Secrets On Security: A Gentle Introduction To Cryptography

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 15792089237316195423570985008687907853269984665640564039457584007913129639935. This number is the same as the estimated number of atoms in the universe.

The National Security Agency (NSA) approved AES in June 2003 for protecting top-level secrets within US governmental agencies (of course subject to their approval of the implementation methods). They are reputedly the ones that can eavesdrop on all telephone conversations going on around the world. Besides, this organization is recognized to be the largest employer of mathematicians in the world and may be the largest buyer of computer hardware in the world. The NSA probably have cryptographic expertise many years ahead of the public and can undoubtedly break many of the systems used in practice. For reasons of national security, almost all information about the NSA - even its budget is classified.

A brute force attack is basically to use all possible combinations in trying to decrypt encrypted materials.

A dictionary attack usually refers to text-based passphrases (passwords) by using commonly used passwords. The total number of commonly used passwords is surprisingly small, in computer terms.

An adversary is somebody, be it an individual, company, business rival, enemy, traitor or governmental agency who would probably gain by having access to your encrypted secrets. A determined adversary is one with more "brains" and resources. The best form of security is to have zero adversary (practically impossible to achieve), the next best is to have zero determined adversary!

A keylogger is a software program or hardware to capture all keystrokes typed. This is by far the most effective mechanism to crack password-based implementations of cryptosystems. Software keylogger programs are more common because they are small, work in stealth-mode and easily downloaded from the internet. Advanced keyloggers have the ability to run silently on a target machine and remotely deliver the recorded information to the user who introduced this covert monitoring session. Keystroke monitoring, as everything else created by man, can either be useful or harmful, depending on the monitor’s intents. All confidential information which passes through the keyboard and reaches the computer includes all passwords, usernames, identification data, credit card details, and confidential documents (as they are typed).

For the last definition, we will use an example. Let's say you have your house equipped with the latest locks, no master keys and no locksmith can tamper with them. Your doors and windows are unbreakable. How then does an adversary get into your house without using a bulldozer to break your front door? Answer: the roof - by removing a few tiles, the adversary can get into your house. This is an exploit (weakness point). Every system, organization, individual has exploits.

See, it is not that difficult after all. If you can understand the material presented in this article, congratulations - you have become crypto-literate (less than 1% of all current computer users). If you do not believe me, try using some of this newfound knowledge on your banker friends or computer professionals.

Stan Seecrets’ Postulate: “The sum total of all human knowledge is a prime number.”

Corollary: “The sum total of all human wisdom is not a prime number.”

This article may be freely reprinted providing it is published in its entirety, including the author’s bio and link to the URL below.

The author, Stan Seecrets, is a veteran software developer with 25+ years experience at (http://www.seecrets.biz) which specializes in protecting digital assets. This site provides quality software priced like books, free-reprint articles on stock charts and computer security, free downloads and numerous free stuff. © Copyright 2005, Stan Seecrets. All rights reserved.

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