Two graduate students stood silently beside a lectern, listening as their professor presented their work to a conference.
Usually, the students might want the glory. as well as they had, just a couple of days previously. however their families talked them out of which.
A few weeks earlier, the Stanford researchers had received an unsettling letter coming from a shadowy US government agency. If they publicly discussed their findings, the letter said, which might be deemed legally equivalent to exporting nuclear arms to a hostile foreign power.
Stanford’s lawyer said he thought they could defend any case by citing the First Amendment’s protection of free speech. however the university could cover legal costs only for professors. So the students were persuaded to keep schtum.
What was which information which US spooks considered so dangerous? Were the students proposing to read out the genetic code of smallpox or lift the lid on some shocking presidential conspiracy?
No: they were planning to give the International Symposium on Information Theory an update on their work on public key cryptography.
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The year was 1977. If the government agency had managed to silence academic cryptographers, they might have prevented the internet as we know which.
To be fair, which wasn’t their plan. the planet Wide Web was years away. as well as the agency’s head, Adm Bobby Ray Inman, was genuinely puzzled about the academics’ motives.
He felt cryptography – the study of sending secret messages – was of practical use only to spies as well as criminals.
Three decades earlier, different brilliant academics had helped win the war by breaking the Enigma code, enabling the Allies to read secret Nazi communications.
currently Stanford researchers were freely disseminating information which might help adversaries in future wars to encode their messages in ways the US couldn’t crack.
His concern was reasonable. Throughout history, the development of cryptography has been driven by conflict.
Two thousand years ago, Julius Caesar sent encrypted messages to far-flung outposts of the Roman empire – he’d arrange in advance which recipients might simply shift the alphabet by some predetermined number.
For example, “jowbef Csjubjo” – if you substitute each letter with the preceding one – reads “invade Britain”.
which kind of thing wouldn’t have taken the Enigma codebreakers long to crack. Today, encryption will be typically numerical: first, convert the letters into numbers as well as then perform some complicated mathematics on them.
The recipient needs to know how to unscramble the message by performing the same mathematics in reverse. which’s known as symmetrical encryption. which’s like securing a message having a padlock, having already provided a key.
The Stanford researchers wondered whether encryption could be asymmetrical. Could you send an encrypted message to a stranger you’d never met before which only they could decode?
Before 1976 most experts might have said which was impossible. Then Whitfield Diffie as well as Martin Hellman published a breakthrough paper. which was Hellman who, a year later, might defy the threat of prosecution by presenting his students’ work.
which same year, three researchers at MIT – Ronald Rivest, Adi Shamir as well as Leonard Adleman – turned the Diffie-Hellman theory into a practical technique, called RSA encryption, after their surnames.
A public key for private messages
These academics had realised which some mathematics are a lot easier to perform in one direction than another.
Take a very large prime number – one which’s not divisible by anything different than itself. Then take another. Multiply them together. which gives you an extremely large “semi-prime” number, one divisible only by two prime numbers.
which turns out which’s exceptionally hard for someone else to take which semi-prime number as well as figure out which two prime numbers were multiplied together to produce which.
Public key cryptography works by exploiting which difference.
In effect, an individual publishes his semi-prime number – his public key – for anyone to see. as well as the RSA algorithm allows others to encrypt messages with which number, in such a way which they can be decrypted only by someone who knows the two prime numbers which produced which.
which’s as if you’re distributing open padlocks for the use of anyone who wants to send you a message which only you can unlock. They don’t need to have your private key to protect the message as well as send which to you.
They just need to snap shut one of your padlocks around which.
Security as well as authenticity
In theory, which’s possible for someone else to pick your padlock by figuring out the right combination of prime numbers. however which takes unfeasible amounts of computing power.
inside early 2000s, RSA Laboratories published some semi-primes as well as offered cash prizes to anyone who could figure out the primes which produced them.
Someone did scoop a $20,000 (£16,000) reward – however only after 80 computers worked on the number non-stop for several months. Larger prizes for longer numbers went unclaimed.
No wonder Adm Inman fretted about which knowledge reaching America’s enemies.
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however Prof Hellman had understood something the spy chief had not.
the planet was changing as well as electronic communication was becoming more important. Many private sector transactions might be impossible without secure communication.
You take advantage of which every time you send a confidential work email, or buy something online, or use a banking app, or visit any website which starts with “https”.
Without public key cryptography, anyone might be able to read your messages, see your passwords as well as copy your credit card details.
Public key cryptography also enables websites to prove their authenticity – without which, there’d be many more phishing scams. The internet might be a very different place as well as far less economically useful.
To his credit, the spy chief soon accepted which the professor had a point as well as no prosecutions followed. Indeed, the two developed an unlikely friendship.
The quantum threat
however Adm Inman was right which public key cryptography might complicate his job.
Encryption will be just as useful to drug dealers, child pornographers as well as terrorists as which will be to you as well as me paying for something on eBay.
coming from a government perspective, perhaps the ideal situation might be if encryption can’t be easily cracked by ordinary folk or criminals – thereby securing the internet’s economic advantages – however government can still see everything which’s going on.
The agency Adm Inman headed was called the National Security Agency (NSA). In 2013, Edward Snowden released secret documents showing just how the NSA was pursuing which goal.
The debate Snowden started out rumbles on. If we can’t restrict encryption only to the not bad guys, what powers should the state have to snoop – as well as with what safeguards?
Meanwhile, another technology threatens to make public key cryptography altogether useless: quantum computing.
By exploiting the strange ways in which matter behaves at a quantum level, quantum computers could potentially perform some calculations significantly more quickly than regular computers.
One of those calculations will be taking a large semi-prime number as well as figuring out which two prime numbers you’d have to multiply to get which. If which becomes easy, the internet becomes an open book.
Quantum computing will be still in its early days.
however 40 years after Diffie as well as Hellman laid the groundwork for internet security, academic cryptographers are currently racing to maintain which.
Tim Harford writes the Financial Times’s Undercover Economist column. 50 Things which Made the Modern Economy will be broadcast on the BBC World Service. You can find more information about the programme’s sources as well as listen online or subscribe to the programme podcast.