Public-key cryptography: Difference between revisions

Revision as of 09:43, 31 May 2025

Revision as of 21:09, 31 May 2025

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1) Alice signs a message with her private key.

2) Using Alice's public key, Bob can verify that Alice sent the message and that the message has not been modified.]]

[[File:Public key shared secret.svg|thumb|250px|right| In the [[Diffie–Hellman key exchange]] scheme, each party generates a public/private key pair and distributes the public key of the pair. After obtaining an authentic (n.b., this is critical) copy of each other's public keys, Alice and Bob can compute a shared secret offline. The shared secret can be used, for instance, as the key for a [[symmetric cipher]], which will be, in essentially all cases, much faster.]]

[[File:Public key encryption.svg|thumb|250px|right|In an asymmetric key encryption scheme, anyone can encrypt messages using a public key, but only the holder of the paired private key can decrypt such a message. The security of the system depends on the secrecy of the private key, which must not become known to any other.]]

'''Public-key cryptography''', or '''asymmetric cryptography''', is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a '''public key''' and a corresponding '''private key'''.{{Ref RFC|4949|notes=no}}<ref>{{Cite journal |last1=Bernstein |first1=Daniel J. |last2=Lange |first2=Tanja |date=2017-09-14 |title=Post-quantum cryptography |url=http://www.nature.com/articles/nature23461 |journal=Nature |language=en |volume=549 |issue=7671 |pages=188–194 |doi=10.1038/nature23461 |pmid=28905891 |bibcode=2017Natur.549..188B |s2cid=4446249 |issn=0028-0836}}</ref> Key pairs are generated with [[cryptographic]] [[algorithms]] based on [[mathematical]] problems termed [[one-way function]]s. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security.<ref>{{Cite book|url=https://books.google.com/books?id=Dam9zrViJjEC|title=Cryptography and Network Security: Principles and Practice|last=Stallings|first=William|date=3 May 1990|publisher=Prentice Hall|isbn=9780138690175|page=165|language=en}}</ref> There are many kinds of public-key cryptosystems, with different security goals, including [[digital signature]], [[Diffie–Hellman key exchange]], [[Key encapsulation mechanism|public-key key encapsulation]], and public-key encryption.