationally infeasible.

The private key is that original number. The public key is the result of the multiplication. Fast to produce. Impossible to reverse.

This isn’t security by obscurity — hiding the method and hoping nobody figures it out. It’s security by mathematics — the method is fully public, the math has been scrutinised by the world’s best cryptographers for decades, and the security holds because reversing the computation is genuinely impossible with any foreseeable technology.

Tomorrow: what is hashing — the one-way function that holds the blockchain together.

— The Daily Bit