Applications of Number Theory in Cryptography
Overview
Cryptography is a division of applied mathematics concerned with developing schemes and formulas to enhance the privacy of communications through the use of codes. Cryptography allows its users, whether governments, military, businesses, or individuals, to maintain privacy and confidentiality in their communications. The goal of every cryptographic scheme is to be "crack proof" (i.e, only able to be decoded and understood by authorized recipients). Cryptography is also a means to ensure the integrity and preservation of data from tampering. Modern cryptographic systems rely on functions associated with advanced mathematics, including a specialized branch of mathematics termed number theory that explores the properties of numbers and the relationships between numbers.
Background
Attempts to preserve the privacy of communications is an age-old quest. From the use of hidden text, disappearing inks, and code pads has evolved the modern science of cryptography. The word cryptography originally derives from the Greek, kryptos (to hide). In essence, cryptography is the study of procedures that allow messages or information to be encoded (obscured) in such a way that it is extremely difficult to read or understand the information without having a specific key (i.e., procedures to decode).
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