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-   -   GDLOG discrete logarithm usage example (https://www.mersenneforum.org/showthread.php?t=19474)

fivemack 2014-07-11 12:52

As far as I'm aware, there's a single point of demand for DL software, which is that Warcraft 3 was for a while secured in a way vulnerable to solving a 256-bit DLP.

Current Blizzard games require solving a 1024-bit DLP, which is impractical.

xkyve 2014-07-11 15:00

There are multiple secure communication protocols which rely on public keys that are similar in one way on another with A = g^a % p

The protocols that I study are implemented on low-power, low-cost, low-performance embedded system in which a trade-off must be made between security and processing power used into implementing that specific protocol.

xkyve 2014-07-14 07:22

@jasonp: Sadly I must be able to solve problems with q larger than 128-bits.

I'm sorry my post has caused so much trouble.

Anyway, I've managed to talk to Oleg Babul (author of GDLOG).
There is a bug in the [B]progs/gdlog.py[/B]:

[QUOTE] _GDLOG_SOLVE_EXEC = 'gdlg_dlog *-s %(seed)s* -if %(job)s.logbase -of
%(job)s.new.logbase %(job)s'[/QUOTE]
should be changed to
[QUOTE] _GDLOG_SOLVE_EXEC = 'gdlg_dlog *-s%(seed)s* -if %(job)s.logbase -of
%(job)s.new.logbase %(job)s'[/QUOTE]

Only a space should be removed :)

After the modification it works like a charm:
[QUOTE]Linear Sieve for Lattice (0, 1 - 2048) + (1 x + 0 y, 0 x + 1 y) -2048 <= x < 2048, 1 <= y < 2
t:3s y(q)=33 ny(nq)=32 sp0=0.33(p/s) sp1=0.03(p/y(q)) et=0.05h er=64 s=1
Sieve returned 1 relations, time 3s.
Ideals base 0: size: 2906 logs: 1336 prune threshold: 2179
Pruning...
After pruning ideals base 0: size: 1336
Ideals base 1: size: 3163 logs: 1582 prune threshold: 2372
Pruning...
After pruning ideals base 1: size: 1582
Logarithm of the 709787689553880977598302546337 to the unknown base is 175897608535665572229529683078
Saving number fields
Logarithm of the 709787689553880977598302546337 to the 7 is [B]379721093484885118231722056[/B]. Checking result: ok
Solve Time: 3 s
----------------------------
Total Time 69 s[/QUOTE]

Note that the output of the program is also not 100% mathematically clear, but the meaning can be deduced.

Thank you all for you support.
I hope someone will find this post useful. Topic can be close (if wanted).

jasonp 2014-07-14 09:40

Well done!

xkyve 2014-07-14 15:30

I recommend closing the topic. The problem has been solved.

xilman 2014-07-14 15:59

[QUOTE=xkyve;378059]I recommend closing the topic. The problem has been solved.[/QUOTE]Your wish is my command.


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