Secrets On Security: A Gentle Introduction To Cryptography

Let us take the example of scrambling an egg. First, crack the shell, pour the contents into a bowl and beat the contents vigorously until you achieved the needed result - well, a scrambled egg. This action of mixing the molecules of the egg is encryption. Since the molecules are mixed-up, we say the egg has achieved a higher state of entropy (state of randomness). To return the scrambled egg to its original form (including uncracking the shell) is decryption. Impossible?

However, if we substitute the word "egg" and replace it with "number", "molecules" with "digits", it is POSSIBLE. This, my friend, is the exciting world of cryptography (crypto for short). It is a new field dominated by talented mathematicians who uses vocabulary like "non-linear polynomial relations", "overdefined systems of multivariate polynomial equations", "Galois fields", and so forth. These cryptographers uses language that mere mortals like us cannot pretend to understand.

In the computer, everything stored are numbers. Your MP3 file is a number. Your text message is a number. Your address book is a longer number. The number 65 represents the character "A", 97 for the small "a", and so on.

For humans, we recognize numbers with the digits from 0 to 9, where else, the computer can only recognize 0 or 1. This is the binary system which uses bits instead of digits. To convert bits to digits, just simply multiply the number of bits by 0.3 to get a good estimation. For example, if you have 256-bits of Indonesian Rupiah (one of the lowest currency denomination in the world), Bill Gates' wealth in comparison would be microscopic.

The hexadecimal (base 16) system uses the ten digits from 0 to 9, plus the six extra symbols from A to F. This set has sixteen different "digits", hence the hexadecimal name. This notation is useful for computer workers to peek into the "real contents" stored by the computer. Alternatively, treat these different number systems as currencies, be it Euro, Swiss Franc, British Pound and the like. Just like an object can be priced with different values using these currencies, a number can also be "priced" in these different number systems as well.

To digress a bit, have you ever wondered why you had to study prime numbers in school? I am sure most mathematics teachers do not know this answer. Answer: A subbranch called public-key cryptography which uses prime numbers especially for encrypting e-mails. Over there, they are talking of even bigger numbers like 2048, 4096, 8192 bits.)

When we want to encrypt something, we need to use a cipher. A cipher is just an algorithm similar to a recipe for baking a cake. It has precise, unambiguous steps. To carry out the encryption process, you need a key (some called it passphrase). A good practice in cryptography needs the key used by a cipher must be of high entropy to be effective.

Data Encryption Standard (DES), introduced as a standard in the late 1970's, was the most commonly used cipher in the 1980's and early 1990's. It uses a 56-bit key. It was broken in the late 1990's with specialized computers costing about US$250,000 in 56 hours. With today's (2005) hardware, it is possible to crack within a day.

Subsequently, Triple-DES superseded DES as the logical way to preserve compatibility with earlier investments by big corporations (mainly banks). It uses two 56-bit key using three steps:-

1. Encrypt with Key 1.
2. Decrypt with Key 2.
3. Encrypt with Key 1.

The effective key length used is only 112-bits (equivalent to 34 digits). The key is any number between 0 and 5192296858534827628530496329220095. Some modify the last process using Key 3, making it more effective at 168-bit keys.

Advanced Encryption Standard (AES) was adopted as a standard by the National Institute of Standards & Technology, U.S.A. (NIST) in 2001. AES is based on the Rijndael (pronounced "rhine-doll") cipher developed by two Belgian cryptographers, Victor Rijmen and Joan Daemen. Typically, AES uses 256-bits (equivalent to 78 digits) for its keys. The key is any number between 0 and 1579208923731619542357098500868790785326998466564056403