Tag: crack

Posted in Science & Nature

Cryptography: Book Cipher

Posted on by Jinavie

So far, the three ciphers introduced could all easily be cracked using frequency analysis and the Kasiski examination. Is there a cipher that is easy to implement yet difficult to break for a beginner cryptanalyst? An extremely popular and surprisingly powerful cipher is the book cipher. Essentially, the book cipher replaces a keyword with an entire book. Instead of replacing a letter for a letter or symbol in a systematic and mathematical way (such as a set shift number or using a tabula recta), the book cipher replaces letters for numbers that refer to a certain text within a book. As the only way to decode the message is to have the book, it is an extremely secure way of enciphering a message given that both parties have an identical copy of the book.

There are many variations of the book cipher. The most popular type is giving a page number, with the first letter of the page being the plaintext. A variant of this is giving a set of three numbers for every letter: the page number, the line number and the word number (or just two: page and line, then take the first letter). Ironically, this may be less secure at times as it may reveal that it is a book cipher. However, doing this for each letter makes the enciphering and deciphering process incredibly long and arduous.

A shortcut method is to refer to a word within a page (using the three-number set coordinates method described above) to shorten the ciphertext. Although this method is much easier in practice, it poses the challenge of finding a book that includes all the words in the plaintext, which may be difficult if the code is for military or espionage purposes.

Because of this, and the fact that both parties (or everyone in the ring) need identical versions of the book while not standing out too much, the most common books used are the dictionary (typically a famous version such as the Oxford Dictionary) or the bible (again, a standard version is used). These books are not only good because they incorporate a massive vocabulary, but they are also inconspicuous while being carried around in an enemy territory.

The book cipher is a very difficult code to crack for most people without advanced cryptanalysis training. Thus, the easiest way to crack is to deduce what book is the keytext. There are numerous ways to do this, but one way would be to cross-match the books of two known spies until common books are found. In the setting of spies in a foreign country, a book such as a traveller’s guide or phrasebook dictionary can be considered a likely target as it can be carried around easily while containing many words. Ergo, the secret behind cracking the book cipher is less about cryptography and more about using the science of deduction.

Posted in Science & Nature

Cryptography: Vigenere Cipher

Posted on by Jinavie

It has thus been proven that the Caesar cipher, the pigpen cipher and any substitution cipher can be simply broken using frequency analysis. The basis for this is that each letter or symbol can only represent a single letter, meaning that letter frequencies (e, t, a, o…) are directly translated onto the cipher language. Ergo, by making each letter represent more than one letter, the letter frequencies can be masked and an additional level of security can be added to the cipher. This is called polyalphabetic substitution and it is the basis for a type of cipher known as the Vigenère cipher.

The cipher was first conceived in 1553 by Giovan Battista Bellaso and has been improved since. It is famous for being rather simple to use despite the difficult to decipher it at a beginner’s level. This trait earned the cipher the nickname “le chiffre indéchiffrable”, which is French for “the indecipherable cipher”.

The Vigenère cipher can be thought of a stack of Caesar ciphers (essentially a cipher within a cipher), where each letter is shifted by a variable key (in a normal Caesar shift, every letter is shifted by the same key). This is achieved by the implementation of a keyword and a table called a tabula recta. A tabula recta is simply a grid made from 26 rows of the alphabet, each row of which is made by shifting the previous one to the left. This table essentially shows all the possible outcomes of a Caesar shift.

Now, let us try encoding a message using the Vigenère cipher. The message “attack at dawn” is encoded using the keyword “nothing”. Ideally, there should be no repeating letters in the keyword for the sake of security. Therefore, if there are any repeating letters, just remove the repeated letters (e.g. “crocodile” -> “crodile”). First, repeat the keyword until it matches the number of letters of the message (e.g. “attackatdawn” is aligned with “nothingnothi”). Then, use the tabula recta to encrypt the message. The rule of thumb is “key-row, message-column”, meaning that the row of the tabula recta starting with the letter of the key is matched against the column starting with the respective letter of the message. To take the first letter as an example, the key letter is “n” and the message letter is “a”. The letter corresponding to where the “n” row and “a” column meets is “N”. If this rule is followed for each letter, the encrypted message becomes: “NHMHKXGGRTDV”. Although it takes some effort to find each letter on the table, the message becomes “indecipherable” to a beginner cryptanalyst as frequency analysis becomes useless. For example, the repeating letter “H” can represent either “t” or “a”. The longer the keyword is, the more secure the Vigenère cipher becomes.

However, the Vigenère cipher is not indecipherable. Next, we will look at a cryptanalysis method called the Kasiski examination that attacks a polyalphabetic cipher such as the Vigenère cipher to gain access to the keyword.