Cipher

Originating from the Arabic word for zero صفر (sifr), the word "cipher" spread to Europe as part of the Arabic numeral system during the Middle Ages. The Roman numeral system lacked the concept of zero, and this limited advances in mathematics. In this transition, the word was adopted into Medieval Latin as cifra, and then into Middle French as cifre. This eventually led to the English word cipher (minority spelling cypher). One theory for how the term came to refer to encoding is that the concept of zero was confusing to Europeans, and so the term came to refer to a message or communication that was not easily understood.[1]

The term cipher was later also used to refer to any Arabic digit, or to calculation using them, so encoding text in the form of Arabic numerals is literally converting the text to "ciphers".

In casual contexts, "code" and "cipher" can typically be used interchangeably, however, the technical usages of the words refer to different concepts. Codes contain meaning; words and phrases are assigned to numbers or symbols, creating a shorter message.

An example of this is the commercial telegraph code which was used to shorten long telegraph messages which resulted from entering into commercial contracts using exchanges of telegrams.

Another example is given by whole word ciphers, which allow the user to replace an entire word with a symbol or character, much like the way written Japanese utilizes Kanji (meaning Chinese characters in Japanese) characters to supplement the native Japanese characters representing syllables. An example using English language with Kanji could be to replace "The quick brown fox jumps over the lazy dog" by "The quick brown 狐 jumps 上 the lazy 犬". Stenographers sometimes use specific symbols to abbreviate whole words.

Ciphers, on the other hand, work at a lower level: the level of individual letters, small groups of letters, or, in modern schemes, individual bits and blocks of bits. Some systems used both codes and ciphers in one system, using superencipherment to increase the security. In some cases the terms codes and ciphers are used synonymously with substitution and transposition, respectively.

Historically, cryptography was split into a dichotomy of codes and ciphers, while coding had its own terminology analogous to that of ciphers: "encoding, codetext, decoding" and so on.

However, codes have a variety of drawbacks, including susceptibility to cryptanalysis and the difficulty of managing a cumbersome codebook. Because of this, codes have fallen into disuse in modern cryptography, and ciphers are the dominant technique.

There are a variety of different types of encryption. Algorithms used earlier in the history of cryptography are substantially different from modern methods, and modern ciphers can be classified according to how they operate and whether they use one or two keys.

Historical

Visual representation of how Caesar's Cipher works.

The Caesar Cipher is one of the earliest known cryptographic systems. Julius Caesar used a cipher that shifts the letters in the alphabet in place by three and wrapping the remaining letters to the front to write to Marcus Tullius Cicero in approximately 50 BC.[11]

Historical pen and paper ciphers used in the past are sometimes known as classical ciphers. They include simple substitution ciphers (such as ROT13) and transposition ciphers (such as a Rail Fence Cipher). For example, "GOOD DOG" can be encrypted as "PLLX XLP" where "L" substitutes for "O", "P" for "G", and "X" for "D" in the message. Transposition of the letters "GOOD DOG" can result in "DGOGDOO". These simple ciphers and examples are easy to crack, even without plaintext-ciphertext pairs.[2][3]

William Shakespeare often used the concept of ciphers in his writing to symbolize nothingness. In Shakespeare's Henry V, he relates one of the accounting methods that brought the Arabic Numeral system and zero to Europe, to the human imagination. The actors who perform this play were not at the battles of Henry V's reign, so they represent absence. In another sense, ciphers are important to people who work with numbers, but they do not hold value. Shakespeare used this concept to outline how those who counted and identified the dead from the battles used that information as a political weapon, furthering class biases and xenophobia.

In the 1640s, the Parliamentarian commander, Edward Montagu, 2nd Earl of Manchester, developed ciphers to send coded messages to his allies during the English Civil War.[4]

Simple ciphers were replaced by polyalphabetic substitution ciphers (such as the Vigenère) which changed the substitution alphabet for every letter. For example, "GOOD DOG" can be encrypted as "PLSX TWF" where "L", "S", and "W" substitute for "O". With even a small amount of known or estimated plaintext, simple polyalphabetic substitution ciphers and letter transposition ciphers designed for pen and paper encryption are easy to crack.[5] It is possible to create a secure pen and paper cipher based on a one-time pad though, but the usual disadvantages of one-time pads apply.

During the early twentieth century, electro-mechanical machines were invented to do encryption and decryption using transposition, polyalphabetic substitution, and a kind of "additive" substitution. In rotor machines, several rotor disks provided polyalphabetic substitution, while plug boards provided another substitution. Keys were easily changed by changing the rotor disks and the plugboard wires. Although these encryption methods were more complex than previous schemes and required machines to encrypt and decrypt, other machines such as the British Bombe were invented to crack these encryption methods.

In a pure mathematical attack, (i.e., lacking any other information to help break a cipher) two factors above all count:

• Computational power available, i.e., the computing power which can be brought to bear on the problem. It is important to note that average performance/capacity of a single computer is not the only factor to consider. An adversary can use multiple computers at once, for instance, to increase the speed of exhaustive search for a key (i.e., "brute force" attack) substantially.
• Key size, i.e., the size of key used to encrypt a message. As the key size increases, so does the complexity of exhaustive search to the point where it becomes impractical to crack encryption directly.

Since the desired effect is computational difficulty, in theory one would choose an algorithm and desired difficulty level, thus decide the key length accordingly.

An example of this process can be found at Key Length which uses multiple reports to suggest that a symmetrical cipher with 128 bits, an asymmetric cipher with 3072 bit keys, and an elliptic curve cipher with 256 bits, all have similar difficulty at present.

Claude Shannon proved, using information theory considerations, that any theoretically unbreakable cipher must have keys which are at least as long as the plaintext, and used only once: one-time pad.[6]

• Autokey cipher
• Cover-coding
• Encryption software
• List of ciphertexts
• Steganography
• Telegraph code

• Richard J. Aldrich, GCHQ: The Uncensored Story of Britain's Most Secret Intelligence Agency, HarperCollins July 2010.
• Helen Fouché Gaines, "Cryptanalysis", 1939, Dover. ISBN 0-486-20097-3
• Ibrahim A. Al-Kadi, "The origins of cryptology: The Arab contributions", Cryptologia, 16(2) (April 1992) pp. 97–126.
• David Kahn, The Codebreakers - The Story of Secret Writing (ISBN 0-684-83130-9) (1967)
• David A. King, The ciphers of the monks - A forgotten number notation of the Middle Ages, Stuttgart: Franz Steiner, 2001 (ISBN 3-515-07640-9)
• Abraham Sinkov, Elementary Cryptanalysis: A Mathematical Approach, Mathematical Association of America, 1966. ISBN 0-88385-622-0
• William Stallings, Cryptography and Network Security, principles and practices, 4th Edition
• Stinson, Douglas R. (1995), Cryptogtaphy / Theory and Practice, CRC Press, ISBN 0-8493-8521-0
• "Ciphers vs. Codes (Article) | Cryptography." Khan Academy, Khan Academy, https://www.khanacademy.org/computing/computer-science/cryptography/ciphers/a/ciphers-vs-codes.
• Caldwell, William Casey. "Shakespeare's Henry V and the Ciphers of History." SEL Studies in English Literature, 1500-1900, vol. 61, no. 2, 2021, pp. 241–68. EBSCOhost, doi:10.1353/sel.2022.0003.
• Luciano, Dennis, and Gordon Prichett. "Cryptology: From Caesar Ciphers to Public-Key Cryptosystems." The College Mathematics Journal, vol. 18, no. 1, 1987, pp. 2–17. JSTOR, https://doi.org/10.2307/2686311. Accessed 19 Feb. 2023.
• Ho Yean Li, et al. "Heuristic Cryptanalysis of Classical and Modern Ciphers." 2005 13th IEEE International Conference on Networks Jointly Held with the 2005 IEEE 7th Malaysia International Conf on Communic, Networks, 2005. Jointly Held with the 2005 IEEE 7th Malaysia International Conference on Communication., 2005 13th IEEE International Conference on, Networks and Communications, vol. 2, Jan. 2005. EBSCOhost, doi:10.1109/ICON.2005.1635595.

Look up cipher in Wiktionary, the free dictionary.

• Kish cypher