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 (Frösen
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methods within feasible time without the data being outdated cannot break the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 (Frösen 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).
