Bruce Sterling - Essays. FSF Columns

In the new public-key cryptography, however, there are two keys. The first is a key for writing secret text, the second the key for reading that text. The keys are related to one another through a complex mathematical dependency; they determine one another, but it is mathematically extremely difficult to deduce one key from the other.

The user simply gives away the first key, the "public key," to all and sundry. The public key can even be printed on a business card, or given away in mail or in a public electronic message. Now anyone in the public, any random personage who has the proper (not secret, easily available) cryptographic software, can use that public key to send the user a cyphertext message. However, that message can only be read by using the second key -- the private key, which the user always keeps safely in his own possession.

Obviously, if the private key is lost, all is lost. But only one person knows that private key. That private key is generated in the user's home computer, and is never revealed to anyone but the very person who created it.

To reply to a message, one has to use the public key of the other party. This means that a conversation between two people requires four keys. Before computers, all this key-juggling would have been rather unwieldy, but with computers, the chips and software do all the necessary drudgework and number-crunching.

The public/private dual keys have an interesting alternate application. Instead of the public key, one can use one's private key to encrypt a message. That message can then be read by anyone with the public key, i.e,. pretty much everybody, so it is no longer a "secret" message at all. However, that message, even though it is no longer secret, now has a very valuable property: it is authentic. Only the individual holder of the private key could have sent that message.

This authentication power is a crucial aspect of the new cryptography, and may prove to be more socially important than secrecy. Authenticity means that electronic promises can be made, electronic proofs can be established, electronic contracts can be signed, electronic documents can be made tamperproof. Electronic impostors and fraudsters can be foiled and defeated -- and it is possible for someone you have never seen, and will never see, to prove his bona fides through entirely electronic means.

That means that economic relations can become electronic. Theoretically, it means that digital cash is possible -- that electronic mail, e-mail, can be joined by a strange and powerful new cousin, electronic cash, e- money.

Money that is made out of text -- encrypted text. At first consideration such money doesn't seem possible, since it is so far outside our normal experience. But look at this:

ASCII-picture of US dollar

This parody US banknote made of mere letters and numbers is being circulated in e-mail as an in-joke in network circles. But electronic money, once established, would be no more a joke than any other kind of money. Imagine that you could store a text in your computer and send it to a recipient; and that once gone, it would be gone from your computer forever, and registered infallibly in his. With the proper use of the new encryption and authentication, this is actually possible. Odder yet, it is possible to make the note itself an authentic, usable, fungible, transferrable note of genuine economic value, without the identity of its temporary owner ever being made known to anyone. This would be electronic cash -- like normal cash, anonymous -- but unlike normal cash, lightning-fast and global in reach.

There is already a great deal of electronic funds transfer occurring in the modern world, everything from gigantic currency-exchange clearinghouses to the individual's VISA and MASTERCARD bills. However, charge- card funds are not so much "money" per se as a purchase via proof of personal identity. Merchants are willing to take VISA and MASTERCARD payments because they know that they can physically find the owner in short order and, if necessary, force him to pay up in a more conventional fashion. The VISA and MASTERCARD user is considered a good risk because his identity and credit history are known.

VISA and MASTERCARD also have the power to accumulate potentially damaging information about the commercial habits of individuals, for instance, the video stores one patronizes, the bookstores one frequents, the restaurants one dines in, or one's travel habits and one's choice of company.

Digital cash could be very different. With proper protection from the new cryptography, even the world's most powerful governments would be unable to find the owner and user of digital cash. That cash would secured by a "bank" -- (it needn't be a conventional, legally established bank) -- through the use of an encrypted digital signature from the bank, a signature that neither the payer nor the payee could break.

The bank could register the transaction. The bank would know that the payer had spent the e-money, and the bank could prove that the money had been spent once and only once. But the bank would not know that the payee had gained the money spent by the payer. The bank could track the electronic funds themselves, but not their location or their ownership. The bank would guarantee the worth of the digital cash, but the bank would have no way to tie the transactions together.

The potential therefore exists for a new form of network economics made of nothing but ones and zeroes, placed beyond anyone's controls by the very laws of mathematics. Whether this will actually happen is anyone's guess. It seems likely that if it did happen, it would prove extremely difficult to stop.

Public-key cryptography uses prime numbers. It is a swift and simple matter to multiply prime numbers together and obtain a result, but it is an exceedingly difficult matter to take a large number and determine the prime numbers used to produce it. The RSA algorithm, the commonest and best-tested method in public-key cryptography, uses 256-bit and 258-bit prime numbers. These two large prime numbers ("p" and "q") are used to produce very large numbers ("d" and "e") so that (de-1) is divisible by (p-1) times (q-1). These numbers are easy to multiply together, yielding the public key, but extremely difficult to pull apart mathematically to yield the private key.

To date, there has been no way to mathematically prove that it is inherently difficult to crack this prime-number cipher. It might be very easy to do if one knew the proper advanced mathematical technique for it, and the clumsy brute-power techniques for prime-number factorization have been improving in past years. However, mathematicians have been working steadily on prime number factorization problems for many centuries, with few dramatic advances. An advance that could shatter the RSA algorithm would mean an explosive breakthrough across a broad front of mathematical science. This seems intuitively unlikely, so prime-number public keys seem safe and secure for the time being -- as safe and secure as any other form of cryptography short of "the one-time pad." (The one-time pad is a truly unbreakable cypher. Unfortunately it requires a key that is every bit as long as the message, and that key can only be used once. The one-time pad is solid as Gibraltar, but it is not much practical use.)

Prime-number cryptography has another advantage. The difficulty of factorizing numbers becomes drastically worse as the prime numbers become larger. A 56-bit key is, perhaps, not entirely outside the realm of possibility for a nationally supported decryption agency with large banks of dedicated supercomputers and plenty of time on their hands. But a 2,048 bit key would require every computer on the planet to number-crunch for hundreds of centuries.

Decrypting a public-keyed message is not so much a case of physical impossibility, as a matter of economics. Each key requires a huge computational effort to break it, and there are already thousands of such keys used by thousands of people. As a further blow against the decryptor, the users can generate new keys easily, and change them at will. This poses dire problems for the professional electronic spy.