We had a number of possible topics to choose from and I choose cryptology, because I already had a passing interest in thanks to my attempts to code encryption algorithms for my computer programs. This Merchant Taylors’ School Webring site is owned by Oliver Pell. The use of obsolete and insecure DES cipher of cryptology is the science of secure communications, formed from the Greek words kryptós, “hidden”, and lógos, “word”.
Much of the terminology of cryptography can be linked back to the time when only written messages were being encrypted and the same terminology is still used regardless of whether it is being applied to a written message or a stream of binary code between two computers. The encrypted form of the PLAINTEXT. An unvarying rule for replacing a piece of information with another object, not necessarily of the same sort e. The science of the enciphering and deciphering of messages in secret code or cipher. The process of converting the CIPHER back into PLAINTEXT. The process of converting the PLAINTEXT into a CIPHER.
The secret information known only to the transmitter and the receiver which is used to secure the PLAINTEXT. A method of encryption where a letter in the plaintext is always replaced by the same letter in the ciphertext. The source information to be secured. A method of encryption where a letter in the plaintext is not always replaced by the same letter in the ciphertext. It seems reasonable to assume that people have tried to conceal information in written form since writing was developed and examples survive in stone inscriptions and papyruses showing that many ancient civilisations including the Egyptians, Hebrews and Assyrians all developed cryptographic systems. The Greeks were therefore the inventors of the first transposition cipher and in the fourth century BC the earliest treatise on the subject was written by a Greek, Aeneas Tacticus, as part of a work entitled On the Defence of Fortifications.
Another Greek, Polybius later devised a means of encoding letters into pairs of symbols using a device known as the Polybius checkerboard which contains many elements common to later encryption systems. The Polybius checkerboard consists of a five by five grid containing all the letters of the alphabet. Each letter is converted into two numbers, the first is the row in which the letter can be found and the second is the column. Hence the letter A becomes 11, the letter B 12 and so forth. The Arabs were the first people to clearly understand the principles of cryptography and to elucidate the beginning of cryptanalysis.
They devised and used both substitution and transposition ciphers and discovered the use of letter frequency distributions in cryptanalysis. As a result of this by approximately 1412 al-Kalka-shandi could include in his encyclopaedia Subh al-a’sha a respectable if elementary treatment of several cryptographic systems. European cryptography dates from the Middle Ages during which it was developed by the Papal and Italian city states. Circa 1379 the first European manual on cryptography, consisting of a compilation of ciphers, was produced by Gabriele de Lavinde of Parma, who served Pope Clement VII. During the US Civil War the Federal Army extensively used transposition ciphers. The Confederate Army primarily used the Vigenère cipher and on occasional monoalphabetic substitution. During the first world war both sides employed cipher systems almost exclusively for tactical communications while code systems were still used mainly for high-command and diplomatic communications.
Although field cipher systems such as the U. Signal Corps cipher disk lacked sophistication some complicated cipher systems were used for high-level communications by the end of the war. The most famous of these was the German ADFGVX fractionation cipher. In the 1920s the maturing of mechanical and electromechanical technology came together with the needs of telegraphy and radio to bring about a revolution in cryptodevices – the development of rotor cipher machines.
The Japanese cipher machines of World War 2 have an interesting history linking them to both the Hebern and the Enigma machines. After Herbert Yardley, an American cryptographer who organised and directed the U. The greatest triumphs of cryptanalysis occurred during the second world war – the Polish and British cracking of the Enigma ciphers and the American cryptanalysis of the Japanese RED, ORANGE and PURPLE ciphers. These developments played a major role in the Allies’ conduct of World War 2.
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After World War 2 the electronics that had been developed in support of radar were adapted to cryptomachines. The first electrical cryptomachines were little more than rotor machines where the rotors had been replaced by electronic substitutions. The only advantage of these electronic rotor machines was their speed of operation and they inherited the inherent weaknesses of the mechanical rotor machines. There is little information available regarding the secret cipher machines of the 1960s and it is likely that this subject will remain the shrouded in rumour until the relevant information is de-classified. The mathematical operation that changes the plaintext into the ciphertext using the encryption key.
Whether a block or a stream cipher is produced. The type of key system used – single or two key. The actual order of the units of the plaintext is not changed. The simplest substitution cipher is one where the alphabet of the cipher is merely a shift of the plaintext alphabet, for example, A might be encrypted as B, C as D and so forth. Of this type of cipher, the most well known is the Caesar cipher, used by Julius Caesar in which A becomes D etc.
It is easy to guess that cyclical-shift substitution ciphers of this sort are not at all secure because individual letter frequencies are left completely intact. There are primarily two approaches that have been used with substitution ciphers to reduce the extent to which the structure of the plaintext, including the letter frequencies, survives into the ciphertext. One of these methods is to treat more than a single letter as one element i. The other method is to use several different cipher alphabets. By treating two successive letters as a single unit the extent to which the original letter frequency distribution survives is reduced, thus making the job of the cryptanalysts harder, but not impossible since it can be shown that digraphs themselves have a high degree of correlation. Charles Wheatstone was a 19th century English physicist, born on February 6th, 1802. As well as devising the Playfair cipher he also invented the Wheatstone bridge, a device for accurately measuring electrical resistance which became widely used in laboratories.
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He also initiated the usage of electromagnets in electric generators and devised the stereoscope, a device for viewing pictures in three dimensions still used today. Here is an example of a Playfair cipher. If the plaintext contains an odd number of letters then an X is appended to the last word to make it an even number. Also, if any of the digraphs consist of identical letters e. SUMMER, then an extra letter is placed between them. The first step in performing the encryption is to locate the two letters from the plaintext in the matrix. If the pair of letters are in different rows and columns.
The rows of the ciphertext letters are kept the same as the rows of the plaintext letters, however the columns swap. If the pair of letters are in the same row. The ciphertext letters are the letters to the right of the plaintext letters. For example, T and A are in the same row so T will encrypt to S and A will encrypt to B, forming SB. If the pair of letters are in the same column. The ciphertext letters are the letters below the plaintext letters.
For example, Y and L are in the same column so Y becomes A and L becomes R, forming AR. The other approach to concealing plaintext structure in the ciphertext involves using several different substitution ciphers. The resulting ciphers, which are generically known as polyalphabetics, have a long history of usage. For many years this cipher was thought to be impregnable and it is rumoured that a well known scientific magazine pronounced it “uncrackable” as late as 1917, despite the fact that it had been broken by then.
In the simplest system of the Vigenère type the key is a word or a phrase which is repeated over and over again. The plaintext is encrypted using the table shown as Figure 4. The ciphertext letter is found at the intersection of the column headed by the plaintext letter and the row indexed by the key letter. To decrypt the plaintext letter is found at the head of the column determined by the intersection of the diagonal containing the cipher letter and the row containing the key letter. It is the periodicity of the repeating key which leads to the weaknesses in this method and its vulnerabilities to cryptanalysis.
This periodicity of a repeating key can be eliminated by the use of a running-key Vigenère cipher, produced when a non-repeating key is used. Transposition ciphers rearrange the letters of the plaintext without changing the letters themselves. For example, a very simple transposition cipher is the rail fence, in which the plaintext is staggered between two rows and then read off to give the ciphertext. Which is read out as: MRHNTYOSCOLECATALRSHO.
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The rail fence is the simplest example of a class of transposition ciphers called route ciphers. These were quite popular in the early history of cryptography. Obviously, to even approach an acceptable level of security, the route would have to be much more complicated than the one in this example. One form of transposition that has enjoyed widespread use relies on identifying the route by means of an easily remembered keyword. This can be done in several ways.
One way, as in this example, is to define the order in which each column is written depending on the alphabetical position of each letter of the keyword relative to the other letters. Unlike the previous example the plaintext has been written into the columns from left to right as normal, and the ciphertext will be formed by reading down the columns. The order in which the columns are written to form the ciphertext is determined by the key. This matrix therefore yields the ciphertext: MNOOHYCZCASZETRORTSLALHZ. The first column is first because C is the earliest in the alphabet, followed by the second to last column because E is the next in the alphabet. The security of this method of encryption can be significantly improved by re-encrypting the resulting cipher using another transposition. Because the product of the two transpositions is also a transposition, the effect of multiple transpositions is to define a complex route through the matrix which would not by itself by easy to define with a simply remembered mnemonic.
In modern cryptography transposition cipher systems serve mainly as one of several methods used as a step in forming a product cipher. In the days of manual cryptography i. There was also some use of a particular class of product ciphers called fractionation systems. One of the most famous field ciphers ever was a fractionation system – the ADFGVX cipher which was employed by the German Army during the first world war. 6 matrix to substitution-encrypt the 26 letters of the alphabet and 10 digits into pairs of the symbols A, D, F, G, V and X. Here is an example of enciphering the phrase “Merchant Taylors” with this cipher using the key word “Subject”. This intermediate ciphertext can then be put in a transposition matrix based on a different key.
The final cipher is therefore: FAFDFGDDFAVXAAFGXVDXADDVGFDAFA. Generally, ciphers transform pieces of plaintext of a fixed size into ciphertext. A block cipher is a type of symmetric-key encryption algorithm that changes a fixed-length block of the plaintext into the same length of ciphertext. The encryption works by means of a key. Decryption is simply the reverse of the encryption process using the same secret key. The fixed length is called the block size and for modern block ciphers is usually 64 bits. As processors become more sophisticated, however, it is likely that this block size will increase to 128 bits.
Since different plaintext blocks are mapped to different ciphertext blocks, a block cipher effectively provides a permutation of the set of all possible messages. The actual permutation produced during any particular operation is of course secret, and determined by the key. An example of an iterated block cipher is a Feistel cipher. Feistel ciphers are a special class of iterated block ciphers. In this type of cipher the ciphertext is calculated from the repeated application of the same round function. A stream cipher also breaks the plaintext into units, this time it is normally a single character. It then encrypts the nth unit of the plaintext with the nth unit of the key stream.
Stream ciphers can be designed to be exceptionally fast, much faster than any block cipher. A stream cipher generates what is known as a keystream – a sequence of bits, which is used as a key. The encryption process involves combining the keystream with the plaintext. The majority of stream cipher designs are for synchronous stream ciphers. Interest in stream ciphers is currently attributed to the appealing properties of the one-time pad. A one-time pad, which is sometimes called the Vernam cipher, uses a keystream which is the same length as the plaintext message and consists of a series of bits generated completely at random. At this time there is no de facto standard for stream ciphers although the most widely used stream cipher is RC4, a stream cipher designed by Rivest for RSA Data Security Inc.
It is a variable key-size stream cipher with an algorithm based on the use of a random permutation. Strangely, certain modes of operation of a block cipher transform it into a keystream generator and so, in this way, any block cipher can be used as a stream cipher. Stream ciphers with a dedicated design and typically much faster, however. This is a mechanism for generating a sequence of binary bits. LFSRs are easy to implement and fast operating in both hardware and software however a single LFSR is not secure because over the years a mathematical framework has been developed which allows for the analysis of their output. National Institute of Standards and Technology played a substantial role in the final stages of developing DES. DES is the most well known and widely used symmetric algorithm in the world.
DES has a 64-bit block size and uses a 56-bit key during encryption. DES is a 16-round Feistel cipher and was originally designed for implementation in hardware. Because it is a single-key cryptosystem, when used for communication both sender and receiver must know the same secret key which can be used to encrypt or decrypt the message. DES can also be used by a single-user, for example to store files on a hard disk securely. No easy attack on DES has yet been discovered, despite research efforts over many years. There is no feasible way to “break” DES other than an exhaustive search – a process which takes 255 steps on average.
However, cryptanalysis methods which rely on knowledge of some of the plaintext have had some success. The consensus of the cryptography community is that, if it is not currently so, DES will soon be insecure. Up to this point all the examples have assumed that the encryption process is undertaken with the same key as the decryption process, and that only the sender and the receiver possess the secret key. A major problem in the practical use of single-key cryptography is the key distribution problem. This problem basically occurs because both the sender and receiver must hold a copy of the key, but they must also prevent others from gaining a copy of the key. This does not, on the face of it, appear to be a problem, but it can be one as is probably best illustrated by an example. Suppose that two individuals, O and L, wish to exchange information securely but can not guarantee the security of the transmission itself.
They would probably use some sort of encryption to ensure that even if the message was intercepted its contents would remain secret. In order for this to operate they would both have to know a secret key which could be used to encrypt the data. However, since the transmission medium is not secure they would have to meet in person to decide upon the key. This appears to be working perfectly, except a problem could soon arrive. Suppose that O or L then wanted to correspond with another individual, T. If they were to give T the key they would further compromise it because C would now have another source from which he might obtain it. Now consider a system with 1,000 members, all of whom wish to communicate in secret with each other.
In this case, each individual would need to hold a key for every individual besides himself, in other words 999 keys for other people. Each individual would also have to protect those 999 keys from being compromised. It is possible to calculate the number of keys present in a system with any number of members using these facts as I have done below, calculating the number of keys required by multiplying the number of members minus one by the number of members and divided by two. The reason why I have included a column containing the number of members squared is made obvious below.
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As you can see the number of different keys required is nearly proportional to the square of the number of members in the system. This is the key distribution problem. A solution to the key distribution problem can be found in public key, or two-key, cryptography. Public Key cryptography is based on the idea that a user can possess two keys – one public and one private key.
The public key can only be used to encrypt the data to be sent and the private key can only be used to decrypt it. The fact that anyone can use a single “locking” key to encrypt a message which they are confident can still only be read by a single authorised user means that the number of keys required can be greatly reduced. For example I will use a far simpler three user system. An individual, say P, could distribute his public key to two other individuals, A and C. A could then send a message to P by encrypting it with the public key. When P receives the message he could then decrypt and read the message using his private key. There is a problem with this solution however.
In this example, although C can not read or alter a message sent to P by A, he or she could easily fake a message because C has the same public key as A. Therefore, with a public key system the ability to authenticate messages has been given up in return for privacy. In many cases this will not be a problem however there are times when it will be so. There is an alternative to this method. A could then encrypt messages with his public key and send them to either P or C. P and C can now decrypt the message. In this example secrecy has been sacrificed in order to maintain an ability to authenticate the message.
This is a problem with the public key system which can only be solved by increasing the number of keys in the system. It can be solved however, by combining the two methods outlined above. If each user had two sets of public and private keys and distributed one key from each set then the capability to authenticate messages and to keep them secret would be maintained. For example, another three individuals P, D and W are using this system. Under this system each message is encrypted twice, once in a way which only the intended receiver can decrypt it, and once in which only the authentic sender could have encrypted it. Even though the number of keys required has been increased it still does not approach the number of keys which would be required for a single-key system of the same size.