Exploring Kangaroo Methods for Logarithm Problems

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falcon2019Full Member
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#1Sep 26, 2019, 09:42 PM
Been thinking about Pollard's kangaroo method lately and found a paper on it. It’s titled "Kangaroo Methods for Solving the Interval Discrete Logarithm Problem". Seems like the author is claiming he can beat the 4-kangaroo approach with a 5-kangaroo method.
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ben.cipherFull Member
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#2Sep 28, 2019, 11:46 PM
Honestly, seems kinda limited. I mean, why not just subtract G from the initial pubkey? Keep both versions and at least one will have an even private key. Then you can 'divide' them and find your way into the right interval.
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falcon2019Full Member
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#3Sep 29, 2019, 03:49 AM
That could work, but what’s the catch? If the private key is 0x1, adding G would be better. If we go the other way, we have to check for the point at infinity, which slows things down a bit.
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CyberDefiMember
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#4Sep 29, 2019, 09:52 AM
Totally agree on that. But then we’re left with two points to compare. Like, how do we know which one lies in the lower interval? It's a bit of a hassle searching both.
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falcon2019Full Member
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#5Sep 30, 2019, 06:42 PM
Papers like that are usually about getting degrees, no real innovation. Honestly, you won’t get better than K=1.7 no matter how many kangaroos you use. Super boring. Why not try a different approach?
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CyberDefiMember
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#6Sep 30, 2019, 07:15 PM
Yeah, we all know that paper. I’ve even put it into my own Python script. It does bring C down to around 1.25-1.45, but the logic is a mess and it’s super complex to handle. Plus, starting points are costly.
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0xKingFull Member
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#7Oct 2, 2019, 11:12 PM
Fair point. But if you’re okay with 1.7, then why change anything?
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falcon2019Full Member
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#8Oct 3, 2019, 04:58 AM
Can you share that link you mentioned?
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0xKingFull Member
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#9Oct 3, 2019, 06:59 AM
Sure, here it is. Just got experimental proof that it works. It’s like mixing the 3-kangaroo method with the van Oorschot idea, but no dynamic programming involved.
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CyberDefiMember
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#10Oct 3, 2019, 01:00 PM
BSGS on secp256k1 needs about 1.0 sqrt(N) operations on average. You only have to store a fraction of the keys, so it’s not all that bad.
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0xKingFull Member
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#11Oct 3, 2019, 04:37 PM
Yeah, right. But when you consider memory for 0.5*sqrt(2^134, that’s gonna make you rethink BSGS.
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bridge_nonceLegendary
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#12Oct 3, 2019, 10:20 PM
For cracking a private key in a 2^134 interval, BSGS definitely isn't the way to go.
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falcon2019Full Member
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#13Oct 3, 2019, 11:03 PM
BSGS might be faster, but Kangaroo is way better at targeting specific keys. How efficient is it really?
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bridge_nonceLegendary
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#14Oct 4, 2019, 04:17 AM
Kangaroo doesn’t really need fast memory. It’s a fair trade-off.
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falcon2019Full Member
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#15Oct 4, 2019, 09:34 AM
But remember, Kangaroo is still probabilistic. Don’t lose sight of that. It’s all about the birthday paradox.
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bridge_nonceLegendary
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#16Oct 4, 2019, 12:10 PM
How is that relevant? Fast memory for 2^67 elements is still a huge stretch. We have to work with what we have, no matter how probabilistic it gets.
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CyberDefiMember
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#17Oct 4, 2019, 03:54 PM
You’re overselling it. Precomputing values risks ruining the randomness, which is what makes the birthday paradox work. You might just end up in a mess.
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falcon2019Full Member
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#19Oct 6, 2019, 01:26 AM
The birthday paradox relies on randomness, which lets you find collisions easier. If you make kangaroo more deterministic, you lose that edge and it just becomes brute force.
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bridge_nonceLegendary
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#20Oct 6, 2019, 02:09 AM
Not sure why some people make new accounts just to mess with serious conversations. @ElonMusk, if that's really you, maybe get some help.
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