Detail Caesar cipher The action of a Caesar cipher is to replace each plaintext letter with one a fixed number of places down the alphabet. This example is with a shift of three, so that a B in the plaintext becomes E in the ciphertext. substitution cipher Susceptible to frequency analysis and brute force attacks. In Cryptography, a substitution cipher is a method of Encryption by which units of plaintext are substituted with Ciphertext according to a regular system Cryptanalysis (from the Greek kryptós, "hidden" and analýein, "to loosen" or "to untie" is the study of methods for In Cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a Ciphertext.

In cryptography, a Caesar cipher, also known as a Caesar's cipher, the shift cipher, Caesar's code or Caesar shift, is one of the simplest and most widely known encryption techniques. Cryptography (or cryptology; from Greek grc κρυπτός kryptos, "hidden secret" and grc γράφω gráphō, "I write" It is a type of substitution cipher in which each letter in the plaintext is replaced by a letter some fixed number of positions down the alphabet. In Cryptography, a substitution cipher is a method of Encryption by which units of plaintext are substituted with Ciphertext according to a regular system In Cryptography, plaintext is the information which the sender wishes to transmit to the receiver(s An alphabet is a standardized set of letters basic written symbols each of which roughly represents a Phoneme, a Spoken language, either For example, with a shift of 3, A would be replaced by D, B would become E, and so on. The method is named after Julius Caesar, who used it to communicate with his generals.

The encryption step performed by a Caesar cipher is often incorporated as part of more complex schemes, such as the Vigenère cipher, and still has modern application in the ROT13 system. The Vigenère cipher is a method of encrypting Alphabetic text by using a series of different Caesar ciphers based on the letters of a keyword ROT13 (" rotate by 13 places " sometimes hyphenated ROT-13) is a simple Substitution cipher used in Online forums as a means of As with all single alphabet substitution ciphers, the Caesar cipher is easily broken and in practice offers essentially no communication security.

## Example

The transformation can be represented by aligning two alphabets; the cipher alphabet is the plain alphabet rotated left or right by some number of positions. An alphabet is a standardized set of letters basic written symbols each of which roughly represents a Phoneme, a Spoken language, either For instance, here is a Caesar cipher using a left rotation of three places (the shift parameter, here 3, is used as the key):

`Plain:   ABCDEFGHIJKLMNOPQRSTUVWXYZCipher:  DEFGHIJKLMNOPQRSTUVWXYZABC`

To encrypt a message, simply look up each letter of the message in the "plain" line and write down the corresponding letter in the "cipher" line. In Cryptography, a key is a piece of information (a Parameter) that determines the functional output of a cryptographic algorithm To decipher, do the reverse.

`Plaintext:  the quick brown fox jumps over the lazy dogCiphertext: WKH TXLFN EURZQ IRA MXPSV RYHU WKH ODCB GRJ`

The encryption can also be represented using modular arithmetic by first transforming the letters into numbers, according to the scheme, A = 0, B = 1,. In Mathematics, modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of Arithmetic for Integers . . , Z = 25. Encryption of a letter x by a shift n can be described mathematically as,

$E_n(x) = (x + n) \mod {26}.$

Decryption is performed similarly,

$D_n(x) = (x - n) \mod {26}.$

(Note, there are different definitions for the modulo operation. In the above, the result is in the range 0. . . 25. I. e. , if x+n or x-n are not in the range 0. . . 25, we have to subtract or add 26. )

The replacement remains the same throughout the message, so the cipher is classed as a type of monoalphabetic substitution, as opposed to polyalphabetic substitution. In Cryptography, a substitution cipher is a method of Encryption by which units of plaintext are substituted with Ciphertext according to a regular system A polyalphabetic cipher is any cipher based on substitution, using multiple substitution alphabets

## History and usage

The Caesar cipher is named for Julius Caesar, who used an alphabet with a left shift of three.

The Caesar cipher is named after Julius Caesar, who, according to Suetonius, used it with a shift of three to protect messages of military significance:

If he had anything confidential to say, he wrote it in cipher, that is, by so changing the order of the letters of the alphabet, that not a word could be made out. If anyone wishes to decipher these, and get at their meaning, he must substitute the fourth letter of the alphabet, namely D, for A, and so with the others.

While Caesar's was the first recorded use of this scheme, other substitution ciphers are known to have been used earlier. Gaius Suetonius Tranquillus, commonly known as Suetonius (ca 69/75 &ndash after 130 was an equestrian and a historian during the Roman Empire. His nephew, Augustus, also used the cipher, but with a right shift of one, and it did not wrap around to the beginning of the alphabet:

Whenever he wrote in cipher, he wrote B for A, C for B, and the rest of the letters on the same principle, using AA for X. Augustus ( Latin: IMPERATOR·CAESAR·DIVI·FILIVS·AVGVSTVS September 23 63 BC – August 19 AD 14) born Gaius Octavius Thurinus, was

SuetoniusLife of Augustus 88

There is evidence that Julius Caesar used more complicated systems as well, and one writer, Aulus Gellius, refers to a (now lost) treatise on his ciphers:

There is even a rather ingeniously written treatise by the grammarian Probus concerning the secret meaning of letters in the composition of Caesar's epistles. Gaius Suetonius Tranquillus, commonly known as Suetonius (ca 69/75 &ndash after 130 was an equestrian and a historian during the Roman Empire. Aulus Gellius (ca 125 AD—after 180 AD Latin author and grammarian possibly of African origin probably born and certainly brought up at Rome.

Aulus GelliusAttic Nights 17. Aulus Gellius (ca 125 AD—after 180 AD Latin author and grammarian possibly of African origin probably born and certainly brought up at Rome. 9. 1–5

It is unknown how effective the Caesar cipher was at the time, but it is likely to have been reasonably secure, not least because few of Caesar's enemies would have been literate in Latin or even familiar with written language, let alone able to consider cryptanalysis. traditional definition of literacy is considered to be the ability to read and write or the ability to use Language to read, write, listen, Cryptanalysis (from the Greek kryptós, "hidden" and analýein, "to loosen" or "to untie" is the study of methods for Assuming that an attacker could read the message, there is no record at that time of any techniques for the solution of simple substitution ciphers. The earliest surviving records date to the 9th century works of Al-Kindi in the Arab world with the discovery of frequency analysis. ( أبو يوسف يعقوب إبن إسحاق الكندي) (c The araB gene Promoter is a bacterial promoter activated by e L-arabinose binding In Cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a Ciphertext. [1]

A Caesar cipher with a shift of one appears on the back of the Mezuzah. A mezuzah (מזוזה "doorpost" (plural mezuzot (מזוזות is a piece of Parchment (usually contained in a decorative case [2]

In the 19th century, the personal advertisements section in newspapers would sometimes be used to exchange messages encrypted using simple cipher schemes. Kahn (1967) describes instances of lovers engaging in secret communications enciphered using the Caesar cipher in The Times. David Kahn (b February 7, 1930) is a US Historian, Journalist and Writer. The Times is a daily national Newspaper published in the United Kingdom since 1785 when it was known as The Daily Universal Register. [3] Even as late as 1915, the Caesar cipher was in use: the Russian army employed it as a replacement for more complicated ciphers which had proved to be too difficult for their troops to master; German and Austrian cryptanalysts had little difficulty in decrypting their messages. [4]

Caesar ciphers can be found today in children's toys such as secret decoder rings. A secret decoder was an inexpensive toy popular among young children from the 1930s through the rest of the 20th century A Caesar shift of thirteen is also performed in the ROT13 algorithm, a simple method of obfuscating text used in some Internet forums to obscure text (such as joke punchlines and story spoilers), but not used as a method of encryption. ROT13 (" rotate by 13 places " sometimes hyphenated ROT-13) is a simple Substitution cipher used in Online forums as a means of In Mathematics, Computing, Linguistics and related subjects an algorithm is a sequence of finite instructions often used for Calculation

The Vigenère cipher uses a Caesar cipher with a different shift at each position in the text; the value of the shift is defined using a repeating keyword. The Vigenère cipher is a method of encrypting Alphabetic text by using a series of different Caesar ciphers based on the letters of a keyword If a single-use keyword is as long as the message and chosen randomly then this is a one-time pad cipher, unbreakable if the users maintain the keyword's secrecy. In Cryptography, the one-time pad (OTP is an Encryption Algorithm where the Plaintext is combined with a random key or "pad" Keywords shorter than the message (e. g. , "Complete Victory"), used historically, introduce a cyclic pattern that might be detected with a statistically advanced version of frequency analysis. The Vigenère cipher is a method of encrypting Alphabetic text by using a series of different Caesar ciphers based on the letters of a keyword

In April 2006, fugitive Mafia boss Bernardo Provenzano was captured in Sicily partly because of cryptanalysis of his messages written in a variation of the Caesar cipher. The Mafia (also known as Cosa Nostra) is a Sicilian Criminal Secret society which is believed to have first developed in the mid-19th century Bernardo Provenzano (born January 31, 1933 in Corleone, Italy) is a member of the Sicilian Mafia ( Cosa Nostra Sicily ( Italian and Sicilian: Sicilia) is an autonomous region of Italy. Provenzano's cipher used numbers, so that "A" would be written as "4", "B" as "5", and so on. [5]

## Breaking the cipher

Decryption
shift
Candidate plaintext
0exxegoexsrgi
1dwwdfndwrqfh
2cvvcemcvqpeg
3buubdlbupodf
4attackatonce
5zsszbjzsnmbd
6yrryaiyrmlac
. . .
23haahjrhavujl
24gzzgiqgzutik
25fyyfhpfytshj

The Caesar cipher can be easily broken even in a ciphertext-only scenario. In Cryptography, a ciphertext-only attack (COA or known ciphertext attack is an Attack model for Cryptanalysis where the attacker is assumed Two situations can be considered:

1. an attacker knows (or guesses) that some sort of simple substitution cipher has been used, but not specifically that it is a Caesar scheme;
2. an attacker knows that a Caesar cipher is in use, but does not know the shift value.

In the first case, the cipher can be broken using the same techniques as for a general simple substitution cipher, such as frequency analysis or pattern words. In Cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a Ciphertext. While solving, it is likely that an attacker will quickly notice the regularity in the solution and deduce that a Caesar cipher is the specific algorithm employed.

The distribution of letters in a typical sample of English language text has a distinctive and predictable shape. A Caesar shift "rotates" this distribution, and it is possible to determine the shift by examining the resultant frequency graph.

In the second instance, breaking the scheme is even more straightforward. Since there are only a limited number of possible shifts (26 in English), they can each be tested in turn in a brute force attack. In Cryptanalysis, a brute force attack is a method of defeating a Cryptographic scheme by trying a large number of possibilities for example possible keys [6] One way to do this is to write out a snippet of the ciphertext in a table of all possible shifts — a technique sometimes known as "completing the plain component". [7] The example given is for the ciphertext "EXXEGOEXSRGI"; the plaintext is instantly recognisable by eye at a shift of four. Another way of viewing this method is that, under each letter of the ciphertext, the entire alphabet is written out in reverse starting at that letter. This attack can be accelerated using a set of strips prepared with the alphabet written down them in reverse order. The strips are then aligned to form the ciphertext along one row, and the plaintext should appear in one of the other rows.

Another brute force approach is to match up the frequency distribution of the letters. By graphing the frequencies of letters in the ciphertext, and by knowing the expected distribution of those letters in the original language of the plaintext, a human can easily spot the value of the shift by looking at the displacement of particular features of the graph. This is known as frequency analysis. In Cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a Ciphertext. For example in the English language the plaintext frequencies of the letters E, T, (usually most frequent), and Q, Z (typically least frequent) are particularly distinctive. English is a West Germanic language originating in England and is the First language for most people in the United Kingdom, the United States Computers can also do this by measuring how well the actual frequency distribution matches up with the expected distribution; for example, the chi-square statistic can be used. Pearson's chi-square (&chi2 test is the best-known of several Chi-square tests – statistical procedures whose results are evaluated by reference

For natural language plaintext, there will, in all likelihood, be only one plausible decryption, although for extremely short plaintexts, multiple candidates are possible. For example, the ciphertext MPQY could, plausibly, decrypt to either "aden" or "know" (assuming the plaintext is in English); similarly, "ALIIP" to "dolls" or "wheel"; and "AFCCP" to "jolly" or "cheer" (see also unicity distance). Aden (ˈeɪdən Arabic: عدن) is a city in Yemen, 170 kilometers east of Bab-el-Mandeb. Unicity distance is a term used in Cryptography referring to the length of an original Ciphertext needed to break the cipher by reducing the number of possible

Multiple encryptions and decryptions provide no additional security. This is because two encryptions of, say, shift A and shift B, will be equivalent to an encryption with shift A + B. In mathematical terms, the encryption under various keys forms a group. In Mathematics, a group is a set of elements together with an operation that combines any two of its elements to form a third element

## Footnotes

1. ^ Singh, Simon (2000). Simon Lehna Singh, MBE (born 1964) is an Indian-British Author of Punjabi background who has specialised in writing about mathematical The Code Book. Anchor, pp. 14-20. ISBN 0385495323.
2. ^ Alexander Poltorak. Mezuzah and Astrology. chabad.org. Chabadorg is the flagship Website of the Chabad-Lubavitch Hasidic movement Retrieved on 2008-06-13. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 1525 - Martin Luther marries Katharina von Bora, against the Celibacy rule decreed by the Roman Catholic Church for
3. ^ Kahn, David (1967). David Kahn (b February 7, 1930) is a US Historian, Journalist and Writer. The Codebreakers, pp. 775-6. ISBN 978-0-684-83130-5).
4. ^ Kahn, David (1967). David Kahn (b February 7, 1930) is a US Historian, Journalist and Writer. The Codebreakers, pp. 631-2. ISBN 978-0-684-83130-5).
5. ^ Leyden, John. "Mafia boss undone by clumsy crypto", The Register, 2006-04-19. The Register (" El Reg " to its staff and readers is a British technology news and opinion website Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Events 1012 - Martyrdom of Alphege in Greenwich London. 1529 - At the Second Diet of Speyer Retrieved on 2008-06-13. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 1525 - Martin Luther marries Katharina von Bora, against the Celibacy rule decreed by the Roman Catholic Church for
6. ^ Beutelspacher, Albrecht (1994). Albrecht Beutelspacher (born June 5, 1950) is a German mathematician Cryptology. Mathematical Association of America, pp. The Mathematical Association of America ( MAA) is a professional society that focuses on Mathematics accessible at the undergraduate level 8-9. ISBN 0-88385-504-6.
7. ^ Sinkov, Abraham; Paul L. Dr Abraham Sinkov (1907-1998 was a US cryptanalyst. Biography Sinkov the son of immigrants from Russia, was born in Philadelphia Irwin (1966). Elementary Cryptanalysis: A Mathematical Approach. Mathematical Association of America, pp. 13-15. ISBN 0883856220.

## Bibliography

• David Kahn, The Codebreakers — The Story of Secret Writing, 1967. David Kahn (b February 7, 1930) is a US Historian, Journalist and Writer. ISBN 0-684-83130-9.
• F.L. Bauer, Decrypted Secrets, 2nd edition, 2000, Springer. Friedrich Ludwig Bauer (born June 10, 1924 in Regensburg) is a German Computer scientist and professor emeritus at ISBN 3-540-66871-3.
• Chris Savarese and Brian Hart, The Caesar Cipher, 1999