Editing Rabin cryptosystem (section)

==History==
The Rabin trapdoor function was first published as part of the [[Rabin signature]] scheme in 1978 by [[Michael O. Rabin]].<ref name="rabin1978digsigs">{{cite book
|author1-last=Rabin
|author1-first=Michael O.
|author1-link=Michael O. Rabin
|editor1-last=DeMillo
|editor1-first=Richard A.
|editor1-link=Richard DeMillo
|editor2-last=Dobkin
|editor2-first=David P.
|editor2-link=David P. Dobkin
|editor3-last=Jones
|editor3-first=Anita K.
|editor3-link=Anita K. Jones
|editor4-last=Lipton
|editor4-first=Richard J.
|editor4-link=Richard Lipton
|title=Foundations of Secure Computation
|year=1978
|publisher=Academic Press
|location=New York
|isbn=0-12-210350-5
|pages=155–168
|chapter=Digitalized Signatures
}}</ref><ref name="rabin1979lcs-tr">{{cite tech report
|last=Rabin
|first=Michael O.
|author-link=Michael O. Rabin
|title=Digitalized Signatures and Public Key Functions as Intractable as Factorization
|number=TR-212
|institution=MIT Laboratory for Computer Science
|date=January 1979
|location=Cambridge, MA, United States
|url=http://publications.csail.mit.edu/lcs/pubs/pdf/MIT-LCS-TR-212.pdf
}}</ref><ref name="bellare-rogaway1996exactsigs">{{cite conference
|last1=Bellare
|first1=Mihir
|author-link1=Mihir Bellare
|last2=Rogaway
|first2=Phillip
|author-link2=Phillip Rogaway
|title=The Exact Security of Digital Signatures—How to Sign with RSA and Rabin
|editor-last=Maurer
|editor-first=Ueli
|editor-link=Ueli Maurer (cryptographer)
|conference=Advances in Cryptology – EUROCRYPT ’96
|date=May 1996
|conference-url=https://link.springer.com/book/10.1007/3-540-68339-9
|volume=1070
|series=Lecture Notes in Computer Science
|publisher=Springer
|location=Saragossa, Spain
|isbn=978-3-540-61186-8
|pages=399–416
|doi=10.1007/3-540-68339-9_34
|doi-access=free
}}</ref>
The Rabin signature scheme was the first [[digital signature]] scheme where forging a signature could be proven to be as hard as factoring.

The trapdoor function was later repurposed in textbooks as an example of a [[public-key encryption]] scheme,<ref name=stinson>{{cite book
|title=Cryptography: Theory and Practice
|last=Stinson
|first=Douglas
|author-link=Doug Stinson
|edition=3rd
|isbn=978-1-58488-508-5
|publisher=Chapman & Hall/CRC
|date=2006
|section=5.8
|pages=211–214
}}</ref><ref name="hac">{{cite book
|author1-last=Menezes
|author1-first=Alfred J.
|author1-link=Alfred Menezes
|author2-last=van Oorschot
|author2-first=Paul C.
|author2-link=Paul van Oorschot
|author3-last=Vanstone
|author3-first=Scott A.
|author3-link=Scott Vanstone
|title=Handbook of Applied Cryptography
|publisher=CRC Press
|date=October 1996
|isbn=0-8493-8523-7
|section=§8.3: Rabin public-key encryption
|url=https://cacr.uwaterloo.ca/hac/about/chap8.pdf#page=11
|pages=292–294
}}</ref><ref name="galbraith2012mathpkc"/>
which came to be known as the Rabin cryptosystem even though Rabin never published it as an encryption scheme.