**Cryptography**

**Contents**

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PUBLIC KEY
CRYPTOGRAPHY:__

In a
groundbreaking 1976 paper, Whitfield Difie and Martin Hellman proposed the
notion of *public-key* (also, more generally, called *asymmetric key*)
cryptography in which two different but mathematically related keys are used — a
*public* key and a *private* key. A public key system is so
constructed that calculation of one key (the 'private key') is computationally
infeasible from the other (the 'public key'), even though they are necessarily
related. Instead, both keys are generated secretly, as an interrelated pair.The

historian ‘David Kahn’ described public-key cryptography as “the most revolutionary new concept in the field since polyalphabetic substitution emerged”.

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·
In public-key
cryptosystems, the public key may be freely distributed, while its paired
private key must remain secret. The *public key* is typically used for
encryption, while the *private* or *secret key* is used for
decryption. In 1997, it finally became publicly known that asymmetric key
cryptography had been invented by James H Ellisat GCHQ, a British intelligence
organization, in the early 1970s.

·
In addition to
encryption, public-key cryptography can be used to implement digital signature
schemes. A digital signature is reminiscent of an ordinary signature; they both
have the characteristic that they are easy for a user to produce.Digital
signatures can also be permanently tied to the content of the message being
signed; they cannot be 'moved' from one document to another, for any attempt
will be detectable. In digital signature schemes, there are two algorithms: one
for *signing*, in which a secret key is used to process the message (or a
hash of the message, or both), and one for *verification,* in which the
matching public key is used with the message to check the validity of the
signature. RSA and DSA are two of the most popular digital signature.

· Public-key algorithms are most often based on the computational complexity of "hard" problems, often fromnumber theory. For example, the hardness of RSA is related to the integer factorization problem, while Diffie-Hellman and DSA are related to the discrete algorithm problem. More recently, elliptic curve cryptography has developed in which security is based on number theoretic problems involving elliptic curves. Because of the difficulty of the underlying problems, most public-key algorithms involve operations such as modular multiplication and exponentiation, which are much more computationally expensive than the techniques used in most block ciphers, especially with typical key sizes. As a result, public-key cryptosystems are commonlyhybrid cryptosystems, in which a fast high-quality symmetric-key encryption algorithm is used for the message itself, while the relevant symmetric key is sent with the message, but encrypted using a public-key algorithm. Similarly, hybrid signature schemes are often used, in which a cryptographic hash function is computed, and only the resulting hash is digitally signed.

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