What is the Vigenère cipher?

The Vigenère cipher is a polyalphabetic substitution cipher that uses multiple monoalphabetic substitution ciphers to conceal the original plaintext structure. A code key determines which substitution is used for each plaintext symbol. In the simplest form, the key is a word or phrase repeated to match the message length. For example, using "DECEPTIVE" as the key to encrypt "WE ARE DISCOVERED SAVE YOURSELF" results in a complex cipher. Though once considered unbreakable, German cryptanalyst Friedrich Kasiski published a solution in 1861 that exploited repetitions to determine the key length and solve the cipher.

How does the Vigenère cipher work?

The Vigenère cipher is a method of encrypting data that uses multiple monoalphabetic substitution ciphers to conceal the original text's structure. Instead of using just one substitution, the code key determines which substitution to use for each plaintext symbol. In the simplest form, the key is a word or phrase repeated to match the message length. For instance, using "DECEPTIVE" as the key to encrypt "WE ARE DISCOVERED SAVE YOURSELF" would yield a complex cipher. Though once deemed unbreakable, German cryptanalyst Friedrich Kasiski discovered that repeating patterns between the message and key generate identical cipher symbols, which can be exploited to decipher the code.

What is a cipher key in the Vigenère cipher?

In the Vigenère cipher, the cipher key is a word or phrase that is repeated as many times as needed to encrypt a message. This key determines which monoalphabetic substitution cipher is used for each plaintext symbol, concealing the original plaintext structure. For instance, with the key "DECEPTIVE" and the message "WE ARE DISCOVERED SAVE YOURSELF," the resulting cipher would be a different set of letters. The keying formula is P+K=C, where P is the plaintext letter's position, C is the ciphertext letter's position, and K is the key letter's position in the normal alphabet. Positions are numbered 0-25, and 26 is subtracted from sums above 25.

Why is the Vigenère cipher harder to break than a simple substitution cipher?

The Vigenère cipher is more difficult to crack than a simple substitution cipher because it uses multiple monoalphabetic substitution ciphers , which conceals the original plaintext structure. In a simple substitution cipher, each letter is replaced with another, and the frequency of letters in the plaintext and ciphertext is identical. This makes it easy to decipher with only about 25 symbols of ciphertext. The Vigenère cipher, however, uses a key to choose among multiple monoalphabetic substitution rules, making it a polyalphabetic substitution . This obscures the frequency of occurrence pattern, requiring more ciphertext to solve.

How are the letters encrypted and decrypted using the Vigenère cipher?

The Vigenère cipher is a method of encrypting text by using a series of different monoalphabetic ciphers based on the letters of a keyword. Encryption: 1. Choose a keyword and repeat it until it matches the length of the plaintext message. 2. Use a Vigenère tableau , which is a grid of alphabets where each row is shifted cyclically to the left compared to the previous one. 3. To encrypt a letter, find the intersection of the row corresponding to the keyword letter and the column corresponding to the plaintext letter. The letter at this intersection is the ciphertext letter. Decryption:

What methods can be used to break or decode messages encrypted with the Vigenère cipher?

The Vigenère cipher is a polyalphabetic substitution cipher that uses multiple monoalphabetic substitution ciphers to conceal the original plaintext, with the key determining the substitution for each plaintext symbol. Though once considered unbreakable, methods exist to decrypt it.

Vigenère cipher

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A Vigenere cipher table displays the alphabet in both the top row and left column, with rows shifted to create a grid for encryption and decryption. Highlighted letters illustrate how to use the table. An explanation and example using the words cipher, key, and plaintext appears to the right.

Letter frequency analysis of a Vigenère cipher

Quick Facts

Related Topics:: Vernam-Vigenère cipher; substitution cipher

On the Web:: IOPscience - IOP Conference Series: Materials Science and Engineering - Vigenere cipher algorithm modification by adopting RC6 key expansion and double encryption process (PDF) (Oct. 18, 2026)

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Vigenère cipher

cryptology

Written by

Gustavus J. Simmons

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Britannica Editors

Last updated

Oct. 18, 2026 •History

Top Questions

What is the Vigenère cipher?
The Vigenère cipher is a polyalphabetic substitution cipher that uses multiple monoalphabetic substitution ciphers to conceal the original plaintext structure. A code key determines which substitution is used for each plaintext symbol.

In the simplest form, the key is a word or phrase repeated to match the message length. For example, using "DECEPTIVE" as the key to encrypt "WE ARE DISCOVERED SAVE YOURSELF" results in a complex cipher. Though once considered unbreakable, German cryptanalyst Friedrich Kasiski published a solution in 1861 that exploited repetitions to determine the key length and solve the cipher.
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How does the Vigenère cipher work?
The Vigenère cipher is a method of encrypting data that uses multiple monoalphabetic substitution ciphers to conceal the original text's structure. Instead of using just one substitution, the code key determines which substitution to use for each plaintext symbol.

In the simplest form, the key is a word or phrase repeated to match the message length. For instance, using "DECEPTIVE" as the key to encrypt "WE ARE DISCOVERED SAVE YOURSELF" would yield a complex cipher. Though once deemed unbreakable, German cryptanalyst Friedrich Kasiski discovered that repeating patterns between the message and key generate identical cipher symbols, which can be exploited to decipher the code.
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What is a cipher key in the Vigenère cipher?
In the Vigenère cipher, the cipher key is a word or phrase that is repeated as many times as needed to encrypt a message. This key determines which monoalphabetic substitution cipher is used for each plaintext symbol, concealing the original plaintext structure. For instance, with the key "DECEPTIVE" and the message "WE ARE DISCOVERED SAVE YOURSELF," the resulting cipher would be a different set of letters. The keying formula is P+K=C, where P is the plaintext letter's position, C is the ciphertext letter's position, and K is the key letter's position in the normal alphabet. Positions are numbered 0-25, and 26 is subtracted from sums above 25.
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Why is the Vigenère cipher harder to break than a simple substitution cipher?
The Vigenère cipher is more difficult to crack than a simple substitution cipher because it uses multiple monoalphabetic substitution ciphers, which conceals the original plaintext structure.

In a simple substitution cipher, each letter is replaced with another, and the frequency of letters in the plaintext and ciphertext is identical. This makes it easy to decipher with only about 25 symbols of ciphertext.

The Vigenère cipher, however, uses a key to choose among multiple monoalphabetic substitution rules, making it a polyalphabetic substitution. This obscures the frequency of occurrence pattern, requiring more ciphertext to solve.
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How are the letters encrypted and decrypted using the Vigenère cipher?
The Vigenère cipher is a method of encrypting text by using a series of different monoalphabetic ciphers based on the letters of a keyword.

Encryption:
1. Choose a keyword and repeat it until it matches the length of the plaintext message.
2. Use a Vigenère tableau, which is a grid of alphabets where each row is shifted cyclically to the left compared to the previous one.
3. To encrypt a letter, find the intersection of the row corresponding to the keyword letter and the column corresponding to the plaintext letter. The letter at this intersection is the ciphertext letter.

Decryption:
1. To decrypt, find the row that matches the keyword letter and locate the ciphertext letter within that row.
2. The column header of that ciphertext letter is the plaintext letter.
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What methods can be used to break or decode messages encrypted with the Vigenère cipher?
The Vigenère cipher is a polyalphabetic substitution cipher that uses multiple monoalphabetic substitution ciphers to conceal the original plaintext, with the key determining the substitution for each plaintext symbol. Though once considered unbreakable, methods exist to decrypt it.

Methods to break the Vigenère cipher
- Kasiski Examination This method, developed by Friedrich Kasiski in 1861, exploits the repetition of identical pairings of message and key symbols that generate the same cipher symbols. Cryptanalysts search for these repetitions to determine the key length and then solve each monoalphabetic substitution cipher.
- Statistical Analysis This approach assumes that the ciphertext and key share the same frequency distribution of symbols and applies statistical analysis, such as the frequency of the letter E in English plaintext, to decrypt the cipher.
- Probable-Word Method This method involves subtracting likely words from the cipher, which may produce meaningful English fragments that can be extended using other techniques.
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Vigenère cipher, type of substitution cipher used for data encryption in which the original plaintext structure is somewhat concealed in the ciphertext by using several different monoalphabetic substitution ciphers rather than just one; the code key specifies which particular substitution is to be employed for encrypting each plaintext symbol. Such resulting ciphers, known generically as polyalphabetics, have a long history of usage. The systems differ mainly in the way in which the key is used to choose among the collection of monoalphabetic substitution rules. The cipher was invented in 1553 by the Italian cryptographer Giovan Battista Bellaso but for centuries was attributed to the 16th-century French cryptographer Blaise de Vigenère, who devised a similar cipher in 1586.

For many years this type of cipher was thought to be impregnable and was known as le chiffre indéchiffrable, literally “the unbreakable cipher.” The procedure for encrypting and decrypting Vigenère ciphers is illustrated in the figure.

In the simplest systems of the Vigenère type, the key is a word or phrase that is repeated as many times as required to encipher a message. If the key is DECEPTIVE and the message is WE ARE DISCOVERED SAVE YOURSELF, then the resulting cipher will be Example of a Vigenere cipher.

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cryptology: Vigenère ciphers

The graph shows the extent to which the raw frequency of occurrence pattern is obscured by encrypting the text of an article using the repeating key DECEPTIVE. Nevertheless, in 1861 Friedrich W. Kasiski, formerly a German army officer and cryptanalyst, published a solution of repeated-key Vigenère ciphers based on the fact that identical pairings of message and key symbols generate the same cipher symbols. Cryptanalysts look for precisely such repetitions. In the example given above, the group VTW appears twice, separated by six letters, suggesting that the key (i.e., word) length is either three or nine. Consequently, the cryptanalyst would partition the cipher symbols into three and nine monoalphabets and attempt to solve each of these as a simple substitution cipher. With sufficient ciphertext, it would be easy to solve for the unknown key word.

The periodicity of a repeating key exploited by Kasiski can be eliminated by means of a running-key Vigenère cipher. Such a cipher is produced when a nonrepeating text is used for the key. Vigenère actually proposed concatenating the plaintext itself to follow a secret key word in order to provide a running key in what is known as an autokey.

Even though running-key or autokey ciphers eliminate periodicity, two methods exist to cryptanalyze them. In one, the cryptanalyst proceeds under the assumption that both the ciphertext and the key share the same frequency distribution of symbols and applies statistical analysis. For example, E occurs in English plaintext with a frequency of 0.0169, and T occurs only half as often. The cryptanalyst would, of course, need a much larger segment of ciphertext to solve a running-key Vigenère cipher, but the basic principle is essentially the same as before—i.e., the recurrence of like events yields identical effects in the ciphertext. The second method of solving running-key ciphers is commonly known as the probable-word method. In this approach, words that are thought most likely to occur in the text are subtracted from the cipher. For example, suppose that an encrypted message to President Jefferson Davis of the Confederate States of America was intercepted. Based on a statistical analysis of the letter frequencies in the ciphertext, and the South’s encryption habits, it appears to employ a running-key Vigenère cipher. A reasonable choice for a probable word in the plaintext might be “PRESIDENT.” For simplicity a space will be encoded as a “0.” PRESIDENT would then be encoded—not encrypted—as “16, 18, 5, 19, 9, 4, 5, 14, 20” using the rule A = 1, B = 2, and so forth. Now these nine numbers are added modulo 27 (for the 26 letters plus a space symbol) to each successive block of nine symbols of ciphertext—shifting one letter each time to form a new block. Almost all such additions will produce randomlike groups of nine symbols as a result, but some may produce a block that contains meaningful English fragments. These fragments can then be extended with either of the two techniques described above. If provided with enough ciphertext, the cryptanalyst can ultimately decrypt the cipher. What is important to bear in mind here is that the redundancy of the English language is high enough that the amount of information conveyed by every ciphertext component is greater than the rate at which equivocation (i.e., the uncertainty about the plaintext that the cryptanalyst must resolve to cryptanalyze the cipher) is introduced by the running key. In principle, when the equivocation is reduced to zero, the cipher can be solved. The number of symbols needed to reach this point is called the unicity distance—and is only about 25 symbols, on average, for simple substitution ciphers. See also Vernam-Vigenère cipher.

Gustavus J. Simmons

Vigenère cipher

Methods to break the Vigenère cipher

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