Posted in History & Literature

Ides Of March

“Beware the Ides of March”.

This is one of the most famous prophecies in literature (and history). It was said by a soothsayer to the great Julius CaesarDictator Perpetuo (“dictator in perpetuity”).

The Ides of March (Idus Martiae) refer to a date, specifically March 15. The ancient Romans did not number the days of the month but instead referred to three specific dates within a month. The Ides referred to the middle of the month.

The Ides of March have become an infamous date due to an event that changed the course of Roman history – the assassination of Julius Caesar.
Julius Caesar became the sole leader of the Roman Republic after a great civil war. There was much dissent from the senate, who had lost much of their power through Caesar’s uprising. On March 15, 44BC, Brutus (Caesar’s adopted son) and members of the senate conspired to assassinate Caesar to end his rule.

In William Shakespeare’s eponymous play, it is said that Caesar passed the soothsayer who had warned him of this day and said to him: “The Ides of March are come”, mocking the failed prophecy. The seer simply replied: “Aye, Caesar; but not gone.
Not long after, Caesar was ambushed by 60 men led by Brutus and was stabbed multiple times to his death. With his dying breath, he uttered: “Et tu, Brute?” – meaning “You too, Brutus?”, showing his despair at the betrayal by his own son.

The Ides of March was traditionally the date when Romans would settle their debt. Perhaps Brutus, who had actually fought against his father in the civil war but then forgiven by Caesar, chose this date to symbolise settling the political tension of the time – to liberate Rome from Caesar’s monarchy.

Ironically, the assassination triggered a series of events that led to another civil war, ultimately causing the transition from the Roman Republic to the Roman Empire, led by Caesar’s other adopted heir, Octavian (later known as Augustus). Augustus proceeded to round up 300 conspirators complicit in the murder of Caesar and executed them as a tribute to the now deified CaesarDivus Julius.

Posted in Science & Nature

Cryptography: Vigenere Cipher

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.

Posted in Science & Nature

Cryptography: Caesar Cipher

One of the earliest known uses of cryptography can be traced back to ancient Rome. Julius Caesar was well-known for his use of a type of substitution cipher dubbed “Caesar cipher” or “Caesar shift”. The encryption is very simple: shift every letter a certain value down the alphabet (the value is known as the key). For example, Caesar used a key of 3 to encrypt his messages to his general, so the message “ATTACK AT DAWN” would be encrypted into “DWWDFN DW GDZQ” (use the scheme of a=0, b=1, c=2, d=3…).

Although it was an efficient encryption system in ancient times, since then it has been revised to be much more secure. The Caesar cipher has thus been demoted to the preferred code used by children and teenagers for basic decoding puzzles.

Due to the simplicity of the encryption, cracking the Caesar cipher is quite easy with the use frequency analysis, pattern recognition and brute force analysis. Brute force analysis can be used if the attacker knows that a Caesar cipher has been used. If that is the case, the message can be decrypted using every possible key (e.g. 1, 2, 3…) until a message that makes sense is acquired.

Posted in History & Literature

Playing Cards

Playing cards are the basis of so many games due to their diversity and adaptability. It can be used for any game from poker to the Eleusis game, from house of cards to magic tricks.
One thing that is often overlooked is the long history of cards and the various symbolisms hidden within. For example, the suits may have the following symbolism:

Spades            Nobility, swords, war
Hearts             Church, cups, love and romance
Diamonds    Merchants, coins, wealth
Clubs               Peasants, clubs/batons, agriculture

Although there are many debates regarding this issue, there is substantial evidence that the court cards (Kings, Queens and Jacks/Knaves) are based on historical or mythical heroes and heroines, at least for the French deck that is commonly used nowadays. The following is the list of presumed models for each card:

King of Spades                David (biblical hero)
King of Hearts                Charlemagne (great king of Franks)
King of Diamonds        Julius Caesar (great Roman emperor)
King of Clubs                   Alexander the Great (the king of Macedon)

Queen of Spades             Joan of Arc (the French heroine) or Athena (the goddess of war)
Queen of Hearts             Judith (either the biblical heroine or the tragic queen of Bavaria)
Queen of Diamonds    Rachel (wife of Jacob in the bible – he waited 14 years for her)
Queen of Clubs               Argine (anagram of regina, Latin for queen) or Hera (queen of gods)

Jack of Spades                Holger Le Danois (knight of Charlemagne)
Jack of Hearts                La Hire (comrade of Joan of Arc, member of Charles VII’s court)
Jack of Diamonds       Hector (the hero of the Trojan War or the knight of Charlemagne)
Jack of Clubs                  Lancelot (King Arthur’s most trusted knight)

Although the models for the Kings and Jacks are quite clear, the Queens are still subject to many discussions. As modern playing cards originate from France circa 15th century, the above models (official names for each card back then) appearto be valid.
This also explains the ordering of suits (spades/nobility first, clubs/peasants last, hearts/church second and diamonds/merchants third) and how the Ace sometimes trumps the King (possibly symbolising how peasant hold the power, as in the French Revolution).

Sometimes, knowing the history behind a game can make it even more fun.