Mathematical Codes Essays - Cryptography, Cipher,

Mathematical Codes Mathematical Codes Mathematical codes are used by millions everyday for a variety reasons, but all intending to keep something private. The coding theory has actual applications in consumer electronics and with other areas of mathematics. Encryption, which involves enciphering and encoding, is used to protect data against organized crime, government and multinational institutions. A use of arithmetic, prime numbers, and prime factorization is used within coding theory. The study of enciphering and encoding, and deciphering and decoding is called cryptography (Gardner 17). Encryption is encoding or enciphering a message so that the contents are hidden from outsiders (Fr?sen 10). Strong encryption is not a technical standard, it means that current known methods within feasible time without the data being outdated cannot break the encryption. Strong encryption is used to protect data against organized crime, government and multinational institutions. Strong encryption brings possible applications into daily life. Electric money, secure communications, passwords, and others are among many. Applications that require privacy, trust and access control should all use strong encryption methods when possible. It is suggested that people's legal, medical, personal data about themselves should stay confidential to the instances that have a permit to collect the databases. Encryption is not a new concept. Militaries and diplomatic forces have been using it for thousand of years, trying to keep information from the enemy. Given, it was more simplistic back then, but it was still used during War. For example, the Americans have used Morse code for years. There is a distinct difference between ciphers and codes. Substituting one word for another word or sentence is using a code (Gardner 18). Mixing up or substituting existing letters for one word or sentence is using a cipher (18). The majority of encryptions use ciphers versus codes. The algorithm is the method used to encipher the original message, known as the plaintext (20). A key is used with the algorithm to allow the plaintext to be both enciphered and deciphered (20). Ciphers are broken into two main categories: substitution ciphers and transportation ciphers. Substitution ciphers replace letters in the plaintext with other letters or symbols, keeping the order in which the symbols fall the same (25). By definition, substitution ciphers could be, in most cases, called codes. Transposition ciphers keep all of the original letters intact, but mix up the order (25). The resulting text is referred to as the ciphertext. Some cryptographic methods rely on the secrecy of algorithms used in the cipher, security by obscurity (Fr?sen 2). All modern algorithms use a key to control the encryption and decryption. The message can only be decrypted if the key matches the on it was encrypted with. The key used for decryption can be different from the key used in encryption, and this divides the algorithms in symmetric and asymmetric classes (2). Symmetric cryptosystems use the same key, the secret key, to encrypt and decrypt a message. Since it uses the same key for both encryption and decryption, the key should be changed often and be sufficiently random (2). Symmetric algorithms use different length keys, which usually means higher security. Symmetric algorithms can be divided into two categories: stream ciphers, which take and encrypt one bit of the original data at a time, and block ciphers, which take a number of bits and encrypt them as a single block (2). The majority of ciphers belong to the block cipher class. Symmetric algorithms are generally faster and use a much shorter key than asymmetric ones. DES, Data Encryption Standard, is the notorious symmetric cryptosystem. It has been certified by NIST, National Institution of Standards and Technology, for use as an official US Government encryption standard for less-than-top-secret secret material (2). DES was first certified for government use in 1977 (2). DES is a strong cipher, which encrypts a block of 64 bits at a time. DES encryption consists of many rounds of different transformations and permutations, which are linear and easy to reverse (3). Performing a permutation involves arranging elements in different arrangements, where order does matter. The critical encryption is done using S-boxes. S-boxes, or substitution boxes, are sets of highly non-linear functions, implemented in DES as a set of lookup tables (3). After the