It has been said that the First World War was the chemists’ war, because mustard gas and chlorine were employed for the first time, and that the Second World War was the physicists’ war, because the atom bomb was detonated. Similarly, it has been argued that the Third World War would be the mathematicians’ war, because mathematicians will have control over the next great weapon of war—information.
Ever since reading The Decipherment of Linear B, John Chadwick’s description of how an ancient Mediterranean text was unraveled, I have been struck by the astounding intellectual achievements of those men and women who have been able to decipher the scripts of our ancestors, thereby allowing us to read about
Ever since reading The Decipherment of Linear B, John Chadwick’s description of how an ancient Mediterranean text was unraveled, I have been struck by the astounding intellectual achievements of those men and women who have been able to decipher the scripts of our ancestors, thereby allowing us to read about their civilizations, religions and everyday lives.
I have, however, forsaken accuracy for snappiness.
The only people who are in a position to point out my errors are also those who are not at liberty to reveal them.
To convey his instructions securely, Histaiaeus shaved the head of his messenger, wrote the message on his scalp, and then waited for the hair to regrow. This was clearly a period of history that tolerated a certain lack of urgency.
Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics and linguistics.
Every Muslim is obliged to pursue knowledge in all its forms, and the economic success of the Abbasid caliphate meant that scholars had the time, money and materials required to fulfill their duty.
For example, a brief message discussing the effect of the atmosphere on the movement of striped quadrupeds in Africa would not yield to straightforward frequency analysis: “From Zanzibar to Zambia and Zaire, ozone zones make zebras run zany zigzags.”
Walsingham was determined to minimize Mary’s influence as a martyr, and he ordered that the block, Mary’s clothing, and everything else relating to the execution be burned in order to avoid the creation of any holy relics.
at the age of thirty-nine, Vigenère decided that he had accumulated enough money for him to be able to abandon his career and concentrate on a life of study.
The cost of sending a letter used to depend on the distance the letter had to travel, but Babbage pointed out that the cost of the labor required to calculate the price for each letter was more than the cost of the postage.
He complained that the music “not infrequently gives rise to a dance by little ragged urchins, and sometimes half-intoxicated men, who occasionally accompany the noise with their own discordant voices.
He complained that the music “not infrequently gives rise to a dance by little ragged urchins, and sometimes half-intoxicated men, who occasionally accompany the noise with their own discordant voices. Another class who are great supporters of street music consists of ladies of elastic virtue and cosmopolitan tendencies, to whom it affords a decent excuse for displaying their fascinations at their open windows
Unfortunately for Babbage, the musicians fought back by gathering in large groups around his house and playing as loud as possible.
It was probably this withdrawal of support that later prompted Babbage to make the following complaint: “Propose to an Englishman any principle, or any instrument, however admirable, and you will observe that the whole effort of the English mind is directed to find a difficulty, a defect, or an impossibility in it. If you speak to him of a machine for peeling a potato, he will pronounce it impossible: if you peel a potato with it before his eyes, he will declare it useless, because it will not slice a pineapple.”
Being a keen statistician and compiler of mortality tables, Babbage was irritated by the lines “Every moment dies a man, Every moment one is born,” which are the last lines of the plaintext above. Consequently, he offered a correction to Tennyson’s “otherwise beautiful” poem: It must be manifest that if this were true, the population of the world would be at a standstill … I would suggest that in the next edition of your poem you have it read—“Every moment dies a man, Every moment 1 is born.” … The actual figure is so long I cannot get it onto a line, but I believe the figure 1 will be sufficiently accurate for poetry. I am, Sir, yours, etc., Charles Babbage.
In due course a wider variety of encrypted notes appeared in the newspapers. Cryptographers began to insert blocks of ciphertext merely to challenge their colleagues.
He grappled day and night with the ADFGVX cipher, in the process losing 15 kg in weight.
In Germany, the Foreign Office began an investigation into how the Americans had obtained the Zimmermann telegram. They fell for Admiral Hall’s ploy, and came to the conclusion that “various indications suggest that the treachery was committed in Mexico.” Meanwhile, Hall continued to distract attention from the work of British cryptanalysts. He planted a story in the British press criticizing his own organization for not intercepting the Zimmermann telegram, which in turn led to a spate of articles attacking the British secret service and praising the Americans.
Had the telegram never been intercepted or never been published, inevitably the Germans would have done something else that would have brought us in eventually. But the time was already late and, had we delayed much longer, the Allies might have been forced to negotiate. To that extent the Zimmermann telegram altered the course of history … In itself the Zimmermann telegram was only a pebble on the long road of history. But a pebble can kill a Goliath, and this one killed the American illusion that we could go about our business happily separate from other nations. In world affairs it was a German Minister’s minor plot. In the lives of the American people it was the end of innocence.
(Readers who would like to know about the exact role of the ring should refer to some of the books in the list of further reading, such as Seizing the Enigma by David Kahn.
If necessity is the mother of invention, then perhaps adversity is the mother of cryptanalysis.
as with all mathematics, his work required inspiration as well as logic.
As another wartime mathematical cryptanalyst put it, the creative codebreaker must “perforce commune daily with dark spirits to accomplish his feats of mental ju-jitsu.”
However, unknown to the Polish codebreakers, much of their work was unnecessary. The chief of the Biuro, Major Gwido Langer, already had the Enigma day keys, but he kept them hidden, tucked away in his desk.
However, the remarkably astute Langer decided not to tell Rejewski that the keys existed. By depriving Rejewski of the keys, Langer believed he was preparing him for the inevitable time when the keys would no longer be available.
Langer thought that Rejewski should practice self-sufficiency in peacetime, as preparation for what lay ahead.
The Polish breakthroughs also demonstrated to the Allies the value of employing mathematicians as codebreakers. In Britain, Room 40 had always been dominated by linguists and classicists, but now there was a concerted effort to balance the staff with mathematicians and scientists.
Part of the reason for their success was the bizarre combination of mathematicians, scientists, linguists, classicists, chess grandmasters and crossword addicts within each hut. An intractable problem would be passed around the hut until it reached someone who had the right mental tools to solve it, or reached someone who could at least partially solve it before passing it on again.
Turing became a pupil at Sherborne School, in Dorset. The start of his first term coincided with the General Strike, but Turing was determined to attend the first day, and he cycled 100 km unaccompanied from Southampton to Sherborne, a feat that was reported in the local newspaper. By the end of his first year at the school he had gained a reputation as a shy, awkward boy whose only skills were in the area of science. The aim of Sherborne was to turn boys into well-rounded men, fit to rule the Empire, but Turing did not share this ambition and had a generally unhappy schooling.
Turing believed it was his duty also to win a place at Cambridge, and then to make the discoveries his friend would otherwise have made. He asked Christopher’s mother for a photograph, and when it arrived he wrote back to thank her: “He is on my table now, encouraging me to work hard.”
Although Bletchley was run by the military, they had conceded that they would have to tolerate the scruffiness and eccentricities of these “professor types.”
It seemed as if the Admiralty’s only strategy for pinpointing the location of U-boats was
It seemed as if the Admiralty’s only strategy for pinpointing the location of U-boats was by looking at the sites of sunken British ships.
An alternative strategy for cracking the Naval Enigma depended on stealing keys. One of the most intrepid plans for stealing keys was concocted by Ian Fleming, creator of James Bond and a member of Naval Intelligence during the war.
Champollion dashed into his brother’s office and proclaimed “Je tiens l’affaire!” (“I’ve got it!”), but once again his intense passion for hieroglyphics got the better of him. He promptly collapsed, and was bedridden for the next five days.
Usually these encrypted epitaphs were not intended to be unbreakable, but rather they acted as cryptic puzzles to arouse the curiosity of passersby, who would thus be tempted to linger at a tomb rather than moving on.
there were one or two heretics who argued that the Minoans spoke and wrote Greek. Sir Arthur did not take such dissent lightly, and used his influence to punish those who disagreed with him.
Blegen’s discovery did not necessarily force a single language upon the Mycenaeans and the Minoans. In the Middle Ages, many European states, regardless of their native language, kept their records in Latin. Perhaps the language of Linear B was likewise a lingua franca among the accountants of the Aegean, allowing ease of commerce between nations who did not speak a common language.
“She worked with a subdued intensity,” recalls Eva Brann, a former student who went on to become an archaeologist at Yale University. “She once told me that the only way to know when you have done something truly great is when your spine tingles.”
For the first time in three thousand years, the silent script of Linear B was whispering once again, and the language it spoke was undoubtedly Greek.
An informal test for the accuracy of a decipherment is the number of gods in the text. In the past, those who were on the wrong track would, not surprisingly, generate nonsensical words, which would be explained away as being the names of hitherto unknown deities. However, Chadwick and Ventris claimed only four divine names, all of which were well-established gods.
Colossus, as with everything else at Bletchley Park, was destroyed after the war, and those who worked on it were forbidden to talk about it. When Tommy Flowers was ordered to dispose of the Colossus blueprints, he obediently took them down to the boiler room and burned them. The plans for the world’s first computer were lost forever.
In the 1970s, banks attempted to distribute keys by employing special dispatch riders who had been vetted and who were among the company’s most trusted employees. These dispatch riders would race across the world with padlocked briefcases, personally distributing keys to everyone who would receive messages from the bank over the next week. As business networks grew in size, as more messages were sent, and as more keys had to be delivered, the banks found that this distribution process became a horrendous logistical nightmare, and the overhead costs became prohibitive
Today, more than a hundred million people use the Internet to exchange information and send electronic mail messages, or e-mails.
His colleagues had told him he was crazy to do research in cryptography, because he would be competing with the NSA and their multibillion-dollar budget. How could he hope to discover something that they did not know already? And if he did discover anything, the NSA would classify it.
Ralph, like us, was willing to be a fool. And the way to get to the top of the heap in terms of developing original research is to be a fool, because only fools keep trying. You have idea number 1, you get excited, and it flops. Then you have idea number 2, you get excited, and it flops. Then you have idea number 99, you get excited, and it flops. Only a fool would be excited by the 100th idea, but it might take 100 ideas before one really pays off. Unless you’re foolish enough to be continually excited, you won’t have the motivation, you won’t have the energy to carry it through. God rewards fools.
“I walked into Ron Rivest’s office,” recalls Leonard Adleman, “and Ron had this paper in his hands. He started saying, ‘These Stanford guys have this really blah, blah, blah.’ And I remember thinking, ‘That’s nice, Ron, but I have something else I want to talk about.’ I was entirely unaware of the history of cryptography and I was distinctly uninterested in what he was saying.”
Adleman, a mathematician with enormous stamina, rigor and patience, was largely responsible for spotting the flaws in the ideas of Rivest and Shamir, ensuring that they did not waste time following false leads. Rivest and Shamir spent a year coming up with new ideas, and Adleman spent a year shooting them down.
His only criticism was with the list of authors. “I told Ron to take my name off the paper,” recalls Adleman. “I told him that it was his invention, not mine. But Ron refused and we got into a discussion about it. We agreed that I would go home and contemplate it for one night, and consider what I wanted to do. I went back the next day and suggested to Ron that I be the third author. I recall thinking that this paper would be the least interesting paper that I will ever be on.” Adleman could not have been more wrong. The system, dubbed RSA (Rivest, Shamir, Adleman) as opposed to ARS, went on to become the most influential cipher in modern cryptography.
However, instead of merely nibbling away at the problem, Ellis immediately looked for a radical and complete solution. “He would always approach a problem by asking, ‘Is this really what we want to do?’ ”
Cocks and Ellis had proved that the apparently impossible was possible, but nobody could find a way of making the possible practical.
A quick look on the Internet with a search engine turns up 15 Web pages mentioning Clifford Cocks, compared to 1,382 pages that mention Whitfield Diffie.
Whereas law enforcers argue that encryption should be banned because it would make Echelon ineffective, the civil libertarians argue that encryption is necessary exactly because it would make Echelon ineffective.
Whitfield Diffie states that individuals have enjoyed complete privacy for most of history: In the 1790s, when the Bill of Rights was ratified, any two people could have a private conversation-with a certainty no one in the world enjoys today-by walking a few meters down the road and looking to see no one was hiding in the bushes. There were no recording devices, parabolic microphones, or laser interferometers bouncing off their eyeglasses. You will note that civilization survived. Many of us regard that period as a golden age in American political culture.
Cryptography is a data-protection technology, just as gloves are a hand-protection technology. Cryptography
It is poor policy to clamp down indiscriminately on a technology just because some criminals might be able to use it to their advantage. For example, any U.S. citizen can freely buy a pair of gloves, even though a burglar might use them to ransack a house without leaving fingerprints. Cryptography is a data-protection technology, just as gloves are a hand-protection technology.
Kenneth Neil Cukier, a technology journalist, has written that: “The people involved in the crypto debate are all intelligent, honorable and proescrow, but they never possess more than two of these qualities at once.”
the NSA is still the world’s largest employer of mathematicians
“There was never any doubt that it would work,” recalls Bennett, “only that our fingers might be too clumsy to build it.” Bennett’s
“There was never any doubt that it would work,” recalls Bennett, “only that our fingers might be too clumsy to build it.”
Indeed, it is currently possible to build a quantum cryptography link between the White House and the Pentagon. Perhaps there already is one.