20160901, 14:16  #1 
Aug 2002
3×5^{2}×7 Posts 
Pollard rho questions
"Improved Pollard rho method for computing discrete logarithms over finite extension fields"
by Ping Wang, , Fangguo Zhang, Has anyone read this? I can only find it behind a pay wall. 
20160913, 21:11  #2 
Feb 2011
St Louis, MO
3^{2} Posts 
Plug in the title to scholar.google.com and follow the link to the pdf.

20160914, 13:40  #3 
Aug 2002
3·5^{2}·7 Posts 
Thank You!

20160914, 14:03  #4 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
902_{10} Posts 
I'd be interested in hearing what you or others think. I've had "Experiment with Wang/Zhang 2012 Rho cycle finding" on my todo list for a couple years but haven't tried any implementation. My current implementation is very traditional, and I have it race with a BSGS. Bai/Brent 2008 is also worth looking at.

20160914, 20:50  #5  
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3·419 Posts 
Quote:
Please too refer up to here by. t = g^{l} (mod p). Quote:


20160915, 05:11  #6 
Romulan Interpreter
Jun 2011
Thailand
8635_{10} Posts 
re: "originally posted by Raman"
So, you are now trying to write a book, or what? (the correct term should be "plagiarize" a book). A little bit too empty that book, for out tastes here... Still a lot of things to add to it... 
20160915, 08:29  #7  
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
1257_{10} Posts 
Quote:
So that how did you get that link? such that What concepts do you think that are being newly appropriate / fancy enough / well suited up to add over to that highlighted book that you had mentioned that above? That was something that I had submitted for my B.Tech degree thesis. Who had uploaded it into archive.org? Apparently it cannot be my university from which I had studied and graduated because there were lots of additions that I had made after I had submitted my final thesis for my B.Tech degree, and the latest changes are being present. Some of them were originally prepared for Google Groups Notes, although this feature is being discontinued right now. To compile everything into a website in the future. It should be safe there. I shouldn't trust third party sources for web site hosting but Google sites should be safe at least for centuries. I had previously lost data from Yahoo Briefcase, Yahoo Geocities, Orkut, etc. are all being now closed. Orkut was predicted by me that it would close in 2013, yes that it had been closed up on over Tuesday 30 September 2014. Yahoo Games is also now being deactivated too. Right now that without a personal website things will be metastable in untrustworthy third party web site hosting, i.e. existing for long time  but destroyed at any time at happening of unfortunate things. Hosting website will cost money. Where as, let me at least stay with in a job for a while  the an. Where as, for a while  the an  up  an?  before itself, by earlier, a while ago  for the an. By using be being  right now  does do  does not  do not  not not !? The latest changes that I had made to the material was in the year 2010. At that time, I knew nothing about Cornacchia's algorithm, Ideonal Numbers, Class Numbers, Values of k such that there are no numbers N such that if N cannot be written as a²+kb² form, then N³ can be written as a²+kb² form (or apparently any odd power of N), etc. (end of thinking capacity!) and then so on. although there is article up on over sum of two squares representation, which I first studied in second half of 2009. The final B.Tech degree thesis was being submitted up on over Friday 8 May 2009. See that the newest / latest Mersenne Primes 57885161 and 74207281 are not being there included, Mersenne Prime 42643801 was only being known on Thursday 4 June 2009, although it was first being reported on Sunday 12 April 2009 went unnoticed. Similarly to as like newest / latest Mersenne Prime 74207281 was only being known on Thursday 7 January 2016, although it was first being reported on Thursday 17 September 2015 went unnoticed  for the  an a. See that the newest / latest Wagstaff Primes 13347311 and 13372531 are not being there included also too. Linux / Unix Operating System does do save a ~ back up file, where as while Windows Operating System does not  do not  not not !? Quote:
a)  Cf. After Dark Screen Saver that I do enjoy up with in  What does Cf. mean up  an?  before itself, by earlier, a while ago  for the an. By using be being  right now  does do  does not  do not  not not !? Round neck / polo collar Tshirt / shirt of 7 different colours to wear up on over 7 different days of the week Matching data to be printed out up on over it Logic puzzle / games / sports  matches  data / matter / material. Well, let me know very well about this thing around  variably. think stuff style item step idea SUNDAY  RED MONDAY  WHITE TUESDAY  BLUE WEDNESDAY  PINK THURSDAY  GREEN FRIDAY  YELLOW SATURDAY  BLACK RED  (front side) Ideonal Numbers, (back side) 2Ideonal numbers (just as like 10adic integers only certainly), i.e. values of k such that all the prime numbers representable in the (a/2)²+k(b/2)² form can be given by a set of residue classes (mod 4k), with every prime number of these residue classes being uniquely writable in the (a/2)²+k(b/2)² form, (right sleeve) formula for product of two quadratic forms into a²+kb² quadratic form, (left sleeve) and then formula for product of a quadratic form with a a²+kb² quadratic form into same quadratic form. WHITE  (front side) Mersenne Prime numbers, (back side) Wagstaff Prime numbers, (right sleeve) Repunit Prime numbers, (left sleeve) Prime numbers p for which (10^{p}+1)/11 is being a prime number. BLUE  (front side) Amicable pairs, (back side) Aliquot cycles of length ≥ 4. Does no one do know an Aliquot cycle of length 3 or 7 or 10 to 27 or ≥ 29, or an Amicable pair of opposite parity? PINK  Open end Aliquot sequences (below 10000?)  not a valid sequence at all because computations in progress might reduce these numbers up on over time. To consider with in only lowest distinct members certainly, etc. (end of thinking capacity!) and then so on. Space is being available  not not. GREEN  Values of k such that there are no numbers N such that if N cannot be written as a²+kb² form, then N³ can be written as a²+kb² form (or apparently any odd power of N). YELLOW  (front side) Mersenne Prime / Composite Number Factors (2 to 149?), (back side) Fermat Prime / Composite Number Factors (1 to 32?). BLACK  (front side) π digits, (back side) e digits. Other transcendental / algebraic / irrational constants are being interesting to consider up also too  EulerMascheroni constant, Catalan's constant, Apéry's constant, √2, √3, etc. (end of thinking capacity!) and then so on. Space is being available  not not. i.e. = e.g. ?? Well, let me know very well about this thing around  variably. think stuff style item step idea Mathematical constants can be calculated to infinitely many digits of precision up on over a given fixed computer, but physical constants, e.g. gravitational constant, speed of light in vacuum, charge of electron, mass of electron, mass of proton, mass of neutron, permittivity of vacuum, permeability of vacuum, Avagadro's constant, Boltzmann's constant, Planck's constant, StefanBoltzmann's constant, molar gas constant, Hubble's constant, Dirac's constant, Wien's displacement constant, acceleration due to gravity on earth, atmospheric pressure on earth, mass of earth, radius of earth, cosmological constant, etc. (end of thinking capacity!) and then so on ?? The average atmospheric pressure on the surface of Mars at 610 Pascals is being very close to the triple point of water at 611 Pascals. So that on the surface of Mars, it is possible that three states of matter  solid, liquid, gas can coexist. Although that the atmospheric pressure on the surface of Mars can vary from 30 Pascals to 1155 Pascals. How many states of matter are there? Eighteen and counting! Solid, liquid, gas, plasma, degenerate matter, photonic matter, quantum, boseeinstein condensate, fermionic condensate, superconductivity, superfluid, supersolid, quantum spin liquid, stringnet liquid, supercritical fluid, dropleton, JahnTeller metal, quarkgluon plasma. I do like up with in piling / accumulating of things  during at all @  time period frame duration  does  not not as  stamp collection  a  for the an !? There is much further more difference between white colour font text and then yellow colour font text. @ ?  How old are you at all ?? To consider with in only Mersenne Forum's round neck / polo collar Tshirts / shirts rather than instead of Mersenne Forum's guinness world records prime number badges certainly, etc. (end of thinking capacity!) and then so on ?! Space is being available  not not also too !? Trying out to adding text until / till repeatedly getting from 16384 Mersenne Forum's post character limit to Mersenne Forum's post character limit is being reached up  could be able to  consider it up  up over! Last fiddled with by Raman on 20160915 at 08:37 

20160915, 12:49  #8 
Romulan Interpreter
Jun 2011
Thailand
21BB_{16} Posts 

20160918, 14:42  #9  
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3·419 Posts 
Quote:
But what is the point in searching for something that you don't seek an answer to? Do you use Google for some custom data? What do you exactly mean by 'Internet is a bitch'? A spy that reports a person's own wrongdoings to someone else? You searched for text inside the quote tag? Why didn't you do so for text outside the quote tag? I wrote a full prose. You replied to only the first paragraph? To consider using emoticons. Emoticon = smiley? What is the difference exactly between emoticons and emotions? Man, not only some number theory data is being archived, but also some group theory data. I am not sure if I did it or someone else made it into the archive way back machine. For some reason, in mersenne forum, font text size tag is not being working out at all. Editing one's own post time limit is being one hour exactly. Yellow yellow dirty fellow, white white orbit white. Yellow colour font text is being relevant data being obscured to avoid reader's distractions. Giving away points to convey is being more important than using different kinds of words at all. Short posts without some type of junk is being better than long posts with some type of junk. Trying out to control it up uncontrollably. Good thing to take a few days' break between two successive posts. This is likely being caused by addiction and also by spending too much time with it. They all come to me by instinct. Good thing to divert my own attention, deviate from it and then go out away somewhere outside, enjoy places, every day different places to go out. Going route ≠ coming route. Should have been spending out more time playing out rather than instead of working out every day. All work and no play makes Jack a dull boy. I am not Jack any way and I cannot be any way. Rather than = instead of? My mind is being time variant, mercurial, changing out from between calm state condition to wild state condition frequently often. Frequently = often? Lol = Laughing out loud? At the poles, one year is equal to one day at the equator with sun very low in elevation. Quote tag can be used out for as a separator, rather than instead of quoting text from other people or from myself. Wondering out why I do list out things pointwise! And then numbering things pointwise with alphabets rather than by using numbers? Aliquot sequence 314718 is being approaching the iteration number 17000! When ever things are being compared to it, aliquot sequence 4788 is being: 10540 to be equivalent when ever things are being compared to it? Aliquot sequence 4788: iteration 10400, iteration 10490 nice split up results! Aliquot sequence 4788: iteration 10473, iteration 10489 quick ecm curves results? Aliquot sequence 11040: iteration 9812 nearly nice split up results! 689 divides Aliquot sequence 4788: iteration 10497. How many groups of order 689 are being there? Why? Just asking. Not seeking out an answer to it. I know it by myself. Two groups of order 689 are being there. Cyclic group and then Frobenius group. Why? To predict out to what given fixed family does an open end aliquot sequence does do terminate up. And then to consider by measuring or by estimating the probability with in which an open end aliquot sequence does do terminate up to a given fixed family. By using be being. To respect out (give take out reputation) people who win out games, sports, puzzles by skill rather than instead of by chance. Rather than ≠ instead of? FactorDB has got bandwidth limits and query limits. Attachment tag form format has been getting limits. Why? I have been observing that it is being set up to at a some arbitrary limit levels. Why? Limited mersenne forum attachment tag formats are being to be available up out. I observed that Linux / Unix operating system text editor case file always seeks opening saved stored file pointer to the last restore point score. Why? To consider out with in recharging at 13% battery life limit levels. Why? To consider out with in alerting at 10% battery life limit levels. Why? Mersenne Forum right now that many multiple attachments are being supported out even for the common man up! Why? Confidentially that image tags it is being case they have been disabled out also too up? Why? That is not being a driver at all. But only, let alone a stable guide. Not a downdriver at all  not  not obviously. Cannot be it. That but only = let alone? What do you think the maximum and minimum aliquot sequence growth rate of the next subsequent iteration can be? Why? Quote:
Microsoft Golf 1.0 Lies: Deep Rough, Rough, Fairway, Green, Sand, Water, Dirt, Asphalt, Concrete, Pine Needles, Tall Grass, Mud, Dormant Grass, Lava, Stream, Ocean, Hazard, Tee, In The Hole, Out Of Bounds, Deep Grass. Hazard = Dirt = Lava = Mud? Water = Stream = Ocean? Tall Grass = Deep Grass? Memorize and then ≠ or recall? How much do you think out that you can be recollecting  is being case? Hi, Arrange with in order, man!  Sport / game / puzzle. 

20160918, 15:42  #10 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
2×11×41 Posts 
Can we keep the posts relevant to the subject? We're also not being paid by the word.

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