Public-key cryptography: Difference between revisions

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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, (as is sensible cryptographic practice), keys are frequently changed. In particular, if messages are meant to be secure from other users, a separate key is required for each possible pair of users.

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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[[Non-repudiation]] systems use digital signatures to ensure that one party cannot successfully dispute its authorship of a document or communication.

Further applications built on this foundation include: [[digital cash]], [[password-authenticated key agreement]], [[Trusted timestamping|time-stamping services]] and non-repudiation protocols. Beyond traditional secure communication, public-key cryptography is fundamental to the operation of [[blockchain]] technologies and [[Cryptocurrency|cryptocurrencys]] like [[Bitcoin]] and [[Ethereum]]. It enables secure [[Digital signature|digital signatures]] for transactions, ensuring their authenticity and integrity without relying on a central authority. Additionally, it underpins secure access to cloud services, [[Virtual private network|virtual private networks]] (VPNs), and [[Internet of Things]] (IoT) devices, providing robust authentication and data encryption across diverse digital environments.

== Hybrid cryptosystems ==

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As with all security-related systems, there are various potential weaknesses in public-key cryptography. Aside from poor choice of an asymmetric key algorithm (there are few that are widely regarded as satisfactory) or too short a key length, the chief security risk is that the private key of a pair becomes known. All security of messages, authentication, etc., will then be lost.

Additionally, with the advent of [[quantum computing]], many asymmetric key algorithms are considered vulnerable to attacks, and new quantum-resistant schemes are being developed to overcome the problem.<ref>{{Cite journal |last1=Escribano Pablos |first1=José Ignacio |last2=González Vasco |first2=María Isabel |date=April 2023 |title=Secure post-quantum group key exchange: Implementing a solution based on Kyber |url=https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/cmu2.12561 |journal=IET Communications |language=en |volume=17 |issue=6 |pages=758–773 |doi=10.1049/cmu2.12561 |hdl=10016/37141 |s2cid=255650398 |issn=1751-8628|hdl-access=free }}</ref><ref>{{Citation |last1=Stohrer |first1=Christian |title=Asymmetric Encryption |date=2023 |work=Trends in Data Protection and Encryption Technologies |pages=11–14 |editor-last=Mulder |editor-first=Valentin |place=Cham |publisher=Springer Nature Switzerland |language=en |doi=10.1007/978-3-031-33386-6_3 |isbn=978-3-031-33386-6 |last2=Lugrin |first2=Thomas |editor2-last=Mermoud |editor2-first=Alain |editor3-last=Lenders |editor3-first=Vincent |editor4-last=Tellenbach |editor4-first=Bernhard|doi-access=free }}</ref> The emergence of [[quantum computing]] poses a significant long-term threat to the security of many widely used public-key cryptographic algorithms, particularly [[RSA]] and [[Elliptic Curve Cryptography|ECC]]. These algorithms rely on the computational difficulty of factoring large numbers or solving discrete logarithms, problems that quantum computers could potentially solve efficiently using algorithms like [[Shor's algorithm]]. In response, the field of [[post-quantum cryptography]] is [https://www.ibm.com/think/topics/public-key-encryption actively researching and developing new cryptographic primitives that are resistant to attacks from both classical and quantum computers]. International efforts, such as those led by the [[National Institute of Standards and Technology]] (NIST), are [https://csrc.nist.gov/projects/post-quantum-cryptography underway to standardize these new algorithms for future secure communication].

=== Algorithms ===

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 |chapter-url=https://ieeexplore.ieee.org/document/4568386 |pages=145–152|doi=10.1109/SFCS.1982.5}}</ref> As with all cryptographic functions, public-key implementations may be vulnerable to [[side-channel attack]]s that exploit information leakage to simplify the search for a secret key. These are often independent of the algorithm being used. Research is underway to both discover, and to protect against, new attacks.

=== Alteration of public keys ===