Post
Topic
Board Development & Technical Discussion
Re: Pollard's kangaroo ECDLP solver
by
ssxb
on 06/09/2021, 04:03:04 UTC
little bit more example
dec 33
hex 21
pubkey 021697ffa6fd9de627c077e3d2fe541084ce13300b0bec1146f95ae57f0d0bd6a5
use your program to get 32 keys of above pubkey

you will see 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 in your list
one step ahead pubkey is 1.03125 ( 03bb2228d3ea32cb3c1eb160cc824a4ba8115f9a7f415d18ddcaac8193defc2c47 + 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798  )

and in private key F7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFEC4D965FF79CE5B39E1D3CB9869B48F38
029eda0cebe3c594b59add6dccbff3347f06ad09e83e0b9279dd821cc94284c5d0

hope you will test each zone for your understand

Sorry to rain on this, but this method is useless.

I managed to decode how to split multiple keys using this method (I even made a script that reproduces your example, but it's private at the request of someone else, not that the results would be useful/practical to anyone here), and it turns out you're just using mod(32)-sized ranges.

Now as we all know, when you modinv a small number on secp256k1 you get a very large number (and modinv a "decimal number" is really just modinv(denominator) * numerator so this still holds for that)

This effectively means that the range becomes humungous, way bigger than 2^120 where we started.



The ranges look something like this (P = public key):

1*modinv(32) 2*modinv(32)     1P
2*modinv(32) 3*modinv(32)     2P
...
32*modinv(32) 33*modinv(32) (32*modinv(32) = 1)      32P

The ranges are much bigger than when you divide-and-split them down by a number.

Now of course you can replace 32 with an extremely huge number to make the ranges manageable/smaller but what's the point? Now you have an unmanageable amount of public keys.

i guess we need to figure out how to make range small , as if we use some techniques and range will get bigger and bigger no one is going to beat that as with each bit increment you need to pay your 100 of life's hahahah  Grin