The strange new virtual currency called bitcoin relies on something more trustworthy than people or institutions. It relies on mathematics—in fact, 'trusty' one-way mathematics. Dr Karl Kruszelnicki explains.
Previously, I spoke about how important the concept of trust was to finance, and how this trust usually relied on either people, or institutions (such as banks or governments)—or both.
By the way, if you want to look at the continuous flow of transactions on the Bitcoin Network, check out blockchain.info.
But the strange new virtual currency called bitcoin relies on something more trustworthy than people or institutions. Yes, I'm talking mathematics— in fact, 'trusty' one-way mathematics.
You might think one-way mathematics is impossible. After all, you can add three and two to get five. Then you can use 'subtraction', hit 'reverse', and get back to where you started. Yes, five minus two gets you back to three. This is two-way mathematics. And yes, addition can be reversed with subtraction.
But think about multiplying two really large prime numbers, each 500 digits long. It would take many hours by hand, or a few instants on a computer. The multiplication gives you a really long number, about 1,000 digits long.
Welcome to one-way mathematics.
It's practically impossible to go backwards, to find the only two prime numbers that can be multiplied to generate this 1,000-digit number. You just have to make lots of guesses, and try them out—one after the other. This method is appropriately called the 'brute force method'.
It's not totally impossible to find those two prime numbers—but it would take today's fastest supercomputers many times the age of the universe to find them. So with today's technology, it's effectively (or computationally) impossible to find the only two factors of our 1,000 digit number.
One-way mathematics is at the basis of the two key technologies needed for the blockchain to work. The blockchain is the brilliant invention that stops people from spending their virtual currency more than once.
The first technology (public and private key, or PKI, public key infrastructure)means that if you claim that you bought and sold some bitcoins, everybody can be confident that it was definitely you (and nobody else) that made this claim. It also provides secure communication which nobody can intercept, or change.
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One-way mathematics is essential to this strange encryption method. It was theoretically proven to be possible in 1976 by Whitfield Diffie and Martin Hellman. This set off a race among the mathematicians to make it work.
The first public and private key encryption was actually constructed two years later in 1987 by Ronald Rivest, Adi Shamir and Leonard Adleman, later collectively known as RSA. You might have read of Julian Assange and others using this technology to make totally secure communication.
Here's how it works. In cryptography, the examples always start with Alice and Bob. 'Cryptography' comes from Greek words meaning 'secret writing'.
Alice mathematically constructs two keys, as a related pair—a private key and a public key. (Each key is just a bunch of letters and numbers.) Everybody in the world can have a copy of Alice's public key. They can plug Alice's public key into the RSA algorithm (also freely available to anybody who wants it) when they want to send her a message.
So Bob uses Alice's public key to encode a message, generate a string of gibberish and email it to Alice.
Alice is the only person who has her private key. She applies her secret private key to the gibberish Bob emailed her—and suddenly, Alice can read Bob's original message. This is the weird bit—even though everybody has Alice's public key and a copy of the RSA algorithm, she's the only person who can decode it.
But besides making possible the sending of secret messages, public-key cryptography makes digital signatures possible.
A digital signature is like your regular signature—easy to make, hard to forge. In fact, it's so hard as to be computationally impossible. Again, it's a two-part process. One algorithm is used with your private key to sign the message, and another algorithm is used with your matching public key to check the validity of the message.
You can take it one step further.
You can fuse your digital signature to your message so they can't be separated. Now your digital signature can't be copied and used on another message. This means anybody can verify that the message they received came from you—and only you. The digital signature provides proof of ownership of bitcoins.
This is how human and institutional trust can be replaced by mathematical trust.
This means that you can announce that you promise to send me 10,000 bitcoins—and everybody can be confident that you are the person who made that transaction, and actually own those bitcoins.
The second technology made possible by one-way mathematics, and which is essential for bitcoin and the blockchain to work is the hash function—and I'll talk more about that, next time ...
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