by Simon Singh
Even though we are dealing with computers and numbers, and not machines and letters, the encryption still proceeds by the age-old principles of substitution and transposition, in which elements of the message are substituted for other elements, or their positions are switched, or both. Every encipherment, no matter how complex, can be broken down into combinations of these simple operations. The following two examples demonstrate the essential simplicity of computer encipherment by showing how a computer might perform an elementary substitution cipher and an elementary transposition cipher.
First, imagine that we wish to encrypt the message HELLO, employing a simple computer version of a transposition cipher. Before encryption can begin, we must translate the message into ASCII according to Table 24:
One of the simplest forms of transposition cipher would be to swap the first and second digits, the third and fourth digits, and so on. In this case the final digit would remain unchanged because there are an odd number of digits. In order to see the operation more clearly, I have removed the spaces between the ASCII blocks in the original plaintext to generate a single string, and then lined it up against the resulting ciphertext for comparison:
An interesting aspect of transposition at the level of binary digits is that the transposing can happen within the letter. Furthermore, bits of one letter can swap places with bits of the neighboring letter. For example, by swapping the seventh and eighth numbers, the final 0 of H is swapped with the initial 1 of E. The encrypted message is a single string of 35 binary digits, which can be transmitted to the receiver, who then reverses the transposition to re-create the original string of binary digits. Finally, the receiver reinterprets the binary digits via ASCII to regenerate the message HELLO.
Table 24 ASCII binary numbers for the capital letters.
Next, imagine that we wish to encrypt the same message, HELLO, this time employing a simple computer version of a substitution cipher. Once again, we begin by converting the message into ASCII before encryption. As usual, substitution relies on a key that has been agreed between sender and receiver. In this case the key is the word DAVID translated into ASCII, and it is used in the following way. Each element of the plaintext is “added” to the corresponding element of the key. Adding binary digits can be thought of in terms of two simple rules. If the elements in the plaintext and the key are the same, the element in the plaintext is substituted for 0 in the ciphertext. But, if the elements in the message and key are different, the element in the plaintext is substituted for 1 in the ciphertext:
The resulting encrypted message is a single string of 35 binary digits which can be transmitted to the receiver, who uses the same key to reverse the substitution, thus recreating the original string of binary digits. Finally, the receiver reinterprets the binary digits via ASCII to regenerate the message HELLO.
Computer encryption was restricted to those who had computers, which in the early days meant the government and the military. However, a series of scientific, technological and engineering breakthroughs made computers, and computer encryption, far more widely available. In 1947, AT&T Bell Laboratories invented the transistor, a cheap alternative to the electronic valve. Commercial computing became a reality in 1951 when companies such as Ferranti began to make computers to order. In 1953 IBM launched its first computer, and four years later it introduced Fortran, a programming language that allowed “ordinary” people to write computer programs. Then, in 1959, the invention of the integrated circuit heralded a new era of computing.
During the 1960s, computers became more powerful, and at the same time they became cheaper. Businesses were increasingly able to afford computers, and could use them to encrypt important communications such as money transfers or delicate trade negotiations. However, as more and more businesses bought computers, and as encryption between businesses spread, cryptographers were confronted with new problems, difficulties that had not existed when cryptography was the preserve of governments and the military. One of the primary concerns was the issue of standardization. A company might use a particular encryption system to ensure secure internal communication, but it could not send a secret message to an outside organization unless the receiver used the same system of encryption. Eventually, on May 15, 1973, America’s National Bureau of Standards planned to solve the problem, and formally requested proposals for a standard encryption system that would allow business to speak secretly unto business.
One of the more established cipher algorithms, and a candidate for the standard, was an IBM product known as Lucifer. It had been developed by Horst Feistel, a German émigré who had arrived in America in 1934. He was on the verge of becoming a U.S. citizen when America entered the war, which meant that he was placed under house arrest until 1944. For some years after, he suppressed his interest in cryptography to avoid arousing the suspicions of the American authorities. When he did eventually begin research into ciphers, at the Air Force’s Cambridge Research Center, he soon found himself in trouble with the National Security Agency (NSA), the organization with overall responsibility for maintaining the security of military and governmental communications, and which also attempts to intercept and decipher foreign communications. The NSA employs more mathematicians, buys more computer hardware, and intercepts more messages than any other organization in the world. It is the world leader when it comes to snooping.
The NSA did not object to Feistel’s past, they merely wanted to have a monopoly on cryptographic research, and it seems that they arranged for Feistel’s research project to be canceled. In the 1960s Feistel moved to the Mitre Corporation, but the NSA continued to apply pressure and forced him to abandon his work for a second time. Feistel eventually ended up at IBM’s Thomas J. Watson Laboratory near New York, where for several years he was able to conduct his research without being harassed. It was there, during the early 1970s, that he developed the Lucifer system.
Lucifer encrypts messages according to the following scrambling operation. First, the message is translated into a long string of binary digits. Second, the string is split into blocks of 64 digits, and encryption is performed separately on each of the blocks. Third, focusing on just one block, the 64 digits are shuffled, and then split into two half-blocks of 32, labeled Left0 and Right0. The digits in Right0 are then put through a “mangler function,” which changes the digits according to a complex substitution. The mangled Right0 is then added to Left0 to create a new halfblock of 32 digits called Right1. The original Right0 is relabeled Left1. This set of operations is called a “round.” The whole process is repeated in a second round, but starting with the new half-blocks, Left1 and Right1, and ending with Left2 and Right2. This process is repeated until there have been 16 rounds in total. The encryption process is a bit like kneading a slab of dough. Imagine a long slab of dough with a message written on it. First, the long slab is divided into blocks that are 64 cm in length. Then, one half of one of the blocks is picked up, mangled, folded over, added to the other half and stretched to make a new block. Then the process is repeated over and over again until the message has been thoroughly mixed up. After 16 rounds of kneading the ciphertext is sent, and is then deciphered at the other end by reversing the process.
The exact details of the mangler function can change, and are determined by a key agreed by sender and receiver. In other words, the same message can be encrypted in a myriad of different ways depending on which key is chosen. The keys used in computer cryptography are simply numbers. Hence, the sender and receiver merely have to agree on a number in order to decide the key. Thereafter, encryption requires the sender to input the key number and the message into Lucifer, which then outputs the ciphertext. Decryption requires the receiver to input the same key number and the ciphertext into Lucifer, which then outputs the original message.
Lucifer was generally held to be one of the strongest commercially available encryption products, and consequently it was used by a variety of organizations. It seemed inevitable that this encryption system would be adopt
ed as the American standard, but once again the NSA interfered with Feistel’s work. Lucifer was so strong that it offered the possibility of an encryption standard that was probably beyond the codebreaking capabilities of the NSA; not surprisingly, the NSA did not want to see an encryption standard that they could not break. Hence, it is rumored that the NSA lobbied to weaken one aspect of Lucifer, the number of possible keys, before allowing it to be adopted as the standard.
The number of possible keys is one of the crucial factors determining the strength of any cipher. A cryptanalyst trying to decipher an encrypted message could attempt to check all possible keys, and the greater the number of possible keys, the longer it will take to find the right one. If there are only 1,000,000 possible keys, a cryptanalyst could use a powerful computer to find the correct one in a matter of minutes, and thereby decipher an intercepted message. However, if the number of possible keys is large enough, finding the correct key becomes impractical. If Lucifer were to become the encryption standard, then the NSA wanted to ensure that it operated with only a restricted number of keys.
The NSA argued in favor of limiting the number of keys to roughly 100,000,000,000,000,000 (technically referred to as 56 bits, because this number consists of 56 digits when written in binary). It seems that the NSA believed that such a key would provide security within the civilian community, because no civilian organization had a computer powerful enough to check every possible key within a reasonable amount of time. However, the NSA itself, with access to the world’s greatest computing resource, would just about be able to break into messages. The 56-bit version of Feistel’s Lucifer cipher was officially adopted on November 23, 1976, and was called the Data Encryption Standard (DES). A quarter of a century later, DES remains America’s official standard for encryption.
The adoption of DES solved the problem of standardization, encouraging businesses to use cryptography for security. Furthermore, DES was strong enough to guarantee security against attacks from commercial rivals. It was effectively impossible for a company with a civilian computer to break into a DES-encrypted message because the number of possible keys was sufficiently large. Unfortunately, despite standardization and despite the strength of DES, businesses still had to deal with one more major issue, a problem known as key distribution.
Imagine that a bank wants to send some confidential data to a client via a telephone line, but is worried that there might be somebody tapping the wire. The bank picks a key and uses DES to encrypt the data message. In order to decrypt the message, the client needs not only to have a copy of DES on its computer, but also to know which key was used to encrypt the message. How does the bank inform the client of the key? It cannot send the key via the telephone line, because it suspects that there is an eavesdropper on the line. The only truly secure way to send the key is to hand it over in person, which is clearly a time-consuming task. A less secure but more practical solution is to send the key via a courier. 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.
The problem of key distribution has plagued cryptographers throughout history. For example, during the Second World War the German High Command had to distribute the monthly book of day keys to all its Enigma operators, which was an enormous logistical problem. Also, Uboats, which tended to spend extended periods away from base, had to somehow obtain a regular supply of keys. In earlier times, users of the Vigenère cipher had to find a way of getting the keyword from the sender to the receiver. No matter how secure a cipher is in theory, in practice it can be undermined by the problem of key distribution.
To some extent, government and the military have been able to deal with the problem of key distribution by throwing money and resources at it. Their messages are so important that they will go to any lengths to ensure secure key distribution. The U.S. Government keys are managed and distributed by COMSEC, short for Communications Security. In the 1970s, COMSEC was responsible for transporting tons of keys every day. When ships carrying COMSEC material came into dock, crypto-custodians would march onboard, collect stacks of cards, paper tapes, floppy disks, or whatever other medium the keys might be stored on, and then deliver them to the intended recipients.
Key distribution might seem a mundane issue, but it became the overriding problem for postwar cryptographers. If two parties wanted to communicate securely, they had to rely on a third party to deliver the key, and this became the weakest link in the chain of security. The dilemma for businesses was straightforward-if governments with all their money were struggling to guarantee the secure distribution of keys, then how could civilian companies ever hope to achieve reliable key distribution without bankrupting themselves?
Despite claims that the problem of key distribution was unsolvable, a team of mavericks triumphed against the odds and came up with a brilliant solution in the mid-1970s. They devised an encryption system that appeared to defy all logic. Although computers transformed the implementation of ciphers, the greatest revolution in twentieth-century cryptography has been the development of techniques to overcome the problem of key distribution. Indeed, this breakthrough is considered to be the greatest cryptographic achievement since the invention of the monoalphabetic cipher, over two thousand years ago.
God Rewards Fools
Whitfield Diffie is one of the most ebullient cryptographers of his generation. The mere sight of him creates a striking and somewhat contradictory image. His impeccable suit reflects the fact that for most of the 1990s he has been employed by one of America’s giant computer companies-currently his official job title is Distinguished Engineer at Sun Microsystems. However, his shoulder-length hair and long white beard betray the fact that his heart is still stuck in the 1960s. He spends much of his time in front of a computer workstation, but he looks as if he would be equally comfortable in a Bombay ashram. Diffie is aware that his dress and personality can have quite an impact on others, and comments that, “People always think that I am taller than I really am, and I’m told it’s the Tigger effect—‘No matter his weight in pounds, shillings and ounces, he always seems bigger because of the bounces.’ ”
Diffie was born in 1944, and spent most of his early years in Queens, New York. As a child he became fascinated by mathematics, reading books ranging from The Chemical Rubber Company Handbook of Mathematical Tables to G.H. Hardy’s Course of Pure Mathematics. He went on to study mathematics at the Massachusetts Institute of Technology, graduating in 1965. He then took a series of jobs related to computer security, and by the early 1970s he had matured into one of the few truly independent security experts, a freethinking cryptographer, not employed by the government or by any of the big corporations. In hindsight, he was the first cypherpunk.
Diffie was particularly interested in the key distribution problem, and he realized that whoever could find a solution would go down in history as one of the all-time great cryptographers. Diffie was so captivated by the problem of key distribution that it became the most important entry in his special notebook entitled “Problems for an Ambitious Theory of Cryptography.” Part of Diffie’s motivation came from his vision of a wired world. Back in the 1960s, the U.S. Department of Defense began funding a cutting-edge research organization called the Advanced Research Projects Agency (ARPA), and one of ARPA’s front-line projects was to find a way of connecting military computers across vast distances. This would allow a computer that had been damaged to transfer its responsibilities to another one in the network. The main aim was to make the Pentagon’s computer infrastructure more robust in the face of nuclear attack,
but the network would also allow scientists to send messages to each other, and perform calculations by exploiting the spare capacity of remote computers. The ARPANet was born in 1969, and by the end of the year there were four connected sites. The ARPANet steadily grew in size, and in 1982 it spawned the Internet. At the end of the 1980s, non-academic and nongovernmental users were given access to the Internet, and thereafter the number of users exploded. Today, more than a hundred million people use the Internet to exchange information and send electronic mail messages, or e-mails.
Figure 62 Whitfield Diffie. (photo credit 6.1)
While the ARPANet was still in its infancy, Diffie was farsighted enough to forecast the advent of the information superhighway and the digital revolution. Ordinary people would one day have their own computers, and these computers would be interconnected via phone lines. Diffie believed that if people then used their computers to exchange emails, they deserved the right to encrypt their messages in order to guarantee their privacy. However, encryption required the secure exchange of keys. If governments and large corporations were having trouble coping with key distribution, then the public would find it impossible, and would effectively be deprived of the right to privacy.
Diffie imagined two strangers meeting via the Internet, and wondered how they could send each other an encrypted message. He also considered the scenario of a person wanting to buy a commodity on the Internet. How could that person send an e-mail containing encrypted credit card details so that only the Internet retailer could decipher them? In both cases, it seemed that the two parties needed to share a key, but how could they securely exchange keys? The number of casual contacts and the amount of spontaneous e-mails among the public would be enormous, and this would mean that key distribution would be impractical. Diffie was fearful that the necessity of key distribution would prevent the public from having access to digital privacy, and he became obsessed with the idea of finding a solution to the problem.
