Communications and Security: Cryptography

Cryptography is the practice of several different techniques to secure communication in the presence of any adversaries. Modem cryptography intersects with disciplines such electrical engineering, computer science, and mathematics. Applications of such cryptography include electric commerce, computer passwords, and ATM cards. Since modern cryptography is heavily based on the theory of mathematics and computer science practice, algorithms are designed to prevent any break ins by an adversary. Theoretically, it would be impossible to break into a system that has cryptography.

Symmetric-key cryptography refers to a method of encryption where both the sender and receiver share the same key. Data Encryption Standard (DES) and Advanced Encryption Standard (AES) have been designated cryptography standards. These types of encryptions follow the style of symmetric-key cryptography.

Public-key cryptography is a system of cryptography that uses the same key for encryption and decryption. A significant disadvantage in this system is how the cipher is completely symmetric so it is necessary to use them securely.

Based on the computational complexity of "hard" problems from number theory, there are a large number of public-key algorithms. These algorithms involves exponentiation and modular multiplication. Compared to most block ciphers, these are generally more computationally expensive to do.

In the end, cryptography is important because it allows data to remain discrete from adversaries of any type.

References:
http://web.archive.org/web/20050307081354/www.cacr.math.uwaterloo.ca/hac/
http://www.theregister.co.uk/2011/07/13/eff_piles_in_against_forced_decryption/
http://books.google.com/books?id=cH-NGrpcIMcC&pg=PA6&dq&hl=en#v=onepage&q=&f=false
http://all.net/books/ip/Chap2-1.html