Question

Suppose we have a wheel cipher device that has 4 wheels. Compare the theoretical and practical security of this wheel cipher device with Vigenère cipher with block length equals to 4.

Answer 1

The Vigenère Cipher

The Vigenère cipher, was invented by a Frenchman, Blaise de Vigenère in the 16th century. It is a polyalphabetic cipher because it uses two or more cipher alphabets to encrypt the data. In other words, the letters in the Vigenère cipher are shifted by different amounts, normally done using a word or phrase as the encryption key .

Unlike the monoalphabetic ciphers, polyalphabetic ciphers are not susceptible to frequency analysis, as more than one letter in the plaintext can be represented by a single letter in the encryption.

At the time, and for many centuries since its invention, the Vigenère Cipher was renowned for being a very secure cipher, and for a very long time it was believed to be unbreakable. It was this thought that earned it the nickname "le chiffre indéchiffrable" (French for "the unbreakable cipher"). Although this is not true (it was fully broken by Friedrich Kasiski in 1863), it is still a very secure cipher in terms of paper and pen methods, and is usable as a field cipher.

The Vigenère Square:-

Blaise de Vigenère developed a square to help encode messages. Reading along each row, you can see that it is a really a series of Caesar ciphers the first has a shift of 1, the second a shift of 2 and so.

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The Vigenère cipher uses this table in conjunction with a key to encipher a message.

So, if we were to encode a message using the key COUNTON, we write it as many times as necessary above our message. To find the encryption, we take the letter from the intersection of the Key letter row, and the Plaintext letter column.

Key

C

O

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Encryption

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To decipher the message, the recipient needs to write out the key above the ciphertext and reverse the process.

The maths behind the Vigenère cipher can be written as follows:
To encrypt a message: Ca = Ma + Kb (mod 26)
To decrypt a message: Ma = Ca – Kb (mod 26)
(Where C = Code, M = Message, K = Key, and where a = the ath character of the message bounded by the message, and b is the bth character of the Key bounded by the length of the key.)

In a Caesar cipher, each letter of the alphabet is shifted along some number of places. For example, in a Caesar cipher of shift 3, A would become D, B would become E, Y would become B and so on. The Vigenère cipher has several Caesar ciphers in sequence with different shift values.

To encrypt, a table of alphabets can be used, termed a tabula recta, Vigenère square or Vigenère table. It has the alphabet written out 26 times in different rows, each alphabet shifted cyclically to the left compared to the previous alphabet, corresponding to the 26 possible Caesar ciphers. At different points in the encryption process, the cipher uses a different alphabet from one of the rows. The alphabet used at each point depends on a repeating keyword.

Security :-

My question is regarding the Vigenère cipher: It is my understanding that the security of this cipher is directly related to the length and security of the keys.  Long and tightly secured keys bring this cipher on par with many more complex techniques.

Besides others (e.g. random key, key used only once) it depends on the proportion of cipher text length and key length how difficult it is to break the cipher. There are tools around that can break the cipher if cipher_text_length/key_length is 4 or greater.In some exceptional cases the proportion may be even 3. Thus the Vigenere cipher is rather insecure. But as already said by others: If the key length is equal to the cipher text length then the cipher is absolutely secure if the key is chosen completely randomly and is only used once. This will turn the cipher into a one time pad. Drawback: one time pads are difficult and ineffective to manage.

Discussion
The Vigenère Cipher was the biggest step in cryptography for over 1000 years. The idea of switching between ciphertext alphabets as you encrypt was revolutionary, and an idea that is still used to make ciphers more secure. One of the most famous examples of codes and ciphers in history, the ENIGMA machine, is just a modified polyalphabetic substitution cipher!

But why is the Vigenère Cipher so secure? What is it that makes this cipher better than the Mixed Alphabet Cipher? Let's take a look at an example. We shall encrypt the following text using the Mixed Alphabet Cipher and the Vigenère Cipher, both with the keyword encrypt.

Plain Text:-

Aged twenty six, Vigènere was sent to Rome on a diplomatic mission. It was here that he became acquainted with the writings of Alberti, Trithemius and Porta, and his interest in cryptography was ignited. For many years, cryptography was nothing more than a tool that helped him his diplomatic work, but at the age of thirty nine, Vigènere decided that he had amassed enough money to be able to abandon his career and concentrate on a life of study. It was only then that he began research into a new cipher.

Using the Mixed Alphabet we get:

ETYR QVYIQX OBW, UBTYIYMY VEO OYIQ QJ MJHY JI E RBKGJHEQBC HBOOBJI. BQ VEO AYMY QAEQ AY NYCEHY ECLSEBIQYR VBQA QAY VMBQBITO JP EGNYMQB, QMBQAYHBSO EIR KJMQE, EIR ABO BIQYMYOQ BI CMXKQJTMEKAX VEO BTIBQYR. PJM HEIX XYEMO, CMXKQJTMEKAX VEO IJQABIT HJMY QAEI E QJJG QAEQ AYGKYR ABH ABO RBKGJHEQBC VJMF, NSQ EQ QAY ETY JP QABMQX IBIY, UBTYIYMY RYCBRYR QAEQ AY AER EHEOOYR YIJSTA HJIYX QJ NY ENGY QJ ENEIRJI ABO CEMYYM EIR CJICYIQMEQY JI E GBPY JP OQSRX. BQ VEO JIGX QAYI QAEQ AY NYTEI MYOYEMCA BIQJ E IYV CBKAYM.

And using the Vigenère we get:

ETGU RLXRGA JGM, OMTGECGX ANU JCCM XB TFKT HR N FZNAHQNVZA BBWFKFL. XM ANU YCGX XUCK FT UIPCDC PVUHCZLIXH JKKF IAI JTZRXGKF QW YAUIEVZ, RGBXUGDGJL EAF GMGME, NPU FXL MAVVPTLX VP TPNIXBIIYEAC JCJ GVGMGGU. DDK QNPP WTTVF, EIWEMSTTRNWR ANU EMIAMAI DMGX XUCE Y IHSY VYYI AIYRVB WBQ UKJ BXIPBORRXV ABTB, ZJM EG VYC PZI BH KFXKXL PZLT, OMTGECGX HREZBTW XUCK FT AEQ CDYHLIQ GEMJZL ZQECN MS OG RZAX XB CSYCWSA JZQ RTVRGI YCW GBPTCCMVNVV MC T PVHV MU LXHFP. GI PEF QEJN MLRP KFPM LR DVEPG VRUVYGVL VPKM P GIJ EZNWXV.

The Frequency distribution of the plaintext. The Frequency distribution of the ciphertext using the Vigenère Cipher.

The Frequency distribution of the ciphertext using the Mixed Alphabet Cipher. These frequency distributions show how many times each letter appears in the relevent text. We can see a clear relationship between the top two, with the same peaks just in different places.

The final distribution, for the Vigenère Cipher, is different to the others, and the distribution of letters is much more smoothed out. And even though there is a little bit of a peak at "G" (which we might think to be "e"), in the penultimate word "new" is "GIJ", so "G" is "n", but in the first word "aged" is "ETGU" so "G" is "e". This shows that the same letter can be achieved by different plaintext letters.

Answer 2

The Vigenère Cipher

The Vigenère cipher, was invented by a Frenchman, Blaise de Vigenère in the 16th century. It is a polyalphabetic cipher because it uses two or more cipher alphabets to encrypt the data. In other words, the letters in the Vigenère cipher are shifted by different amounts, normally done using a word or phrase as the encryption key .

Unlike the monoalphabetic ciphers, polyalphabetic ciphers are not susceptible to frequency analysis, as more than one letter in the plaintext can be represented by a single letter in the encryption.

At the time, and for many centuries since its invention, the Vigenère Cipher was renowned for being a very secure cipher, and for a very long time it was believed to be unbreakable. It was this thought that earned it the nickname "le chiffre indéchiffrable" (French for "the unbreakable cipher"). Although this is not true (it was fully broken by Friedrich Kasiski in 1863), it is still a very secure cipher in terms of paper and pen methods, and is usable as a field cipher.

The Vigenère Square:-

Blaise de Vigenère developed a square to help encode messages. Reading along each row, you can see that it is a really a series of Caesar ciphers the first has a shift of 1, the second a shift of 2 and so.

A

B

C

D

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The Vigenère cipher uses this table in conjunction with a key to encipher a message.

So, if we were to encode a message using the key COUNTON, we write it as many times as necessary above our message. To find the encryption, we take the letter from the intersection of the Key letter row, and the Plaintext letter column.

Key

C

O

U

N

T

O

N

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O

U

N

T

O

N

Plaintext

V

I

G

E

N

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Encryption

X

W

A

R

G

S

E

G

Q

C

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A

S

E

To decipher the message, the recipient needs to write out the key above the ciphertext and reverse the process.

The maths behind the Vigenère cipher can be written as follows:
To encrypt a message: Ca = Ma + Kb (mod 26)
To decrypt a message: Ma = Ca – Kb (mod 26)
(Where C = Code, M = Message, K = Key, and where a = the ath character of the message bounded by the message, and b is the bth character of the Key bounded by the length of the key.)

In a Caesar cipher, each letter of the alphabet is shifted along some number of places. For example, in a Caesar cipher of shift 3, A would become D, B would become E, Y would become B and so on. The Vigenère cipher has several Caesar ciphers in sequence with different shift values.

To encrypt, a table of alphabets can be used, termed a tabula recta, Vigenère square or Vigenère table. It has the alphabet written out 26 times in different rows, each alphabet shifted cyclically to the left compared to the previous alphabet, corresponding to the 26 possible Caesar ciphers. At different points in the encryption process, the cipher uses a different alphabet from one of the rows. The alphabet used at each point depends on a repeating keyword.

Security :-

My question is regarding the Vigenère cipher: It is my understanding that the security of this cipher is directly related to the length and security of the keys.  Long and tightly secured keys bring this cipher on par with many more complex techniques.

Besides others (e.g. random key, key used only once) it depends on the proportion of cipher text length and key length how difficult it is to break the cipher. There are tools around that can break the cipher if cipher_text_length/key_length is 4 or greater.In some exceptional cases the proportion may be even 3. Thus the Vigenere cipher is rather insecure. But as already said by others: If the key length is equal to the cipher text length then the cipher is absolutely secure if the key is chosen completely randomly and is only used once. This will turn the cipher into a one time pad. Drawback: one time pads are difficult and ineffective to manage.

Discussion
The Vigenère Cipher was the biggest step in cryptography for over 1000 years. The idea of switching between ciphertext alphabets as you encrypt was revolutionary, and an idea that is still used to make ciphers more secure. One of the most famous examples of codes and ciphers in history, the ENIGMA machine, is just a modified polyalphabetic substitution cipher!

But why is the Vigenère Cipher so secure? What is it that makes this cipher better than the Mixed Alphabet Cipher? Let's take a look at an example. We shall encrypt the following text using the Mixed Alphabet Cipher and the Vigenère Cipher, both with the keyword encrypt.

Plain Text:-

Aged twenty six, Vigènere was sent to Rome on a diplomatic mission. It was here that he became acquainted with the writings of Alberti, Trithemius and Porta, and his interest in cryptography was ignited. For many years, cryptography was nothing more than a tool that helped him his diplomatic work, but at the age of thirty nine, Vigènere decided that he had amassed enough money to be able to abandon his career and concentrate on a life of study. It was only then that he began research into a new cipher.

Using the Mixed Alphabet we get:

ETYR QVYIQX OBW, UBTYIYMY VEO OYIQ QJ MJHY JI E RBKGJHEQBC HBOOBJI. BQ VEO AYMY QAEQ AY NYCEHY ECLSEBIQYR VBQA QAY VMBQBITO JP EGNYMQB, QMBQAYHBSO EIR KJMQE, EIR ABO BIQYMYOQ BI CMXKQJTMEKAX VEO BTIBQYR. PJM HEIX XYEMO, CMXKQJTMEKAX VEO IJQABIT HJMY QAEI E QJJG QAEQ AYGKYR ABH ABO RBKGJHEQBC VJMF, NSQ EQ QAY ETY JP QABMQX IBIY, UBTYIYMY RYCBRYR QAEQ AY AER EHEOOYR YIJSTA HJIYX QJ NY ENGY QJ ENEIRJI ABO CEMYYM EIR CJICYIQMEQY JI E GBPY JP OQSRX. BQ VEO JIGX QAYI QAEQ AY NYTEI MYOYEMCA BIQJ E IYV CBKAYM.

And using the Vigenère we get:

ETGU RLXRGA JGM, OMTGECGX ANU JCCM XB TFKT HR N FZNAHQNVZA BBWFKFL. XM ANU YCGX XUCK FT UIPCDC PVUHCZLIXH JKKF IAI JTZRXGKF QW YAUIEVZ, RGBXUGDGJL EAF GMGME, NPU FXL MAVVPTLX VP TPNIXBIIYEAC JCJ GVGMGGU. DDK QNPP WTTVF, EIWEMSTTRNWR ANU EMIAMAI DMGX XUCE Y IHSY VYYI AIYRVB WBQ UKJ BXIPBORRXV ABTB, ZJM EG VYC PZI BH KFXKXL PZLT, OMTGECGX HREZBTW XUCK FT AEQ CDYHLIQ GEMJZL ZQECN MS OG RZAX XB CSYCWSA JZQ RTVRGI YCW GBPTCCMVNVV MC T PVHV MU LXHFP. GI PEF QEJN MLRP KFPM LR DVEPG VRUVYGVL VPKM P GIJ EZNWXV.

The Frequency distribution of the plaintext. The Frequency distribution of the ciphertext using the Vigenère Cipher.

The Frequency distribution of the ciphertext using the Mixed Alphabet Cipher. These frequency distributions show how many times each letter appears in the relevent text. We can see a clear relationship between the top two, with the same peaks just in different places.

The final distribution, for the Vigenère Cipher, is different to the others, and the distribution of letters is much more smoothed out. And even though there is a little bit of a peak at "G" (which we might think to be "e"), in the penultimate word "new" is "GIJ", so "G" is "n", but in the first word "aged" is "ETGU" so "G" is "e". This shows that the same letter can be achieved by different plaintext letters.