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Author Topic: Pollard's kangaroo ECDLP solver  (Read 59079 times)
hamnaz
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October 15, 2021, 10:46:32 AM
 #2381

Take the privatekey of 4. Half it, you get 2. Take the privatekey of 5 you get 2.5. 2.5 means, 2 + N/2. To get the "half" you subtract 1 and then halve it and get 2.

So if you can determine if the lowest bit is 0 or 1 you can half it properly. But there is no method to determine 0 or 1. Thats why you can theoretically halve multiple times but have to use the false keys. Like you take a big number with 2^120 bit, and can halve it and get two keys were you know one is 2^119 and one is "wrong". Use both keys and halve them. You know one is 2^118 and three are false. Take those four keys and halve them again, one is 2^117 and 7 are false.

So you get exponentially more keys each halving. Which is useful for e.g. 2^60 as you can get 2^45 with 2^15 (15 times halved, you can do more halvings if you like) potential keys to check in very few minutes. But you can not do it with 2^120 as you still get 2^105 range with 2^15 keys, which takes still a long time to crack. Doing 2^120 halvings is basically bruteforcing the key.
any c language script for halve pubkeys with input file ( pubkeys) and output file ( pubkwys) ( for linux )

example
./halve -i inputfile.txt -o output.txt
a.a
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October 15, 2021, 08:20:20 PM
 #2382

notatTether posted a python Script some time ago. But i also have a Javascript Version of it, which can be made to be an standalone executable. interested?
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October 16, 2021, 02:57:07 AM
 #2383

notatTether posted a python Script some time ago. But i also have a Javascript Version of it, which can be made to be an standalone executable. interested?

Definitely. Compiled Node is much faster than any Python script I can throw at here.

How did you make it?

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WanderingPhilospher
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October 16, 2021, 04:23:09 AM
 #2384

Take the privatekey of 4. Half it, you get 2. Take the privatekey of 5 you get 2.5. 2.5 means, 2 + N/2. To get the "half" you subtract 1 and then halve it and get 2.

So if you can determine if the lowest bit is 0 or 1 you can half it properly. But there is no method to determine 0 or 1. Thats why you can theoretically halve multiple times but have to use the false keys. Like you take a big number with 2^120 bit, and can halve it and get two keys were you know one is 2^119 and one is "wrong". Use both keys and halve them. You know one is 2^118 and three are false. Take those four keys and halve them again, one is 2^117 and 7 are false.

So you get exponentially more keys each halving. Which is useful for e.g. 2^60 as you can get 2^45 with 2^15 (15 times halved, you can do more halvings if you like) potential keys to check in very few minutes. But you can not do it with 2^120 as you still get 2^105 range with 2^15 keys, which takes still a long time to crack. Doing 2^120 halvings is basically bruteforcing the key.
any c language script for halve pubkeys with input file ( pubkeys) and output file ( pubkwys) ( for linux )

example
./halve -i inputfile.txt -o output.txt


So halve -i input.txt divide by 2 = -o output.txt ?
hamnaz
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October 16, 2021, 06:20:18 AM
 #2385

Take the privatekey of 4. Half it, you get 2. Take the privatekey of 5 you get 2.5. 2.5 means, 2 + N/2. To get the "half" you subtract 1 and then halve it and get 2.

So if you can determine if the lowest bit is 0 or 1 you can half it properly. But there is no method to determine 0 or 1. Thats why you can theoretically halve multiple times but have to use the false keys. Like you take a big number with 2^120 bit, and can halve it and get two keys were you know one is 2^119 and one is "wrong". Use both keys and halve them. You know one is 2^118 and three are false. Take those four keys and halve them again, one is 2^117 and 7 are false.

So you get exponentially more keys each halving. Which is useful for e.g. 2^60 as you can get 2^45 with 2^15 (15 times halved, you can do more halvings if you like) potential keys to check in very few minutes. But you can not do it with 2^120 as you still get 2^105 range with 2^15 keys, which takes still a long time to crack. Doing 2^120 halvings is basically bruteforcing the key.
any c language script for halve pubkeys with input file ( pubkeys) and output file ( pubkwys) ( for linux )

example
./halve -i inputfile.txt -o output.txt


So halve -i input.txt divide by 2 = -o output.txt ?
yes
hamnaz
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October 17, 2021, 06:38:49 AM
 #2386

Take the privatekey of 4. Half it, you get 2. Take the privatekey of 5 you get 2.5. 2.5 means, 2 + N/2. To get the "half" you subtract 1 and then halve it and get 2.

So if you can determine if the lowest bit is 0 or 1 you can half it properly. But there is no method to determine 0 or 1. Thats why you can theoretically halve multiple times but have to use the false keys. Like you take a big number with 2^120 bit, and can halve it and get two keys were you know one is 2^119 and one is "wrong". Use both keys and halve them. You know one is 2^118 and three are false. Take those four keys and halve them again, one is 2^117 and 7 are false.

So you get exponentially more keys each halving. Which is useful for e.g. 2^60 as you can get 2^45 with 2^15 (15 times halved, you can do more halvings if you like) potential keys to check in very few minutes. But you can not do it with 2^120 as you still get 2^105 range with 2^15 keys, which takes still a long time to crack. Doing 2^120 halvings is basically bruteforcing the key.
any c language script for halve pubkeys with input file ( pubkeys) and output file ( pubkwys) ( for linux )

example
./halve -i inputfile.txt -o output.txt


So halve -i input.txt divide by 2 = -o output.txt ?
yes
i think all cuda developers here, maybe no one have time for write small script in c for halve pubkeys by file ?
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October 17, 2021, 08:25:59 AM
 #2387

There is already a small python script for your needs here in this thread.
hamnaz
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October 17, 2021, 09:42:10 AM
 #2388

There is already a small python script for your needs here in this thread.
i know python scripts, already have it too, but for asking about c script, it will faster then python
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October 18, 2021, 08:51:11 AM
 #2389

i know python scripts, already have it too, but for asking about c script, it will faster then python

Most likely you will have to pay someone to make such a program for you as almost all of us are too busy with side projects and/or our personal lives and matters to work on something as complex as a C program (they'd also have to make the makefile too).

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October 18, 2021, 01:50:03 PM
 #2390

Deny it again if you can.

Shor's algorithm can be used to break elliptic curve cryptography by computing discrete logarithms on a hypothetical quantum computer. The latest quantum resource estimates for breaking a curve with a 256-bit modulus (128-bit security level) are 2330 qubits and 126 billion Toffoli gates. In comparison, using Shor's algorithm to break the RSA algorithm requires 4098 qubits and 5.2 trillion Toffoli gates for a 2048-bit RSA key, suggesting that ECC is an easier target for quantum computers than RSA. All of these figures vastly exceed any quantum computer that has ever been built, and estimates place the creation of such computers at a decade or more away.

Supersingular Isogeny Diffie–Hellman Key Exchange provides a post-quantum secure form of elliptic curve cryptography by using isogenies to implement Diffie–Hellman key exchanges. This key exchange uses much of the same field arithmetic as existing elliptic curve cryptography and requires computational and transmission overhead similar to many currently used public key systems.

In August 2015, the NSA announced that it planned to transition "in the not distant future" to a new cipher suite that is resistant to quantum attacks. "Unfortunately, the growth of elliptic curve use has bumped up against the fact of continued progress in the research on quantum computing, necessitating a re-evaluation of our cryptographic strategy."


 Grin
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October 19, 2021, 12:56:16 AM
 #2391


Can anyonel help to advice code on c++?

I know may be possible 99% not working and fail
I would like to test modify jump of Pollard's kangaroo
refer from kangaroo illustration JeanLucPons github
DP is foot of kangaroo right but jump is up to high right
I think 120 bit is to high  may be make jump to long will be help

yes, it possible to missing some point to found
Just would like to try

on Kangaroo.cpp
void Kangaroo::CreateJumpTable() {

this function right?

may be I change up 2 to  3-10
just testing a little
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October 19, 2021, 04:31:58 AM
 #2392

Shor's algorithm can be used to break elliptic curve cryptography by computing discrete logarithms on a hypothetical quantum computer. The latest quantum resource estimates for breaking a curve with a 256-bit modulus (128-bit security level) are 2330 qubits and 126 billion Toffoli gates.

Link to resource?

on Kangaroo.cpp
void Kangaroo::CreateJumpTable() {

Wrong function.

The code for jumping is in SolveKeyGPU and SolveKeyCPU.

You can just make a for loop between 1 to 3 or 10 that computes 3 or 10 consecutive jumps but only store the last one in the hashtable. It won't improve speed but it will slow down your hashtable from ballooning to a large memory footprint.

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October 19, 2021, 07:01:23 AM
 #2393


Wrong function.

The code for jumping is in SolveKeyGPU and SolveKeyCPU.

You can just make a for loop between 1 to 3 or 10 that computes 3 or 10 consecutive jumps but only store the last one in the hashtable. It won't improve speed but it will slow down your hashtable from ballooning to a large memory footprint.

Thank you

Quick test, result fail
compare test solve problem 65
original CPU finish in 3 minute
original GPU finish in 31 minute

problem 65
modify CPU (3 hour not found any thing)
modify GPU (3 hour not found any thing)
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October 19, 2021, 11:55:37 AM
 #2394

 author=NotATether link=topic=5244940.msg58213662#msg58213662 date=1634617918]
Shor's algorithm can be used to break elliptic curve cryptography by computing discrete logarithms on a hypothetical quantum computer. The latest quantum resource estimates for breaking a curve with a 256-bit modulus (128-bit security level) are 2330 qubits and 126 billion Toffoli gates.



Link to resource?

https://en.wikipedia.org/wiki/Elliptic-curve_cryptography

look for Quantum computing attacks in the end
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October 20, 2021, 08:58:06 AM
 #2395

Shor's algorithm can be used to break elliptic curve cryptography by computing discrete logarithms on a hypothetical quantum computer. The latest quantum resource estimates for breaking a curve with a 256-bit modulus (128-bit security level) are 2330 qubits and 126 billion Toffoli gates.

Link to resource?
https://en.wikipedia.org/wiki/Elliptic-curve_cryptography

look for Quantum computing attacks in the end

Read https://www.reddit.com/r/Bitcoin/comments/6is19z/new_estimate_quantum_computers_require_at_most/ , an x-post of your resource:

blk0  72 points 4 years ago
In all fairness, I have to state that the 2330 qubits refer to ideal, fault-tolerant, logical qubits, whereas the 17 qubits currently achieved by IBM's quantum processor are raw, imperfect qubits which could be used to encode 7 logical qubits. Yet, quantum error-correction of even a single fault-tolerant qubit has not been achieved in experiments today.

As Spock would say, your IBM's quantum computer is "illogical"  Smiley

World's most powerful quantum computer as of today can do 66 qubits.

And *it's* research paper says this:

In conclusion, we have reported the design, fabrication, measurement, and benchmarking of a state-of-the-art 66- qubit superconducting quantum processor that is fully programmable through electric control. ...... We note that the performance of the whole system behaves as predicted when system size grows from small to large, confirming our high fidelity quantum operations and low correlated errors on the Zuchongzhi processor. The quantum processor has a scalable architecture that is compatible with surface-code error correction, which can act as the test-bed for fault-tolerant quantum computing.

In other words, you still have a long shot to make even 66 *logical* (fault-free) Qbits.

So wake me up when you get anywhere near 2000 logical ones.

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October 20, 2021, 11:54:52 AM
 #2396

Does anybody has this script, its gone.


What to use to look at the DP's I have in the workfiles?
If you can compile your own version, you can add the export option that https://github.com/PatatasFritas/FriedKangaroo created.  If you search for PatatasFritas in this thread, they also have a python script that will do the same; export the wild and tame files.



This was previously posted in this thread but deleted for some reason, it's a snippet from iceland2k14's Github that divides a pubkey by an arbitrary number and returning all the parts in between. I polished it a bit to print the compressed and uncompressed keys: https://gist.github.com/ZenulAbidin/286a652b160086b3b0f184a886ba68ca

Here's the script output when called with a random (uninteresting - with no balance) pubkey, divided by 48. The keys divided by 0, 1, 2, 3 and so on are printed in order:

Code:
>>> shiftdown("0267830f83723fa565ccb8677c14d13f7d47bf1008fea826833359f27f866632ab", 48)
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*edit: some text was cut off*
wedom
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October 20, 2021, 12:25:05 PM
 #2397

Does anybody has this script, its gone.
...
If you can compile your own version, you can add the export option that https://github.com/PatatasFritas/FriedKangaroo created.  If you search for PatatasFritas in this thread, they also have a python script that will do the same; export the wild and tame files.

...

it was a forked from JeanLucPons/Kangaroo
https://github.com/JeanLucPons/Kangaroo
I can't tell if there were any changes from the original. I still have the saved page, but there is no archive with the files


for the second question: the link is valid, everything is in place
https://gist.github.com/ZenulAbidin/286a652b160086b3b0f184a886ba68ca

wedom
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October 20, 2021, 01:47:53 PM
 #2398

Does anybody has this script, its gone.
...

I found the code of a script for browsing workfiles

kangaroo-tool.py

Code:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import sys, os
if sys.version_info.major<3:
    print("Python3 required")
    sys.exit(0)

import argparse
from struct import unpack
from binascii import hexlify,unhexlify
from math import log2

HEADW = 0xFA6A8001  # Full work file
HEADK = 0xFA6A8002  # Kangaroo only file

HASH_SIZE = 2**18

TAME=False
WILD=True




def bytes_to_num(b):
    return int(hexlify(b), 16)

def GetTimeStr(dTime):
  tmp = ''
  nbDay = dTime / 86400.0
  if nbDay >= 1:
    nbYear = nbDay / 365.0
    if nbYear > 1:
      if nbYear < 5:
        tmp += "%.1fy" % (nbYear)
      else:
        tmp += "%gy" % (nbYear)
    else:
      tmp += "%.1fd" % (nbDay)

  else:

    iTime = dTime
    nbHour = ((iTime % 86400) / 3600)
    nbMin = (((iTime % 86400) % 3600) / 60)
    nbSec = (iTime % 60)

    if nbHour == 0:
      if nbMin == 0:
        tmp += "%02ds" % (nbSec)
      else:
        tmp += "%02d:%02d" % (nbMin, nbSec)
    else:
      tmp += "%02d:%02d:%02d" % (nbHour, nbMin, nbSec)

  return tmp


def checkhead(wf):
    head = unpack('I', wf.read(4))[0]
    if head==HEADW:
        return head
    else:
        print('HEADER ERROR %08x %08x' % (head, HEADW))
        return False

def workinfo(workfile):

  wf = open(workfile, 'rb')
  head = checkhead(wf)
  if not head:
    print('Invalid WorkFile Header')
    return
  version = unpack('I', wf.read(4))[0]
  dp1 = unpack('I', wf.read(4))[0]
  RangeStart = bytes(wf.read(32))[::-1]
  RangeEnd = bytes(wf.read(32))[::-1]
  x = bytes(wf.read(32))[::-1]
  y = bytes(wf.read(32))[::-1]
  count = unpack('Q', wf.read(8))[0]
  time = unpack('d', wf.read(8))[0]

  print('Header   : %08x' % head)
  print('Version  : %d' % version)
  print('DP Bits  : %08x' % dp1)
  print('Start    : %x' % bytes_to_num(RangeStart))
  print('Stop     : %x' % bytes_to_num(RangeEnd))
  print('PubKey X : %s' % hexlify(x).decode())
  print('PubKey Y : %s' % hexlify(y).decode())

  if count>0:
    print('Count    : %d 2^%.3f' % (count, log2(count)))
  else:
    print('Count    : %d' % (count))

  print('Time     : %s' % GetTimeStr(time))

  wf.close()


def workexport(workfile):

    wf = open(workfile, 'rb')
    head = checkhead(wf)
    if not head:
      print('Invalid WorkFile Header')
      return
    wf.seek(156,0) # Skip WorkFile header

    tameFile = open('tame.txt','a')
    wildFile = open('wild.txt','a')

    for h in range(HASH_SIZE):
      nbItem = unpack('I', wf.read(4))[0]
      maxItem = unpack('I', wf.read(4))[0]
      for i in range(nbItem):
        x = bytes(wf.read(16))[::-1]
        d = bytes(wf.read(16))[::-1]

        sign = (bytes_to_num(d) & 0x80000000000000000000000000000000)>0
        htype = (bytes_to_num(d) & 0x40000000000000000000000000000000)>0

        if htype==TAME:
          tameFile.write('%05x%032x ' % (h, bytes_to_num(x)))
          tameFile.write('%032x\n' % (bytes_to_num(d) & 0x3fffffffffffffffffffffffffffffff))
        else:
          wildFile.write('%05x%032x ' % (h, bytes_to_num(x)))
          if sign:
            wildFile.write('-')
          wildFile.write('%032x\n' % (bytes_to_num(d) & 0x3fffffffffffffffffffffffffffffff))

        if args.verbose:
          sys.stdout.write('%s' % ('Tame' if htype==TAME else 'Wild'))
          sys.stdout.write(' %05x%032x ' % (h, bytes_to_num(x)))
          if sign:
            sys.stdout.write('-')
          sys.stdout.write('%032x\n' % (bytes_to_num(d) & 0x3fffffffffffffffffffffffffffffff))


if __name__ == '__main__':
    parser = argparse.ArgumentParser()
    parser.add_argument('-f', dest='workfile', type=str, required=True, help='WorkFile path')
    parser.add_argument('--winfo', dest='winfo', action='store_true', help='Show workfile info')
    parser.add_argument('--wexport', dest='wexport', action='store_true', help='Export workfile into tame.txt and wild.txt')
    parser.add_argument('-v', dest='verbose', action='store_true', help='Verbose')
    args = parser.parse_args()

    if args.workfile:
        print("[+] Workfile %s" % args.workfile)

    if args.winfo:
        workinfo(args.workfile)

    if args.wexport:
        workexport(args.workfile)

https://gist.github.com/PatatasFritas/a0409df4306fb1bb81f9a53e70151ddc
bigvito19
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October 20, 2021, 02:40:23 PM
 #2399

Does anybody has this script, its gone.
...

I found the code of a script for browsing workfiles

kangaroo-tool.py

Code:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import sys, os
if sys.version_info.major<3:
    print("Python3 required")
    sys.exit(0)

import argparse
from struct import unpack
from binascii import hexlify,unhexlify
from math import log2

HEADW = 0xFA6A8001  # Full work file
HEADK = 0xFA6A8002  # Kangaroo only file

HASH_SIZE = 2**18

TAME=False
WILD=True




def bytes_to_num(b):
    return int(hexlify(b), 16)

def GetTimeStr(dTime):
  tmp = ''
  nbDay = dTime / 86400.0
  if nbDay >= 1:
    nbYear = nbDay / 365.0
    if nbYear > 1:
      if nbYear < 5:
        tmp += "%.1fy" % (nbYear)
      else:
        tmp += "%gy" % (nbYear)
    else:
      tmp += "%.1fd" % (nbDay)

  else:

    iTime = dTime
    nbHour = ((iTime % 86400) / 3600)
    nbMin = (((iTime % 86400) % 3600) / 60)
    nbSec = (iTime % 60)

    if nbHour == 0:
      if nbMin == 0:
        tmp += "%02ds" % (nbSec)
      else:
        tmp += "%02d:%02d" % (nbMin, nbSec)
    else:
      tmp += "%02d:%02d:%02d" % (nbHour, nbMin, nbSec)

  return tmp


def checkhead(wf):
    head = unpack('I', wf.read(4))[0]
    if head==HEADW:
        return head
    else:
        print('HEADER ERROR %08x %08x' % (head, HEADW))
        return False

def workinfo(workfile):

  wf = open(workfile, 'rb')
  head = checkhead(wf)
  if not head:
    print('Invalid WorkFile Header')
    return
  version = unpack('I', wf.read(4))[0]
  dp1 = unpack('I', wf.read(4))[0]
  RangeStart = bytes(wf.read(32))[::-1]
  RangeEnd = bytes(wf.read(32))[::-1]
  x = bytes(wf.read(32))[::-1]
  y = bytes(wf.read(32))[::-1]
  count = unpack('Q', wf.read(8))[0]
  time = unpack('d', wf.read(8))[0]

  print('Header   : %08x' % head)
  print('Version  : %d' % version)
  print('DP Bits  : %08x' % dp1)
  print('Start    : %x' % bytes_to_num(RangeStart))
  print('Stop     : %x' % bytes_to_num(RangeEnd))
  print('PubKey X : %s' % hexlify(x).decode())
  print('PubKey Y : %s' % hexlify(y).decode())

  if count>0:
    print('Count    : %d 2^%.3f' % (count, log2(count)))
  else:
    print('Count    : %d' % (count))

  print('Time     : %s' % GetTimeStr(time))

  wf.close()


def workexport(workfile):

    wf = open(workfile, 'rb')
    head = checkhead(wf)
    if not head:
      print('Invalid WorkFile Header')
      return
    wf.seek(156,0) # Skip WorkFile header

    tameFile = open('tame.txt','a')
    wildFile = open('wild.txt','a')

    for h in range(HASH_SIZE):
      nbItem = unpack('I', wf.read(4))[0]
      maxItem = unpack('I', wf.read(4))[0]
      for i in range(nbItem):
        x = bytes(wf.read(16))[::-1]
        d = bytes(wf.read(16))[::-1]

        sign = (bytes_to_num(d) & 0x80000000000000000000000000000000)>0
        htype = (bytes_to_num(d) & 0x40000000000000000000000000000000)>0

        if htype==TAME:
          tameFile.write('%05x%032x ' % (h, bytes_to_num(x)))
          tameFile.write('%032x\n' % (bytes_to_num(d) & 0x3fffffffffffffffffffffffffffffff))
        else:
          wildFile.write('%05x%032x ' % (h, bytes_to_num(x)))
          if sign:
            wildFile.write('-')
          wildFile.write('%032x\n' % (bytes_to_num(d) & 0x3fffffffffffffffffffffffffffffff))

        if args.verbose:
          sys.stdout.write('%s' % ('Tame' if htype==TAME else 'Wild'))
          sys.stdout.write(' %05x%032x ' % (h, bytes_to_num(x)))
          if sign:
            sys.stdout.write('-')
          sys.stdout.write('%032x\n' % (bytes_to_num(d) & 0x3fffffffffffffffffffffffffffffff))


if __name__ == '__main__':
    parser = argparse.ArgumentParser()
    parser.add_argument('-f', dest='workfile', type=str, required=True, help='WorkFile path')
    parser.add_argument('--winfo', dest='winfo', action='store_true', help='Show workfile info')
    parser.add_argument('--wexport', dest='wexport', action='store_true', help='Export workfile into tame.txt and wild.txt')
    parser.add_argument('-v', dest='verbose', action='store_true', help='Verbose')
    args = parser.parse_args()

    if args.workfile:
        print("[+] Workfile %s" % args.workfile)

    if args.winfo:
        workinfo(args.workfile)

    if args.wexport:
        workexport(args.workfile)

https://gist.github.com/PatatasFritas/a0409df4306fb1bb81f9a53e70151ddc

Thanks
fxsniper
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October 22, 2021, 04:08:00 AM
 #2400


Can I ask about Pollard's kangaroo python script ?

Did I understand wrong?
Pollard's kangaroo generate random number(in range) to private key for generate public point and compare collision right ?

if I understand correct
What variable is private key Pollard's kangaroo ?

from ask, I mean private key of each generate point for check. ( I not mean private key of result )

https://github.com/JeanLucPons/Kangaroo/blob/master/Kangaroo.cpp
http://fe57.org/forum/thread.php?board=4&thema=1#1
https://github.com/Telariust/pollard-kangaroo/blob/master/pollard-kangaroo-multi.py

pollard_kangaroo.txt
t.append((3 << problem - 2) + random.randint(1, 1 << problem - 1))
w.append(random.randint(1, 1 << problem - 1))

pollard-kangaroo-multi.py
prvkey0 = random.randint(L,U)

Kangaroo.cpp
?
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