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In June 2012 the [[National Institute of Information and Communications Technology]] (NICT), [[Kyushu University]], and [[Fujitsu#Fujitsu Laboratories|Fujitsu Laboratories Limited]] improved the previous bound for successfully computing a discrete logarithm on a [[supersingular elliptic curve]] from 676 bits to 923 bits.<ref>{{cite web |work=Press release from NICT |date=June 18, 2012 |url=http://www.nict.go.jp/en/press/2012/06/18en-1.html |title=NICT, Kyushu University and Fujitsu Laboratories Achieve World Record Cryptanalysis of Next-Generation Cryptography }}</ref>
In 2016, the Extended Tower Number Field Sieve algorithm<ref>{{Cite journal |last1=Kim |first1=Taechan |last2=Barbulescu |first2=Razvan |date=2015 |title=Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case |url=https://eprint.iacr.org/2015/1027 |journal=Cryptology ePrint Archive |language=en}}</ref> allowed to reduce the complexity of finding discrete logarithm in some resulting groups of pairings. There are several variants of the multiple and extended tower number field sieve algorithm expanding the applicability and improving the complexity of the algorithm. A unified description of all such algorithms with further improvements was published in 2019.<ref>{{cite journal |last1=Sarkar |first1=Palash |last2=Singh |first2=Shashank |year=2019 |title=A unified polynomial selection method for the (tower) number field sieve algorithm |journal=Advances in the Mathematics of Communications |volume=13 |issue=3 |pages=435–455 |doi=10.3934/amc.2019028|doi-access=free }}</ref> In view of these advances, several works<ref>{{citation|last1=Menezes|first1=Alfred|last2=Sarkar|first2=Palash|last3=Singh|first3=Shashank|title=Challenges with assessing the impact of NFS advances on the security of pairing-based cryptography|publisher=Springer-Verlag|series=Lecture Notes in Computer Science|volume=10311|year=2016|pages=83–108|doi=10.1007/978-3-319-61273-7_5 |url=https://doi.org/10.1007/978-3-319-61273-7_5|isbn=978-3-319-61272-0|url-access=subscription}}</ref><ref>{{Cite journal |last1=Barbulescu |first1=Razvan |last2=Duquesne |first2=Sylvain |date=2019-10-01 |title=Updating Key Size Estimations for Pairings |url=https://doi.org/10.1007/s00145-018-9280-5 |journal=Journal of Cryptology |language=en |volume=32 |issue=4 |pages=1298–1336 |doi=10.1007/s00145-018-9280-5 |s2cid=253635514 |issn=1432-1378}}</ref> provided revised concrete estimates on the key sizes of secure pairing-based cryptosystems.
==References==
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