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Public-key cryptography is a form of modern cryptography which allows users to communicate securely without previously agreeing on a shared secret key. For most of the history of cryptography, a key had to be kept absolutely secret and would be agreed upon beforehand using a secure, but non-cryptographic, method; for example, a face-to-face meeting or a trusted courier. There are a number of significant practical difficulties in this approach to distributing keys . Public-key cryptography was invented to address these drawbacks — with public-key cryptography, users can communicate securely over an insecure channel without having to agree upon a key beforehand.

Public-key algorithms typically use a pair of two related keys — one key is private and must be kept secret, while the other is made public and can be widely distributed; it should not be possible to deduce one key of a pair given the other. The terminology of "public-key cryptography" derives from the idea of making part of the key public information. The term asymmetric-key cryptography is also used because not all parties hold the same information. Some public-key algorithms operate a little differently, and use other methods to enable parties to agree on secret keys without having previously exchanged key material.

Public-key cryptography has two main applications. First, is encryption — keeping the contents of messages secret. Second, digital signatures can be implemented using public key techniques. Typically, public-key techniques are much more computationally intensive than symmetric algorithms.

1 History

The first asymmetric key algorithm was invented, secretly, by Clifford Cocks (then a recent mathematics graduate and a new staff member at GCHQ in the UK) early in the 1970s, and reinvented by Rivest, Shamir and Adleman all then at MIT. Their work was published in 19761976 is a leap year starting on Thursday (link will take you to calendar). Events January January 12 UN Security Council votes 11-1 to admit the Palestinian Liberation Organization January 15 Would-be Gerald Ford presidential assassin Sara Jane Moore is s, and the algorithm was named RSAThis article is about the RSA cryptosystem. For other meanings, see RSA (disambiguation). RSA is a cipher algorithm. It is an asymmetric algorithm and plays a key role in public key cryptography. It is widely used in electronic commerce protocols. The alg after the initials of their last names. Since then, several other asymmetric key algorithms have been developed, but the most widely known remains Cocks/RSA. It uses exponentiation modulo a product of two large primesIn mathematics, a prime number or prime for short, is a natural number whose only distinct positive divisors are 1 and itself; otherwise it is called a composite number . Hence a prime number has exactly two divisors. The number 1 is neither prime nor com to encrypt and decrypt. The public key exponent differs from the private key exponent, and determining one from the other is believed to be fundamentally hard without knowing the primes; these are in turn (if large enough) computationally infeasible to determine at the current state of the computer hardware and large integer factorization arts. Another algorithm is ElGamal (invented by Taher ElGamalTaher Elgamal (sometimes seen El Gamal and ElGamal but Elgamal is preferred, see below) is an American-Egyptian cryptographer who published in 1985 a paper titled A Public key Cryptosystem and A Signature Scheme based on discrete Logarithms in which he pr then of NetscapeNetscape Communications Corporation Netscape Navigator Netscape Communicator.) which relies on the (similar, and related) difficulty of the discrete logarithm problem. A third is a group of algorithms based on elliptic curveIn mathematics, elliptic curves are defined by certain cubic (the superscript exponent is three, a. third degree) equations. They have been used in the proof of Fermat's last theorem and they also find applications in cryptography (for details, see the ars, first discovered by Neal Koblitz in the mid '80s.

The NSA — the US signals security agency — has also claimed to have invented public-key cryptography, in the 1960s; however, there is currently ( as of 2004) little supporting evidence for their claims [1].