Bifid Cipher in Cryptography

The Bifid Cipher is a polygraphic substitution cipher that was invented by the French amateur cryptographer Felix Delastelle at the end of the 19th century. It is considered a polygraphic cipher because it encrypts pairs of letters at a time, rather than single letters like monoalphabetic ciphers such as the Caesar Cipher.

The Bifid Cipher is based on a polybius square, which is a 5x5 grid of letters that is used to encrypt the plaintext. The grid is usually filled with a combination of the alphabet and a keyword or phrase. The letters in the keyword or phrase are placed in the grid first, and the remaining letters of the alphabet are filled in after that.

To encrypt a message using the Bifid Cipher, the plaintext is first written in pairs of letters and then each pair is located in the polybius square. The letters in the pair correspond to the row and column coordinates of the letter in the square. The coordinates are then written down in the order in which they appear in the plaintext, forming a new set of numbers. This new set of numbers is then used to determine the coordinates of the letters in the ciphertext.

To decrypt a message encoded with Bifid Cipher, it is needed to transform the ciphertext numbers into a new set of coordinates. Then, use this set of coordinates to find the corresponding letters on the polybius square and combine them into pairs. Finally, combine each pairs to form the original plaintext

It is a relatively strong cipher for its time, because of the use of pairs of letters and the use of the polybius square which increases the number of possible keys. However, it is still considered to be relatively easy to break, especially by modern cryptanalysis techniques.

In general, today's modern ciphers like RSA and AES are considered much stronger than classical ciphers like Bifid, as they use much more complex mathematical operations and have a much larger key space.

Encrypting Algorithm

The encryption algorithm for the Bifid Cipher involves a few steps −

• Create a Polybius square − This is a 5x5 grid of letters, usually filled with a combination of the alphabet and a keyword or phrase. The letters in the keyword or phrase are placed in the grid first, and the remaining letters of the alphabet are filled in after that.

• Write the plaintext in pairs − The plaintext is written in pairs of letters. If the plaintext has an odd number of letters, a filler character (such as 'X') is added to make it even.

• Find the coordinates of each letter in the plaintext − Each pair of letters in the plaintext corresponds to the row and column coordinates of the letter in the Polybius square. The coordinates are then written down in the order in which they appear in the plaintext, forming a new set of numbers.

• Use the new set of numbers to determine the coordinates of the letters in the ciphertext − The new set of numbers that represent the coordinates is used to look up the corresponding letters in the Polybius square. The letters at these coordinates make up the ciphertext.

• Output the Ciphertext − The final step is to output the resulting ciphertext.

For example, to encrypt the plaintext "HELLO" with the keyword "CRYPTOGRAPHY" we will create the polybius square as follow

| C | R | Y | P | T |
| O | G | A | H | B |
| D | E | F | I | J |
| K | L | M | N | X |
| U | V | W | S | Z |

Then we will split the plaintext in pairs to − "HE", "LL", "OX"

Then we will look for the coordinates of the first pair "HE", we will find that the H is in the 4th row and the 2nd column and the E is in the 3rd row and the 5th column.

So, the new set of numbers are 42,35

Then we will use this set of numbers to find the letters in the polybius square, in this case we will get − "UZ"

This is the ciphertext for this pair of plaintext "HE".

Finally, we will follow the same process for the rest of the pairs, to obtain the final ciphertext − "UZBDXO"

This is just a basic example to explain the algorithm, the security of the cipher can be enhanced by using different polybius squares for different parts of the plaintext and using more complex keys.

One of the ways the security of the Bifid Cipher can be enhanced is by using a different polybius square for each pair of letters in the plaintext, rather than using a single square for the entire message. This is known as fractionation. Fractionating the plaintext increases the number of possible keys and makes it more difficult for an attacker to break the cipher.

Another way to enhance the security of the Bifid Cipher is to use a more complex key. Instead of using a simple keyword or phrase, the key can be generated using a random number generator or a cryptographic hash function. This makes the key much harder to guess and increases the number of possible keys.

One of the weakness of the Bifid Cipher is that it doesn't conceal the frequency of letters in the plaintext. An attacker can perform a frequency analysis of the ciphertext and use this information to break the cipher. One way to address this weakness is to use a transposition cipher in conjunction with the Bifid Cipher. The transposition cipher can be used to scramble the order of the letters in the ciphertext and make it more difficult to perform a frequency analysis.

Finally, it's important to note that the Bifid Cipher, despite some of its weaknesses, is still a relatively strong cipher for its time and it can still be used today to encrypt short messages. However, it is generally considered to be less secure than modern ciphers such as AES or RSA, which use much more complex mathematical operations and have a much larger key space.

Conclusion

In summary, the Bifid Cipher is a polygraphic substitution cipher that encrypts pairs of letters at a time, it has a relatively strong security compared to monoalphabetic ciphers. However, it can be strengthened by using a different polybius square for each pair of letters in the plaintext, using more complex keys and combining it with a transposition cipher. Also, it should be noted that it is still considered less secure than the currently used ciphers.