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== Description ==
Before the mid-1970s, all cipher systems used [[symmetric key algorithm]]s, in which the same [[cryptographic key]] is used with the underlying algorithm by both the sender and the recipient, who must both keep it secret. Of necessity, the key in every such system had to be exchanged between the communicating parties in some secure way prior to any use of the system – for instance, via a [[secure channel]]. This requirement is never trivial and very rapidly becomes unmanageable as the number of participants increases, or when secure channels are not available, or when
By contrast, in a public-key cryptosystem, the public keys can be disseminated widely and openly, and only the corresponding private keys need be kept secret.
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All public key schemes are in theory susceptible to a "[[brute-force attack|brute-force key search attack]]".<ref>{{cite book|last1=Paar|first1=Christof|first2=Jan|last2=Pelzl|first3=Bart|last3=Preneel|url=http://www.crypto-textbook.com|title=Understanding Cryptography: A Textbook for Students and Practitioners|publisher=Springer|year=2010|isbn=978-3-642-04100-6}}</ref> However, such an attack is impractical if the amount of computation needed to succeed – termed the "work factor" by [[Claude Shannon]] – is out of reach of all potential attackers. In many cases, the work factor can be increased by simply choosing a longer key. But other algorithms may inherently have much lower work factors, making resistance to a brute-force attack (e.g., from longer keys) irrelevant. Some special and specific algorithms have been developed to aid in attacking some public key encryption algorithms; both [[RSA (algorithm)|RSA]] and [[ElGamal encryption]] have known attacks that are much faster than the brute-force approach.{{cn|date=June 2024}} None of these are sufficiently improved to be actually practical, however.
Major weaknesses have been found for several formerly promising asymmetric key algorithms. The [[Merkle–Hellman knapsack cryptosystem|"knapsack packing" algorithm]] was found to be insecure after the development of a new attack.<ref>{{Cite book|last1=Shamir|first1=Adi|title=23rd Annual Symposium on Foundations of Computer Science (SFCS 1982) |chapter=A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem |date=November 1982
=== Alteration of public keys ===
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