Talk:Pollard's rho algorithm for logarithms

message: The first paragraph says "Divide G into three subsets (not necessarily subgroups) of approximately equal size".
As no two subgroups of any group G are ever distinct, the remark does not make any sense. I would recommend removing it. Better explanation could be for instance:
"Partition G into three disjoint subsets G_0, G_1, and G_2 of approximately equal size. Note that these are not subgroups, as subgroups are never disjoint."
Jsedenka (talk) 13:13, 4 May 2012 (UTC)
replies: text: That is 2^{172} 5^{378} = 1010 = 2^{301} 5^{416} \pmod{1019}
2^{172} 5^{378} \pmod{1019} does not equal 1010; it equals 9. 2^{301} 5^{416} \pmod{1019} does however equal 1010. Does anyone know what's going on here or know what to change to fix it?  --Unclewalrus 18:54, 27 March 2006 (UTC)
thread_title:  not necessarily subgroups 

message: Hi, as far as I know, Pollard created two \Rho(Rho)-algorithms, one for computing the Integer_factorization and one for computing the Discrete_logarithm. Both are documented in Menezes', Vanstone's and Oorshots's "Handbook of applied Cryptography". So we should get rid of this redirect and start an article stub, and rename the Pollard%27s_rho_algorithm article into something like Pollard%27s_rho_algorithm_for_factorization and make the original page a disambition page, I would suggest. I do not have the mathematical skills yet to write a good article containing Pollards Rho-Algorithm, so I'd first just do the structural stuff. We could just start with a stub and then fill it somehow.  --Bjoern.thalheim 13:43, 23 September 2005 (UTC)
thread_title:  Redirect 

message: Hi,
I was just wondering.  In the functions g and h wouldn't you calculate the values for a and b mod (p - 1)?  Because a and b are just the exponents of alpha and beta and when working mod p exponents cannot be larger than (p - 1).
Douglas Robinson 23:54, 29 December 2006 (UTC)
thread_title:  The functions changing a and b 

message: I'm not particularly familiar with this algorithm, but shouldn't we be clearer and say the time complexity is sqrt(N) rather than sqrt(n), and perhaps emphasize that this is pseudo-polynomial, not polynomial, time... 71.194.163.223 21:48, 5 September 2007 (UTC)
replies: text: I would move the estimated loop-detection length analysis under the complexity section, and detail the computation of this square root of pi times n over eight. Cilisso (talk) 10:27, 30 March 2023 (UTC)
thread_title:  Complexity 

message: The article says "we can calculate \gamma as a solution of the equation (B-b)\gamma = (a-A) \pmod{n}", but not *every* solution of this equation will be a solution to the discrete logarithm problem. This confused me at first, and the only reason I saw that we have to actually try multiple solutions is the example. The use of p as group order in the algorithm suggests that it is prime, but it need not be (and is not required in article), and then the algorithm is wrong, because there is not necessarily a solution to (B-b)\gamma = (a-A) \pmod{n} (or is there in this case?), and even then it is not necessarily unique.  — Preceding unsigned comment added by 145.116.189.186 (talk) 20:08, 16 November 2016 (UTC)
thread_title:  Calculation of <math>\gamma</math> 

message: The notation in the article is inconsistent, sometimes using n for the group order and sometimes p. I'll switch it to n throughout unless anyone objects.2001:470:1F09:11ED:0:0:0:12 (talk) 16:20, 22 October 2020 (UTC)
thread_title:  Notation