20110828, 18:57  #1 
4,003 Posts 
Discrete logarithm software
Hi, i'm searching for software that can perform discrete logarithm.
base: 47 modulus: 256 bit long power: 160 bit long Can this be calculated in acceptable time? If yes, do you know software that can perform it? 
20110828, 19:20  #2  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Quote:


20110828, 19:42  #3 
(loop (#_fork))
Feb 2006
Cambridge, England
18E9_{16} Posts 
Yes, this can be done in acceptable time, though I'm not sure what the best tool is. The online Magma calculator can do discrete logs mod 2^1271 in about eight seconds, mod 2^100+277 in about one second, mod 2^140+37 in about 16 seconds ... it ought to be not all that much harder than factoring a number of the size of the modulus.

20110828, 19:49  #4 
Tribal Bullet
Oct 2004
2·3·19·31 Posts 
Given a 256bit integer y, the result of raising 47 to a 160bit integer x modulo a 256bit prime, the OP wants to be able to find x. This is actually a cryptographic size discrete log problem, and the size of the numbers involved is in the range where you pretty much have to use the discrete log version of the number field sieve. Implementations of DLP NFS are vanishingly rare, the only one I know is GDLOG, but this problem is probably far out of its range.
Edit: I assume that DLP gets harder when the modulus has no special form? Last fiddled with by jasonp on 20110828 at 20:05 
20110828, 20:02  #5 
16177_{8} Posts 

20110828, 20:08  #7 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 

20110828, 20:28  #8 
Tribal Bullet
Oct 2004
2×3×19×31 Posts 
Actually, the GDLOG readme gives examples of 100digit discrete log problems it has solved, so it should only take a few days for your problem.
I've been toying with moving msieve into the DLP domain, though I currently have no idea of what it would entail. The CADONFS developers also have plans to modify their software to handle DLPs; they specifically mention adding in the ability to use basicsounding things like doublelargeprimes, which makes me think there's a lot of lowhanging fruit to be gathered unless the DLP domain is so strange that basicsounding factorization techniques don't apply. 
20110828, 21:12  #9 
7·97 Posts 
Can someone please give detailed manual how to calculate discrete log to a case given in OP post?

20110829, 11:26  #10  
Nov 2003
2^{2}×5×373 Posts 
Quote:
the matrix modulo the order of the group rather than over Z/2Z. 

20110829, 11:28  #11 
Nov 2003
2^{2}×5×373 Posts 

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