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{{WikiProject
{{WikiProject
{{WikiProject Numismatics |importance=low }}
{{WikiProject Cryptocurrency|importance=mid}}
{{WikiProject Mathematics|priority=Mid }}
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{{annual readership|scale=log}}
==Security analysis of ECC==
Interesting research and summary of security for different ECC: https://safecurves.cr.yp.to/ <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/153.46.253.213|153.46.253.213]] ([[User talk:153.46.253.213#top|talk]]) 14:18, 4 August 2023 (UTC)</small> <!--Autosigned by SineBot-->
==Cite required==
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See www.nist.gov/encryption for a list of recommended elliptic curves. ANSI X9 requires a minimum of 80 bits of *symmetric key equivalent* security. THis means use of SHA-1 with 160 bit output, use of RSA/DSA with 1024 bit keys and use of ECC with 160 bit keys. Don Johnson
The references of 256 bit ECC keys providing 128-bit security need citation.
[[User:Bdamm|Bdamm]] ([[User talk:Bdamm|talk]]) 17:23, 13 August 2018 (UTC)
== Non-mathematical description needed ==
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In reference to quantum computing attacks the article reads "Elliptic curve cryptography is vulnerable to a modified Shor's algorithm for solving the discrete logarithm problem on elliptic curves" with two citations (<ref>{{cite journal |title=Using the Quantum Computer to Break Elliptic Curve Cryptosystems |first=Jodie |last=Eicher |first2=Yaw |last2=Opoku |date=July 29, 1997 }}</ref><ref>{{cite journal |title=Shor's Discrete Logarithm Quantum Algorithm for Elliptic Curves |first=John |last=Proos |first2=Christof |last2=Zalka |year=2003 |journal=Quantum Information and Computing |volume=3 |issue=4 |pages=317–344 |doi= |arxiv=quant-ph/0301141 |bibcode=2003quant.ph..1141P }}</ref>). Looking through both of these citations, they both work over fields of prime order, with the latter paper explicitly stating that they did not consider fields of prime power order. If ECC over fields of prime power order is truly vulnerable to QC attacks, I think there should be a citation that references this. [[User:GromXXVII|GromXXVII]] ([[User talk:GromXXVII|talk]]) 22:20, 25 June 2012 (UTC)
:Good catch! I updated the reference. If you need more information or have any other ideas, please share. [[User:Skippydo|Skippydo]] ([[User talk:Skippydo|talk]]) 01:58, 26 June 2012 (UTC)
::I found a copy of the first 1997 Eicher reference if it is still of use: (cite tag: {{cite journal |title=Using the Quantum Computer to Break Elliptic Curve Cryptosystems |first=Jodie |last=Eicher |first2=Yaw |last2=Opoku |date=July 29, 1997 |url=http://www.mathcs.richmond.edu/~jad/summerwork/ellipticcurvequantum.pdf |archiveurl=http://web.archive.org/web/20030509012110/http://www.mathcs.richmond.edu/~jad/summerwork/ellipticcurvequantum.pdf |archivedate=2003-05-09 |dead-url=no}}). I (probably is) be outdated though, though it might be useful for background info (?). [[User:Jimw338|Jimw338]] ([[User talk:Jimw338|talk]]) 04:18, 12 September 2016 (UTC)
I just rewrote the whole section with an updated citation and what I hope is both clearer wording and a more NPOV. [[User:Tarcieri|Tarcieri]] ([[User talk:Tarcieri|talk]]) 18:40, 3 November 2017 (UTC)
{{reflist-talk}}
== Possible NSA backdoor ==
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==Algorithm needed==
This article doesn't contain the algorithm for ECC like the RSA article does. <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/198.52.160.180|198.52.160.180]] ([[User talk:198.52.160.180#top|talk]]) 20:30, 6 December 2019 (UTC)</small> <!--Autosigned by SineBot-->
== The first paragraph seems self-contradictory ==
The first paragraph states that ECC is based on finite fields, as opposed to non-EC cryptography, which is based on plain Galois fields. However, the referenced article on [[Finite field|finite fields]] explains that finite fields and Galois fields are one and the same. I suspect the intended meaning is that non-EC crypto is based structures over finite fields which are not elliptic curves. If so, this is not clear from the text. I won't change the formulation myself, since I'm not an expert in the field. <!-- Template:Unsigned --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:VecLuci|VecLuci]] ([[User talk:VecLuci#top|talk]] • [[Special:Contributions/VecLuci|contribs]]) 04:13, 10 October 2018 (UTC)</small> <!--Autosigned by SineBot-->
== Not a typo. 521, not 512. ==
"Five prime fields <math>\mathbb{F}_p</math> for certain primes ''p'' of sizes 192, 224, 256, 384, and <nowiki>{{Not a typo|521}}</nowiki> bits. For each of the prime fields, one elliptic curve is recommended."
Should there be a footnote about that 521 not being a typo? It really is 521 (see [https://crypto.stackexchange.com/questions/62083/why-would-diffie-hellman-group-21-be-521-bits-rather-than-512] among many, many sources) but it really looks like someone mis-typed "512". [[Special:Contributions/76.216.220.191|76.216.220.191]] ([[User talk:76.216.220.191|talk]]) 04:00, 28 December 2021 (UTC)
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