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I was entirely unaware of the history of cryptography and I was distinctly uninterested in what he was saying.
He always kept up with the latest scientific papers, which inspired him to come up with a whole series of weird and wonderful candidates for the one-way function at the heart of an asymmetric cipher.
The threesome began to lose hope, but they were unaware that this process of continual failure was a necessary part of their research, gently steering them away from sterile mathematical territory and toward more fertile ground.
In April 1977, Rivest, Shamir and Adleman spent Passover at the house of a student, and had consumed significant amounts of Manischewitz wine before returning to their respective homes some time around midnight. Rivest, unable to sleep, lay on his couch reading a mathematics textbook.
Rivest had made a breakthrough, but it had grown out of a yearlong collaboration with Shamir and Adleman, and it would not have been possible without them.
In order to choose her personal value of N, Alice picks two prime numbers, p and q, and multiplies them together.
We can think of N as the public key, the information that is available to everybody, the information required to encrypt messages to Alice. Whereas, p and q are the private key, available only to Alice, the information required to decrypt these messages.
Although some recipes are faster than others, they all essentially involve checking each prime number to see if it divides into NB without a remainder.
For important banking transactions, N tends to be at least 10308
Most mathematicians believe that factoring is an inherently difficult task, and that there is some mathematical law that forbids any shortcut.
RSA was first announced in August 1977, when Martin Gardner wrote an article entitled “A New Kind of Cipher that Would Take Millions of Years to Break” for his “Mathematical Games” column in Scientific American.
When the patent issues were eventually resolved, the trio held a celebratory party at which professors and students consumed pizzas and beer while stuffing envelopes with technical memoranda for the readers of Scientific American.
It is now routine to encrypt a message with a sufficiently large value of N so that all the computers on the planet would need longer than the age of the universe to break the cipher.
Looking ahead to the 1970s, senior military officials imagined a scenario in which miniaturization of radios and a reduction in cost meant that every soldier could be in continual radio contact with his officer.
Any expansion in communications would eventually be choked by the burden of key distribution.
He was brilliant, but he was also unpredictable, introverted and not a natural team worker.
He read any scientific journal he could get his hands on, and never threw anything away.
“He would always approach a problem by asking, ‘Is this really what we want to do?’ ” says Walton.
Ellis began his attack on the problem by searching through his treasure trove of scientific papers.
An existence theorem shows that a particular concept is possible, but is not concerned with the details of the concept.)
In his The Mathematician’s Apology, written in 1940, Hardy had proudly stated: “Real mathematics has no effects on war. No one has yet discovered any warlike purpose to be served by the theory of numbers.”
Encryption via public key cryptography requires much more computer power than encryption via a symmetric cipher like DES.
The scientific press reported the breakthroughs at Stanford and MIT, and the researchers who had been allowed to publish their work in the scientific journals became famous within the community of cryptographers.
Let me just say that you people did much more with it than we did.”
It was the academics who were the first to realize the potential of public key encryption, and it was they who drove its implementation. Furthermore, it is quite possible that GCHQ would never have revealed their work, thus blocking a form of encryption that would enable the digital revolution to reach its full potential.
We were in the middle of Thatcherism, and we were trying to counter a sort of “government is bad, private is good” ethos.
Most professional scientists aim to be the first to publish their work, because it is through dissemination that the work realizes its value.
Money is flowing through cyberspace, and it is estimated that every day half the world’s Gross Domestic Product travels through the Society for Worldwide Interbank Financial Telecommunications network.
Currently, the police use wiretapping as a way of gathering evidence in serious cases, such as organized crime and terrorism, but this would be impossible if criminals used unbreakable ciphers.
On graduation he seemed set for a steady career in the rapidly growing computer industry, but the political events of the early 1980s transformed his life, and he became less interested in the technology of silicon chips and more worried about the threat of nuclear war.
But in the Information Age, cryptography is about political power, and in particular, about the power relationship between a government and its people. It is about the right to privacy, freedom of speech, freedom of political association, freedom of the press, freedom from unreasonable search and seizure, freedom to be left alone.
However, in practice there was a major problem because the actual process of RSA encryption required a substantial amount of computing power in comparison with symmetric forms of encryption, such as DES.
He intended to draw upon his background in computer science to design a product with economy and efficiency in mind, thus not overloading the capacity of an ordinary personal computer. He also wanted his version of RSA to have a particularly friendly interface, so that the user did not have to be an expert in cryptography to operate it.
The name was inspired by Ralph’s Pretty Good Groceries, a sponsor of Garrison Keillor’s Prairie Home Companion, one of Zimmermann’s favorite radio shows.
This might seem convoluted, but the advantage is that the message, which might contain a large amount of information, is being encrypted with a quick symmetric cipher, and only the symmetric IDEA key, which consists of a relatively small amount of information, is being encrypted with a slow asymmetric cipher.
However, Alice only has to wiggle her mouse in an erratic manner, and the PGP program will go ahead and create her private key and public key-the mouse movements
introduce a random factor which PGP utilizes to ensure that every user has their own distinct pair of primes, and therefore their own unique private key and public key.
However, this mode of operation does verify authorship, because if Bob can decrypt a message using Alice’s public key, then it must have been encrypted using her private key-only Alice has access to her private key, so the message must have been sent by Alice.
We can picture the message surrounded by a fragile inner shell, which represents encryption by Alice’s private key, and a strong outer shell, which represents encryption by Bob’s public
key.
Nothing in PGP was original-Diffie and Hellman had already thought of digital signatures and other cryptographers had used a combination of symmetric and asymmetric ciphers to speed up encryption-but Zimmermann was the first to put everything together in one easy-to-use encryption product, which was efficient enough to run on a moderately sized personal computer.
However, as well as forcing companies to guarantee the possibility of wiretapping, the bill also seemed to threaten all forms of secure encryption. A concerted effort by RSA Data Security, Inc., the communications industry, and civil liberty groups forced the clause to be dropped, but the consensus was that this was only a temporary reprieve.
Rather than waiting and risk PGP being banned by the government, he decided that it was more important for it to be available to everybody before it was too late.
Although Zimmermann released PGP as freeware (free software), it contained the RSA system of public key cryptography, and consequently RSA Data Security, Inc. labeled PGP as “banditware.”
Because the U.S. Government included encryption software within its definition of munitions, along with missiles, mortars and machine guns, PGP could not be exported without a license from the State Department.
There were those, like Zimmermann, who believed that the widespread use of secure encryption would be a boon to society, providing individuals with privacy for their digital communications.
On the other side of the debate are the civil libertarians, including groups such as the Center for Democracy and Technology and the Electronic Frontier Foundation.
Presidents Lyndon Johnson and Richard Nixon were guilty of unjustified wiretaps, and President John F. Kennedy conducted dubious wiretaps in the first month of his presidency.
Then, following King’s award of the Nobel Prize, embarrassing details about King’s life were passed to any organization that was considering conferring an honor upon him.
For example, in America in 1994 there were roughly a thousand court-sanctioned wiretaps, compared with a quarter of a million federal cases.
