Cryptography is a division of applied mathematics concerned with developing methods to enhance the privacy of communications and protect data from tampering through the use of coded information. The application of quantum principles to information processing and cryptology fuses mathematical theory and physical reality. Quantum cryptology utilizes the Heisenberg uncertainty principle to describe a system in which a measurement of the system disturbs the system and in so doing yields valuable information about the state of the system.
Cryptography allows its users to maintain confidentiality in their communications and, ideally, cryptographic schemes should only be able to be decoded and understood by authorized recipients (i.e., to be crack proof) who have a specific key (i.e., procedures to decode) that can be used to reverse the encoding procedure. Cryptography is also essential to the development and use of non-reputable transactions in which parties can not later deny involvement in making or authorizing certain transactions (e.g., entering into contracts). Courts around the world are increasingly faced with disputes regarding electronic communications and the development of a global electronic economy is dependent on the development of verifiable (non-reputable) transactions that carry the legal weight of traditional paper contracts.
The art of cryptography is ancient, the word cryptography originally derives from the Greek word Kryptos (to hide). Throughout history, wars and diplomatic negotiations have often turned on the ability of military and political leaders to read the messages of their adversaries. During World War II, for example, the Allied Forces enjoyed a tremendous strategic and tactical advantage from being able to intercept and read the secret messages of Nazi Germany. Although the Germans had encoded their communications with a cipher machine called Enigma, the Allies were able to crack the German code. Both direct physical examination of the encoding machines and mathematical analysis of encrypted communications were essential to the Allied success in cracking the German code. The United States also gained a decided advantage over Imperial Japanese forces through the development of operation MAGIC--a program that cracked Japanüs diplomatic codes.
Although earlier cryptographic algorithms were developed for use by government intelligence agencies, in 1977 Ronald Rivest, Adi Shamir, and Leonard Adleman published what would become known as the RSA algorithm based upon the factoring of very large composite numbers. The RSA algorithm became an essential component in the first cryptologic systems widely available to the public. By the end of the twentieth century, the RSA algorithm became the most commonly used encryption and authentication algorithm in the world as it was incorporated into security programs used by Internet browsers, spreadsheets, email, and word processing programs.
Encryption systems can be simple (e.g., involving only the replacement of letters with numbers) or they can involve the use of highly secure one-time pads (also known as Vernam ciphers). In some cryptologic schemes, encryption is accomplished by calculating the products of certain prime numbers as basis for further mathematical operations. In addition to developing such mathematical keys, the data itself is divided into blocks of specific and limited length to thwart mathematical analysis based on statistical methods. Decryption is usually accomplished by following a reconstruction procedure that itself often involves unique or complex mathematical operations. In other cases, decryption is accomplished by performing the inverse of mathematical operations performed during encryption.
In some cryptographic systems, encoding and decoding procedures are accomplished using two separate keys (mathematical procedures). One key is used to code or lock a message, the other key is used to decode or unlock the message. In a two-key cryptologic systems such as a public key system, the public key is distributed so that a sender can encode a message and send it to the holder of a related private key. Accordingly, although the sender uses the recipient's public key to encode the message, the message can only be decoded with the recipientüs private key. Beginning in 1991 the two-key public key method was used by cryptographers and computer technologists to enhance Internet security through a freely distributed package called Pretty Good Privacy (PGP).
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. Specialized mathematical derivations and equations dealing with elliptical curves are also making an increasing impact on cryptology. Although, in general, larger and more elaborate cryptographic keys provide increased security, applications of number theory and elliptical curves to cryptological algorithms allow the use smaller keys or shorter procedures without a loss of security.
Cryptologic applications increased with the incorporation of security protocol in transistor-based electronic technology originally developed for use with RADAR. Although subsequent microchip technology made possible the production of higher-speed computers, they also rendered cryptologic systems increasingly vulnerable to mathematical analysis. Fortunately, despite advances in number theory and computing power, it remains easier to generate the large composite numbers that underlie most modern cryptologic systems than it is to factor those numbers. Recent advances in number theory, however, now allow factoring of large numbers that, if factored by traditional methods or hand calculations, might have previously taken, at a minimum, millions of man-hours to factor. Accordingly, the use of advanced computers adds a powerful tool to both encryption and decryption programs. Further advances in number theory may lead to the discovery of polynomial time-factoring algorithms that further reduce required computing time
Application of the principles derived from quantum physics to quantum communications systems would make it impossible to interrupt or intercept such a system without alerting the users of said interference.
The National Institute of Standards and Technology (NIST), oversees the development of cryptography standards. As of 2000, cryptographic algorithms were classified as munitions by the United States government. As such, they remained subject to severe export control and restrictions inhibiting their distribution and use.
This is the complete article, containing 956 words
(approx. 3 pages at 300 words per page).
