Cryptography
Broadly speaking, the term cryptography refers to a wide range of security issues in the transmission and safeguarding of information. Historically, the main use of cryptography was to encipher messages; but in recent years other tasks, such as digital si
- PDF / 2,490,595 Bytes
- 21 Pages / 547.087 x 685.984 pts Page_size
- 71 Downloads / 224 Views
Broadly speaking, the term cryptography refers to a wide range of security issues in the transmission and safeguarding of information. Historically, the main use of cryptography was to encipher messages; but in recent years other tasks, such as digital signatures, have become at least as important as encryption. Until the late 1970's, all cryptographic message transmission was by what can be called private key. This means that someone who has enough information to encrypt messages automatically has enough information to decrypt messages as well. As a result, any two users of the system who want to communicate secretly must have exchanged keys in a safe way, e.g., using a trusted courier. The face of cryptography was radically altered when Diffie and Hellman invented an entirely different type of cryptography, called public key (DiffieHellman 1976), and when Rivest, Shamir, and Adleman proposed the first practical implementation of the new cryptography (Rivest-Shamir-Adleman 1978).1 At the heart of this concept is the idea of using a one-way function for encryption. Speaking informally, we say that a one-to-one function I: X -+ Y is "one-way" if it is easy to compute I (x) for any x E X but hard to compute 1-1 (y) for almost all y in the range of I. The functions used for encryption belong to a special class of one-way functions that remain one-way only if some information (the "decryption key") is kept secret. Again using informal terminology, we can define a public key encryption function (also called a "trapdoor" function) as a map from a block of plain text to a block of enciphered text that can be easily computed by anyone having the so-called "public" key but whose inverse function (which deciphers the ciphertext message) cannot be computed in a reasonable amount of time without some additional information (the "private" key). This means that everyone can send a message to a given user using the same enciphering key, which they simply look up in a public directory. There is no need for the sender to have made any secret arrangement with the recipient; indeed, the recipient need never have had any prior contact with the sender at all. It was the invention of public key cryptography that led to a dramatic expansion of the role of algebra and number theory in cryptography. The reason 1 It is now known that these ideas had been developed in secret a few years earlier by James Ellis and Clifford Cocks of the British Government Communications Headquarters (GCHQ). However, the significance of public key cryptography went largely unappreciated at GCHQ, and some of its most important features - such as the possibility of digital signatures - were not recognized until public key cryptography was studied in an academic setting.
B. Engquist et al. (eds.), Mathematics Unlimited — 2001 and Beyond © Springer-Verlag Berlin Heidelberg 2001
750
N.
KOBLITZ
is that this type of mathematics seems to provide the best source of one-way functions. This article is not a survey in the usual sense; I will not attempt to give an ov
Data Loading...
