mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > Factoring

Reply
 
Thread Tools
Old 2015-05-27, 20:14   #1
Stargate38
 
Stargate38's Avatar
 
"Daniel Jackson"
May 2011
14285714285714285714

3×251 Posts
Default How To Calculate SNFS Poly?

How do I calculate a SNFS poly? Is there an easy formula based on N?

Last fiddled with by Stargate38 on 2015-05-27 at 20:17
Stargate38 is online now   Reply With Quote
Old 2015-05-27, 20:21   #2
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

3×1,877 Posts
Default

Give an example of the form of the number you wish to factor. There are many cases.
VBCurtis is online now   Reply With Quote
Old 2015-05-27, 20:35   #3
Stargate38
 
Stargate38's Avatar
 
"Daniel Jackson"
May 2011
14285714285714285714

3×251 Posts
Default

(n2p+1)/(n2+1) with prime p
n2[SUP]x[/SUP]+1
an±bn (take out algebraic factors first)

i.e. 46074500107087988+1 (known factor before I factored it: 449). I wasted 2-3 CPU-days doing GNFS on it, before I realized that I could have done it in a matter of hours with SNFS.

Last fiddled with by Stargate38 on 2015-05-27 at 20:42
Stargate38 is online now   Reply With Quote
Old 2015-05-27, 21:30   #4
wblipp
 
wblipp's Avatar
 
"William"
May 2003
Near Grandkid

3×7×113 Posts
Default

Have you read the Mersenne Wiki article on polynomial selection?
wblipp is offline   Reply With Quote
Old 2015-05-27, 21:47   #5
R.D. Silverman
 
R.D. Silverman's Avatar
 
"Bob Silverman"
Nov 2003
North of Boston

22·1,877 Posts
Default

Quote:
Originally Posted by Stargate38 View Post
How do I calculate a SNFS poly? Is there an easy formula based on N?
Optimal Parameterization of SNFS. J. Math. Cryptology
R.D. Silverman is offline   Reply With Quote
Old 2015-05-27, 21:52   #6
R.D. Silverman
 
R.D. Silverman's Avatar
 
"Bob Silverman"
Nov 2003
North of Boston

11101010101002 Posts
Default

Quote:
Originally Posted by Stargate38 View Post
(n2p+1)/(n2+1) with prime p
n2[SUP]x[/SUP]+1
an±bn (take out algebraic factors first)

i.e. 46074500107087988+1 (known factor before I factored it: 449). I wasted 2-3 CPU-days doing GNFS on it, before I realized that I could have done it in a matter of hours with SNFS.
May I suggest that it would be helpful if you would learn how to perform polynomial algebra??

For your first question (n^2p + 1)/(n^2+1) may I suggest performing the division and looking at the
result? One gets a dense polynomial of degree 2p-2........

n^(2^x) + 1 is algebraically prime.

for a^n +/- b^n, start by factoring it, completely. Or are you asking about the primitive cofactor?

Last fiddled with by R.D. Silverman on 2015-05-27 at 21:54
R.D. Silverman is offline   Reply With Quote
Old 2015-05-27, 22:12   #7
Dubslow
Basketry That Evening!
 
Dubslow's Avatar
 
"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

3·29·83 Posts
Default

Yafu can do automatic snfs poly selection for the example as well as the second two forms (though I don't know if it can take advantage of the power of 2 exponent, or if that's even possible).

Last fiddled with by Dubslow on 2015-05-27 at 22:13
Dubslow is offline   Reply With Quote
Old 2015-05-27, 23:09   #8
R.D. Silverman
 
R.D. Silverman's Avatar
 
"Bob Silverman"
Nov 2003
North of Boston

22·1,877 Posts
Default

Quote:
Originally Posted by Dubslow View Post
Yafu can do automatic snfs poly selection for the example as well as the second two forms (though I don't know if it can take advantage of the power of 2 exponent, or if that's even possible).
Another example of: "don't think, just throw a computer at it".

The OP asked HOW. Suggesting to use a black box does not answer that question.

Indeed. Your statement "I don't know........possible." suggests that you should not
have even tried to answer this question.

(Hint: Once you have decided the degree for the SNFS algebraic polynomial for 2^2^n+1,
it is trivial first year algebra to find the representation).
R.D. Silverman is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
SNFS poly for b^n-1, n prime? ryanp Factoring 6 2013-07-19 17:23
Ooops....SNFS poly for primes? schickel FactorDB 0 2011-12-16 18:07
SNFS Poly creation for n=2*x^2 - 1 JoeCrump Factoring 3 2009-10-29 21:00
Homogeneous Cunningham snfs poly selection? nuggetprime Factoring 22 2008-08-15 10:01
How do you calculate? fropones Lone Mersenne Hunters 1 2003-05-27 23:01

All times are UTC. The time now is 21:34.


Tue Jan 31 21:34:13 UTC 2023 up 166 days, 19:02, 0 users, load averages: 1.40, 1.20, 1.11

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2023, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔