Talk:General number field sieve

message: various other wikipedia articles link to nfs to say that it can be used to compute the discrete logarithm, yet this page doesn't talk about it. At least it should tell that there are some significant differences (e.g. Anna Godusova "Number Field Sieve for Discrete Logarithm")  — Preceding unsigned comment added by 193.8.68.100 (talk) 10:40, 6 February 2019 (UTC)
thread_title:  Discrete logarithms 

message: The current article states that the Big-O notation for GNFS is
:O\left(\exp\left(\left(\begin{matrix}\frac{64}{9}\end{matrix} n\right)^{1\over3} (\log n)^{2\over3}\right)\right) 
However, at this location it states that the Big-O notation is actually
:O\left(\exp\left(\left(\begin{matrix}\frac{64}{9}\end{matrix} n\right)^{1\over3} \log (\log n)^{2\over3}\right)\right)
Nicholasink 02:57, 20 November 2006 (UTC)
thread_title:  Big-O? 

message: Could we get some examples, please? 4.65.244.206 18:12, 23 Mar 2004 (UTC)
thread_title: Examples

message: Thanks alot to whoever wrote the page. I'm reading up and can do it myself soon, but in the mean time can you make it clear which fields we're in throughout the process. The irreducible polynomials for example. I know it's obvious you mean irreducible in Q but it never hurts to get rid of all ambiguity when you're reading it for the first time.--Gtg207u 23:25, 5 November 2007 (UTC)
thread_title:  Which fields 

message: The formulae for the running times of GNFS and SNFS are now inconsistent. The former uses n as the number of digits of the number to be factored, while the latter uses n as the number to be factored itself. To be consistent, I'll change the GNFS running time to the SNFS way. The current formula for GNFS needs to be corrected anyway since it is wrong in both context. Warut 22:07, 21 November 2006 (UTC)
thread_title:  Consistency in running time notation between GNFS and SNFS 

message: How to find square root of product of algebraic numbers ?  —Preceding unsigned comment added by 59.93.211.167 (talk) 10:53, 4 November 2007 (UTC)
thread_title:  Finding square root 

message: The current formula uses the notation  \log n .  I usually interpret this to be the natural logarithm (i.e. the base e logarithm whose derivative is  1/n ), however other parts of the text  say that n consists of  \log n  bits, which implicitly means that the  \log n  notation indicates a base two logarithm.  
As I understand it, the base of the logarithm (i.e. 2 or e) affects the constant c in the main complexity formula.  
According to the Handbook of Applied Cryptography, Example 2.61 and Section 3.2.7, the logarithm is a base e logarithm and the constant c is  (64/9)^{1/3} \approx 1.923 .  I assume that this is correct.  So, I suggest that the article be edited 
* to state explicitly the value of the constant c, as above, 
* to state that the base of the logarithm is e,
* to update text about the bit length of n to say that is  1 + \lfloor \log_2 n \rfloor  and that  \log_2 n = (\log n)/(\log 2) 
Unless somebody objects to this, or somebody else volunteers to make these changes, I may make these changes. DRLB (talk) 14:47, 26 May 2008 (UTC)
replies: text: My recommendation is to remove the mention of the number of bits of n, mention that the logarithm is base e and cite the value of c which you state. Please tell me what you think. Skippydo (talk) 18:47, 26 May 2008 (UTC)
replies: text: I've changed the logarithm notation to ln because it is also used for the L-notation and it is the ISO standard, see Logarithm. Henridv (talk) 17:10, 6 June 2012 (UTC)
thread_title:  Constant ''c'' and the logarithm's base 

message: How about merging this article with Special number field sieve to form a single article simply entitled Number field sieve? Gremagor (talk) 05:06, 8 January 2010 (UTC)
replies: text: That would make more sense to me. I started adding info about the NFSNET project, but it seems more particular to the specialized cases. W Nowicki (talk) 20:34, 9 August 2011 (UTC)
thread_title:  Merge with SNFS 

message: The article should somewhere state that the GNFS is also the (exponentially) fastest known algorithm for computing discrete logarithms over GF(p) (p prime). Some more background on that would be desirable, too. Cheers, Nageh (talk) 18:23, 27 January 2010 (UTC)
thread_title:  GNFS fastest algorithm for computing discrete logs 

message: Article should mention parallel approaches based on Bernstein's proposals for NFS circuits.  I might try to add something but I haven't kept up with current developments.  67.117.130.143 (talk) 22:25, 3 December 2010 (UTC)
thread_title:  special hardware 

message: The quadratic sieve is described as modern by its article and the number field sieve is described as classical. The invention of the quadratic sieve predates the number field sieve. shouldn't the number field sieve be a modern algorithm? 112.204.119.66 (talk)
:It could mean classical in the quantum sense. Regardless, I'll remove both these terms. Skippydo (talk) 04:53, 24 February 2012 (UTC)
replies: text: On second though, it does mean classical in the quantum sense and this should likely be stated in the intro. I'll remove modern from quadratic sieve and leave classical in this article. Skippydo (talk) 04:56, 24 February 2012 (UTC)
thread_title:  classical vs modern algorithm 

message: The complexity formula contains the expression "o(1)", there article contains no explanation of an o function, thus the collective expression is, within the article, incomprehensible. This either needs to be explained, or rewritten to basic maths. As far as I can tell, o(1) must be 0 to give the numbers commonly cited around the internet, so why is it there at all?
EBusiness (talk) 18:47, 30 May 2019 (UTC)
thread_title:  Ghost variable/function/thingy o(1)