Cryptography

Cryptography

Mikusch, Rita

Cryptography is the practice and science of encoding data so that it can only be read by specific individuals. The biggest users of cryptography have traditionally been the military, but the commercial and private use of electronic means of communication has now made cryptography relevant to the broader public.

Historical

Many different cryptographic systems have been used throughout history. One classic example is Julius Caesar’s use of a mono-alphabetic substitution cipher during his military campaigns 2000 years ago. A “cipher” is another term used to mean “encryption method,” and mono-alphabetic substitution refers to the fact that each letter in a message is substituted by another (for example, the letter “A” might be substituted with the letter “C”). Caesar reportedly encrypted his messages by replacing each letter of the alphabet with another letter a fixed distance away. This method of encryption is often referred to as the “Caesar Cipher.”

Ciphers are generally composed of a formula (or algorithm) and a key. In the case of the Caesar Cipher, the formula is to “take each letter and substitute another letter X distance away in the alphabet.” The key here is the distance (X) between the letters. The problem with mono-alphabetic ciphers like the Caesar Cipher is that they’re relatively easy to crack.

The Greeks used another basic form of encryption for messages called a “transposition cipher,” an encryption method that rearranges the letters of a message rather than using substitution. Users would take a long thin ribbon of paper and wrap it around a “scytale” (or cylinder) in such a way that it did not overlap. A message was then written across the ribbon so that each letter in a word ended up on a separate loop. When the ribbon was removed from the scytale, the message was reduced to gibberish, but when it was subsequently wrapped back onto another scytale of the same diameter, the message would once again make sense.

The key in the transposition cipher is the scytale itself. It’s also one of the system’s weaknesses-if somebody steals the scytale, they can immediately decipher the encrypted messages.

A far more recent and well-known cryptographic device was the Enigma machine used by the German army during the second World War (as depicted in the 2001 film “Enigma”). The Enigma machine contained a number of rotors. As a message was typed into the machine, these rotors would spin around and calculate a letter to substitute for each letter of the message. The system involved a poly-alphabetic substitution cipher, which meant that each single letter of a message could be substituted with any number of different single letters. For example, an “A” could be transformed into an “F” in one part of the encrypted message, and into an “M” in another. Moreover, each of the rotors could be set separately, and each clerk who operated the machine had a codebook (the key for this system) detailing the rotor settings for each particular day. This meant that encrypting and decrypting a message sent via the Enigma machine required not only the machine itself, but also a copy of that day’s codebook.

The Enigma ciphers were ultimately broken by Polish and British cryptographers using primitive computers (by today’s standards) and information that had been captured about both the Enigma machine and the codebooks.

Modern

The prevalence of electronic communications in modern times has lead to the widespread use of cryptography by the general public. While the computers and other equipment used are much fancier, the basic theory is the same: The message and the key are run through a formula, producing an encrypted message.

A common means of modern encryption is a one-way system in which encryption is easy but decryption is computationally impractical. Take passwords for instance, which are encrypted using a one-way encryption system. When you sign in, your password is encrypted by the computer (you don’t see the result) and compared to a stored version of the same encrypted password. If these two passwords match, you’ve signed in successfully. If they don’t and you’ve forgotten your password, you’ll need to talk to your systems administrator and ask them to create a new password. Your systems administrator will not be able to recover your old password-they’ll only be able to create a new one for you.

Another application of one-way encryption in data transmission is to ensure that outgoing data has not been corrupted in any way. An encrypted version of the data is sent along with the original data. At the recipient’s end, the data is encrypted again and compared to the encrypted version that was sent simultaneously. If the two encrypted versions of the data match, this means the data has not been corrupted during transmission. The technical term for this is “hash”-the data is put through a “hashing formula,” and the resulting encrypted data is a “hash.”

Another widespread use of encryption today involves the two-way public/private key encryption system. This system operates on the basic premise of two keys-one you use for encryption, the other for decryption. One application for this is with email. By encrypting a message with one key and offering the second key to the reader, you are giving them the means to ensure that the message definitely came from you. (Check out the January 2005 Web Works article for a more in-depth discussion of public/private key encryption.)

More information

Here are a couple of sites that provide overviews of historical and modern encryption systems:

Codes and Ciphers in the second World War (www.codesandciphers.org.uk): This website offers a lot of historical information about the Enigma machine and other forms of cryptography used during WWII. The site was created by Tony Sale, the original founder and creator of the Bletchley Park Museum (Bletchley Park was the headquarters for code-breakers in England during WWII.)

The Crypto Tutorial (www.antilles.kl2. vi.us/math/cryptotut/home.htm): This site provides a tutorial (by the Antilles School) geared towards high school students, but also offers some really interesting historical details on cryptography that might be of interest to other readers.

Cryptonomicon by Neal Stephenson (www.cryptonomicon.com): Cryptonomicon is a science fiction novel featuring cryptography that jumps between the 28th century, the second World War, and the present. The novel itself is available in bookstores, but the website listed above will give you a preview and synopsis so you can decide if it’s something you’d like to check out.

By Rita Mikusch, Webmaster

Copyright Institute of Chartered Accountants of British Columbia Feb/Mar 2005

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