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Author Topic: Bitcoin challenge transaction: ~100 BTC total bounty to solvers!  (Read 3965 times)
BurtW
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August 04, 2019, 03:59:25 PM
 #101

The x coordinate and y coordinate are both binary numbers in the range 2256.
the max is also a little bit less than 2256 but unlike private keys the max is defined by P (the prime) not N (the curve order)
After reading over the description of Pollard's kangaroo algorithm I think I understand it enough to be able to explain it to my 13 year old daughter so she can write the code as a fun educational exercise.  She is always looking for a good subject for her next science fair project and I think this would make a good one.

I have some questions about the PRF that someone might be able to answer.  

The only requirements listed in the article above are:

1) The PRF must map the finite cyclic group to "a set S of integers"
2) The PRF must be able to be changed in order to select a different S in order to create subsequent "kangaroos"

Since the length of the pseudorandom sequence is not specified I assumed 256 bits, is that reasonable?

So, it seems to me that f(X) = SHA256(X || nonce) where X is the binary representation of the the point X, || represents the concatenation operation, and the nonce is selected from a TRNG or is simply incremented would do the trick.

However this seems to be overkill and we want to do this as fast as possible.

Another option that comes to mind is to just define f(X) = (X + nonce) where X is the binary representation of the compressed form of X and the nonce is selected from a TRNG or is simply incremented.

What PRF is generally used?

Now that I think about this I think the science fair project could be something along the lines of measuring the conversion speed of various PRFs and PRF modification algorithms.  The data set would be all the cracked addresses in this thread, the independent variable would be various PRFs and different ways of modifying them to produce the next "kangaroo", and the dependent variable would be the total time it takes to re-crack all the known cracked addresses listed in this thread.

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August 04, 2019, 04:34:43 PM
 #102

The x coordinate and y coordinate are both binary numbers in the range 2256.
the max is also a little bit less than 2256 but unlike private keys the max is defined by P (the prime) not N (the curve order)
After reading over the description of Pollard's kangaroo algorithm I think I understand it enough to be able to explain it to my 13 year old daughter so she can write the code as a fun educational exercise.  She is always looking for a good subject for her next science fair project and I think this would make a good one.

I have some questions about the PRF that someone might be able to answer. 

The only requirements listed in the article above are:

1) The PRF must map the finite cyclic group to "a set S of integers"
2) The PRF must be able to be changed in order to select a different S in order to create subsequent "kangaroos"

Since the length of the pseudorandom sequence is not specified I assumed 256 bits, is that reasonable?

So, it seems to me that f(X) = SHA256(X || nonce) where X is the binary representation of the the point X, || represents the concatenation operation, and the nonce is selected from a TRNG or is simply incremented would do the trick.

However this seems to be overkill and we want to do this as fast as possible.

Another option that comes to mind is to just define f(X) = (X + nonce) where X is the binary representation of the compressed form of X and the nonce is selected from a TRNG or is simply incremented.

What PRF is generally used?

Now that I think about this I think the science fair project could be something along the lines of measuring the conversion speed of various PRFs and PRF modification algorithms.  The data set would be all the cracked addresses in this thread, the independent variable would be various PRFs and different ways of modifying them to produce the next "kangaroo", and the dependent variable would be the total time it takes to re-crack all the known cracked addresses listed in this thread.

The idea is awesome!
I'm happy to wait for the effect...
Meanwhile, digging up the finds - I found this code:
Code:
import random
from Ecc import Ecc
from Ecc import Point

A = -95051
B = 11279326
p = 233970423115425145524320034830162017933
q = 233970423115425145498902418297807005944
ecc = Ecc(A, B, p)

def f(Y):
    (x, y) = Y.coords()
    return pow(2, (y % k))

priv = random.randint(0, q)
print 'You will never guess my private key of %s' % priv


basePoint = Point(4, 85518893674295321206118380980485522083)
pub = ecc.scale(basePoint, priv)

a = priv - pow(2, 20)
b =  priv + pow(2, 20)

print 'a',a
print 'b',b
global k
k = 15
print 'k is set to %d' % k
"""
Tame Kangaroo
    xT := 0
    yT := g^b

    for i in 1..N:
        xT := xT + f(yT)
        yT := yT * g^f(yT)

"""

xT = 0
yT = ecc.scale(basePoint, b)
y = pub

N = ( f(basePoint) + f(ecc.scale(basePoint, b))) / 2  * 2

for i in range(1, N):
    xT += f(yT)
    yT = ecc.add(yT, ecc.scale(basePoint, f(yT)));

print xT, yT
"""
Wild Kangaroo
    xW := 0
    yW := y

    while xW < b - a + xT:
        xW := xW + f(yW)
        yW := yW * g^f(yW)

        if yW = yT:
            return b + xT - xW
"""

print "Setting wild kangaroo off"

def wildKangaroo(ecc, y, yT, xT, basePoint,  b, a):
    xW = 0
    yW = y
    while xW < (b - a + xT):
        xW = xW + f(yW)
        yW = ecc.add(yW, ecc.scale(basePoint, f(yW)));

        if yW == yT:
            print 'catch'
            print yW, yT
            return b + xT - xW


A = wildKangaroo(ecc, y, yT, xT, basePoint, b, a)
print A

The problem is the initial stage, because python error:
Code:
Traceback (most recent call last):
  File "polard3.py", line 2, in <module>
    from Ecc import Ecc
ImportError: cannot import name Ecc

Uncle Google has no idea how to get out of it :-)
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August 04, 2019, 07:32:11 PM
 #103

In that code  the PRF is defined as:

Code:
def f(Y):
    (x, y) = Y.coords()
    return pow(2, (y % k))
where k = 15

And the value of N is selected as:

Code:
N = ( f(basePoint) + f(ecc.scale(basePoint, b))) / 2  * 2

Both interesting and unexpected choices.  Where did you find this code?  Is this from a supposedly working program?

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August 04, 2019, 09:37:06 PM
 #104

...
The problem is the initial stage, because python error:
Code:
Traceback (most recent call last):
  File "polard3.py", line 2, in <module>
    from Ecc import Ecc
ImportError: cannot import name Ecc

Uncle Google has no idea how to get out of it :-)

In terminal:
Code:
pip install ecc

ecc / Pure Python implementation of an elliptic curve cryptosystem based on FIPS 186-3
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August 05, 2019, 04:32:47 AM
 #105

What PRF is generally used?

i am not really familiar with this algorithm but yesterday when i saw your comment mentioning SHA256 as the PRF i did some search on the algorithm and i haven't yet seen anybody use this.
one option is what was posted (f(x) = 2x%k) each choosing k differently from random k in [1,20] to a k based on curve order, here is one in python: https://github.com/crypto-class/random-modnar/blob/master/set8/58/main.py
others use something similar to what you  said here with SHA256 but they simply use their language's Random() function which uses a bunch of hashes under the hood.
another thing i've seen was finding α based on prime (p-1) factors and define f(x) = xα %n

in the end it seems like there is no good answer to the pseudorandom map function that they use. each one is trying to come up with the most efficient function while reducing the cycles to make the algorithm run faster.

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August 05, 2019, 07:20:20 AM
 #106

After reading over the description of Pollard's kangaroo algorithm I think I understand it enough to be able to explain it to my 13 year old daughter so she can write the code as a fun educational exercise.  She is always looking for a good subject for her next science fair project and I think this would make a good one.

It's not so hard to write working Pollard's kangaroo, and there are some example implementation. Problem is writing CUDA implementation of it, as I understood CPU implementation can not compare by speed with CUDA one.
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August 05, 2019, 12:38:57 PM
 #107

After reading over the description of Pollard's kangaroo algorithm I think I understand it enough to be able to explain it to my 13 year old daughter so she can write the code as a fun educational exercise.  She is always looking for a good subject for her next science fair project and I think this would make a good one.

It's not so hard to write working Pollard's kangaroo, and there are some example implementation. Problem is writing CUDA implementation of it, as I understood CPU implementation can not compare by speed with CUDA one.
Good point.

For my real job I am writing all the TCG and secure boot ROM firmware for a next gen SSD controller ASIC.  This SSD controller ASIC happens to have a built in hardware crypto engine for AES, SHA, HMAC, RSA, ECC, etc.  I was thinking I could download a special test firmware into the SSD that would use the built in hardware crypto engine to do this calculation.  It would be incredibly fast.  I could justify downloading it to an entire rack of SSDs during manufacturing in order to do a "burn in test" of the crypto hardware on the drive.  Should be fun.

Our family was terrorized by Homeland Security.  Read all about it here:  http://www.jmwagner.com/ and http://www.burtw.com/  Any donations to help us recover from the $300,000 in legal fees and forced donations to the Federal Asset Forfeiture slush fund are greatly appreciated!
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August 05, 2019, 12:53:15 PM
 #108

What PRF is generally used?

i am not really familiar with this algorithm but yesterday when i saw your comment mentioning SHA256 as the PRF i did some search on the algorithm and i haven't yet seen anybody use this.
one option is what was posted (f(x) = 2x%k) each choosing k differently from random k in [1,20] to a k based on curve order, here is one in python: https://github.com/crypto-class/random-modnar/blob/master/set8/58/main.py
others use something similar to what you  said here with SHA256 but they simply use their language's Random() function which uses a bunch of hashes under the hood.
another thing i've seen was finding α based on prime (p-1) factors and define f(x) = xα %n

in the end it seems like there is no good answer to the pseudorandom map function that they use. each one is trying to come up with the most efficient function while reducing the cycles to make the algorithm run faster.

As far as this PRF:

Code:
def f(Z):
    (x, y) = Z.coords()
    return pow(2, (y % k))
where k is varied to create new kangaroos

To quote King Crimson:

Quote
The more I look at it
The more I like it
Heh, I do think it's good
The fact is..
No matter how closely I study it
No matter how I take it apart
No matter how I'll break it down
It remains consistent
I wish you were here to see it!

Anyway I am going to try the simplest fastest possible thing I can think of and test it to see if it will work:

Code:
def f(Z):
    (x, y) = Z.coords()
    return (y & M)
where M is a bit mask and is varied to create new kangaroos



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August 05, 2019, 03:56:03 PM
 #109

Anyway I am going to try the simplest fastest possible thing I can think of and test it to see if it will work:

Code:
def f(Z):
    (x, y) = Z.coords()
    return (y & M)
where M is a bit mask and is varied to create new kangaroos

They say this fastest pseudo-random generator that is any good: Xorshift

You need few lines of code to vary the mask, why not do this instead?
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August 05, 2019, 06:31:41 PM
 #110

They say this fastest pseudo-random generator that is any good: Xorshift

You need few lines of code to vary the mask, why not do this instead?

I read about and was intrigued by the two xoshiro256 algorithms and i think a great idea would be to create a xoshiro512 version that would be perfect for this application.

1) Expand the PRNG state from 256 bits to 512 bits
2) Seed the PRNG with all 512 bits of the point X that have been modified in a yet TBD way in order to create the various kangaroos
3) have the PRNG output a 256 bit pseudo random number based on the 512 bit state.

This might give better pseudo random coverage of the search space than my ultra simple (but faster) masking system.

Our family was terrorized by Homeland Security.  Read all about it here:  http://www.jmwagner.com/ and http://www.burtw.com/  Any donations to help us recover from the $300,000 in legal fees and forced donations to the Federal Asset Forfeiture slush fund are greatly appreciated!
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August 05, 2019, 07:17:46 PM
 #111

They say this fastest pseudo-random generator that is any good: Xorshift

You need few lines of code to vary the mask, why not do this instead?

I read about and was intrigued by the two xoshiro256 algorithms and i think a great idea would be to create a xoshiro512 version that would be perfect for this application.

1) Expand the PRNG state from 256 bits to 512 bits
2) Seed the PRNG with all 512 bits of the point X that have been modified in a yet TBD way in order to create the various kangaroos
3) have the PRNG output a 256 bit pseudo random number based on the 512 bit state.

This might give better pseudo random coverage of the search space than my ultra simple (but faster) masking system.

Nice idea, but you can simplify it by ignoring Y coordinate, since X is much more important and effectively defining the point on the curve. Then you can stay in 256 bit range instead of venturing to 512 bits, and use this version I've written for you:

Code:
struct xorshift256_state {
  uint64_t a, b, c, d;
};

/* The state array should be initialized to X coordinate */
uint64_t xorshift256(struct xorshift256_state *state)
{
uint64_t t = state->d;

uint64_t const s = state->a;
state->d = state->c;
state->c = state->b;
state->b = s;

t ^= t << 11;
t ^= t >> 8;
return state->a = t ^ s ^ (s >> 19);
}
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August 05, 2019, 08:21:00 PM
 #112

Nice idea, but you can simplify it by ignoring Y coordinate, since X is much more important and effectively defining the point on the curve. Then you can stay in 256 bit range instead of venturing to 512 bits, and use this version I've written for you:

Code:
struct xorshift256_state {
  uint64_t a, b, c, d;
};

/* The state array should be initialized to X coordinate */
uint64_t xorshift256(struct xorshift256_state *state)
{
uint64_t t = state->d;

uint64_t const s = state->a;
state->d = state->c;
state->c = state->b;
state->b = s;

t ^= t << 11;
t ^= t >> 8;
return state->a = t ^ s ^ (s >> 19);
}

Thanks, that looks great (fast).

BTW there is already a 512 bit state version of xoshiro in case we/anyone wants to try it.

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August 05, 2019, 08:35:23 PM
 #113

Hey,

Once my daughter gets this written she would like to run it against every cracked address in this "puzzle" for timing and test purposes.  In order to do that we will need a list of every public key, in whatever form is handy (compressed, uncompressed, binary, encoded, etc.) with preference to uncompressed binary in hex.

Has anyone already done this?  I would hate to have to go into the block chain to recover all the public keys if someone has already done that and can just publish it here.

Also, this would be a great thing to add to the OP of this thread:  A complete listing of all the public keys known for the cracked and still to be cracked addresses.

Thanks.

Burt

Our family was terrorized by Homeland Security.  Read all about it here:  http://www.jmwagner.com/ and http://www.burtw.com/  Any donations to help us recover from the $300,000 in legal fees and forced donations to the Federal Asset Forfeiture slush fund are greatly appreciated!
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August 05, 2019, 10:28:18 PM
Merited by BurtW (5)
 #114

Hey,

Once my daughter gets this written she would like to run it against every cracked address in this "puzzle" for timing and test purposes.  In order to do that we will need a list of every public key, in whatever form is handy (compressed, uncompressed, binary, encoded, etc.) with preference to uncompressed binary in hex.

Has anyone already done this?  I would hate to have to go into the block chain to recover all the public keys if someone has already done that and can just publish it here.

Also, this would be a great thing to add to the OP of this thread:  A complete listing of all the public keys known for the cracked and still to be cracked addresses.

Thanks.

Burt

This is a quick pass of all of the private keys from the OP through bitcoin-tool, outputting the public key.

Note that this conversion assumes a compressed pubkey. (I checked a couple and they were compressed, so I'm making the assumption that they all are.)

Code: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JDScreesh
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August 05, 2019, 11:39:10 PM
Merited by BurtW (5)
 #115

Hey,

Once my daughter gets this written she would like to run it against every cracked address in this "puzzle" for timing and test purposes.  In order to do that we will need a list of every public key, in whatever form is handy (compressed, uncompressed, binary, encoded, etc.) with preference to uncompressed binary in hex.

Has anyone already done this?  I would hate to have to go into the block chain to recover all the public keys if someone has already done that and can just publish it here.

Also, this would be a great thing to add to the OP of this thread:  A complete listing of all the public keys known for the cracked and still to be cracked addresses.

Thanks.

Burt

Here is the list. I hope it helps  Cheesy

Code:
# -              Address               -                         Compressed PubKey                          -                                                            Uncompressed PubKey
1 - 1BgGZ9tcN4rm9KBzDn7KprQz87SZ26SAMH - 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 - 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
2 - 1CUNEBjYrCn2y1SdiUMohaKUi4wpP326Lb - 02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9 - 04f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672
3 - 19ZewH8Kk1PDbSNdJ97FP4EiCjTRaZMZQA - 025cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc - 045cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264da
4 - 1EhqbyUMvvs7BfL8goY6qcPbD6YKfPqb7e - 022f01e5e15cca351daff3843fb70f3c2f0a1bdd05e5af888a67784ef3e10a2a01 - 042f01e5e15cca351daff3843fb70f3c2f0a1bdd05e5af888a67784ef3e10a2a015c4da8a741539949293d082a132d13b4c2e213d6ba5b7617b5da2cb76cbde904
5 - 1E6NuFjCi27W5zoXg8TRdcSRq84zJeBW3k - 02352bbf4a4cdd12564f93fa332ce333301d9ad40271f8107181340aef25be59d5 - 04352bbf4a4cdd12564f93fa332ce333301d9ad40271f8107181340aef25be59d5321eb4075348f534d59c18259dda3e1f4a1b3b2e71b1039c67bd3d8bcf81998c
6 - 1PitScNLyp2HCygzadCh7FveTnfmpPbfp8 - 03f2dac991cc4ce4b9ea44887e5c7c0bce58c80074ab9d4dbaeb28531b7739f530 - 04f2dac991cc4ce4b9ea44887e5c7c0bce58c80074ab9d4dbaeb28531b7739f530e0dedc9b3b2f8dad4da1f32dec2531df9eb5fbeb0598e4fd1a117dba703a3c37
7 - 1McVt1vMtCC7yn5b9wgX1833yCcLXzueeC - 0296516a8f65774275278d0d7420a88df0ac44bd64c7bae07c3fe397c5b3300b23 - 0496516a8f65774275278d0d7420a88df0ac44bd64c7bae07c3fe397c5b3300b23bdacd9a05fb9fb73108c0a99d567fba9b2f75ab36207e1557f6bf255f1337ff0
8 - 1M92tSqNmQLYw33fuBvjmeadirh1ysMBxK - 0308bc89c2f919ed158885c35600844d49890905c79b357322609c45706ce6b514 - 0408bc89c2f919ed158885c35600844d49890905c79b357322609c45706ce6b514d313f3cdd7cdcc16de776fec3b5892c1172d3056112776f06f63f4cea8c95157
9 - 1CQFwcjw1dwhtkVWBttNLDtqL7ivBonGPV - 0243601d61c836387485e9514ab5c8924dd2cfd466af34ac95002727e1659d60f7 - 0443601d61c836387485e9514ab5c8924dd2cfd466af34ac95002727e1659d60f78791c0007c09c94db328034b88c5bbbc113335366679eb099a5e75b583bc2c2a
10 - 1LeBZP5QCwwgXRtmVUvTVrraqPUokyLHqe - 03a7a4c30291ac1db24b4ab00c442aa832f7794b5a0959bec6e8d7fee802289dcd - 04a7a4c30291ac1db24b4ab00c442aa832f7794b5a0959bec6e8d7fee802289dcdd580b4242cf68189ac1309e79c5a2132d2cbf0e18be6d0b37d05a32256ca0c8b
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13 - 1Pie8JkxBT6MGPz9Nvi3fsPkr2D8q3GBc1 - 03aadaaab1db8d5d450b511789c37e7cfeb0eb8b3e61a57a34166c5edc9a4b869d - 04aadaaab1db8d5d450b511789c37e7cfeb0eb8b3e61a57a34166c5edc9a4b869d2ed7caaf2a261616f564190b4bc9f496f3df86353ff76d7f704e48e654bacdf1
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17 - 1HduPEXZRdG26SUT5Yk83mLkPyjnZuJ7Bm - 033f688bae8321b8e02b7e6c0a55c2515fb25ab97d85fda842449f7bfa04e128c3 - 043f688bae8321b8e02b7e6c0a55c2515fb25ab97d85fda842449f7bfa04e128c3393e3b1c529624e56840acbb10243ec9e0cfe99c3cffe1c87537b735bbba2d2f
18 - 1GnNTmTVLZiqQfLbAdp9DVdicEnB5GoERE - 020ce4a3291b19d2e1a7bf73ee87d30a6bdbc72b20771e7dfff40d0db755cd4af1 - 040ce4a3291b19d2e1a7bf73ee87d30a6bdbc72b20771e7dfff40d0db755cd4af1889098969cd1f2642a070ace8aacd681b6c97281ed46d6354f8094614865fba8
19 - 1NWmZRpHH4XSPwsW6dsS3nrNWfL1yrJj4w - 0385663c8b2f90659e1ccab201694f4f8ec24b3749cfe5030c7c3646a709408e19 - 0485663c8b2f90659e1ccab201694f4f8ec24b3749cfe5030c7c3646a709408e19457e3dd2f2a02ea1dd219233e317782fcc39a3594ca5ef4228f9af3b49bdc671
20 - 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum - 033c4a45cbd643ff97d77f41ea37e843648d50fd894b864b0d52febc62f6454f7c - 043c4a45cbd643ff97d77f41ea37e843648d50fd894b864b0d52febc62f6454f7c88020b66e0e1970a0009fa411e77166bca00b1ada6163854362ca33d1ee35ab1
21 - 14oFNXucftsHiUMY8uctg6N487riuyXs4h - 031a746c78f72754e0be046186df8a20cdce5c79b2eda76013c647af08d306e49e - 041a746c78f72754e0be046186df8a20cdce5c79b2eda76013c647af08d306e49e2d5736900aa6d87c26325ccc3d707065de2fb7dd6602f71ffadb33dcdf26c239
22 - 1CfZWK1QTQE3eS9qn61dQjV89KDjZzfNcv - 023ed96b524db5ff4fe007ce730366052b7c511dc566227d929070b9ce917abb43 - 043ed96b524db5ff4fe007ce730366052b7c511dc566227d929070b9ce917abb43700d7526050cc27c80c39aac7e5a930a79914bc74c8808177d58335f69ab72f4
23 - 1L2GM8eE7mJWLdo3HZS6su1832NX2txaac - 03f82710361b8b81bdedb16994f30c80db522450a93e8e87eeb07f7903cf28d04b - 04f82710361b8b81bdedb16994f30c80db522450a93e8e87eeb07f7903cf28d04b97336f10faad1355ee425ca4f3a989bbd929704bfb9ae2371178ae3adef7ab3f
24 - 1rSnXMr63jdCuegJFuidJqWxUPV7AtUf7 - 036ea839d22847ee1dce3bfc5b11f6cf785b0682db58c35b63d1342eb221c3490c - 046ea839d22847ee1dce3bfc5b11f6cf785b0682db58c35b63d1342eb221c3490cd4313e400ac025a18f72b7e4487a3a47676c1e97ba6f8119e9736d4b8c4ce2a9
25 - 15JhYXn6Mx3oF4Y7PcTAv2wVVAuCFFQNiP - 03057fbea3a2623382628dde556b2a0698e32428d3cd225f3bd034dca82dd7455a - 04057fbea3a2623382628dde556b2a0698e32428d3cd225f3bd034dca82dd7455ab7deb4729bedde33c9edc651ecb0c034adc49678ad67414e3e90b01f2d085655
26 - 1JVnST957hGztonaWK6FougdtjxzHzRMMg - 024e4f50a2a3eccdb368988ae37cd4b611697b26b29696e42e06d71368b4f3840f - 044e4f50a2a3eccdb368988ae37cd4b611697b26b29696e42e06d71368b4f3840f076d012b98c9e265dda1a9028ae37f1a4548505fac40524d507b5675c74714ca
27 - 128z5d7nN7PkCuX5qoA4Ys6pmxUYnEy86k - 031a864bae3922f351f1b57cfdd827c25b7e093cb9c88a72c1cd893d9f90f44ece - 041a864bae3922f351f1b57cfdd827c25b7e093cb9c88a72c1cd893d9f90f44ece0340864e1e4a939cf2eb8511e833c1c2bdd51a55bd204368332ae70d68a65c61
28 - 12jbtzBb54r97TCwW3G1gCFoumpckRAPdY - 03e9e661838a96a65331637e2a3e948dc0756e5009e7cb5c36664d9b72dd18c0a7 - 04e9e661838a96a65331637e2a3e948dc0756e5009e7cb5c36664d9b72dd18c0a709f531540a4ca59f50f93b8bf7b0c060045754aaae7ce1bea5a136c0d5874b97
29 - 19EEC52krRUK1RkUAEZmQdjTyHT7Gp1TYT - 026caad634382d34691e3bef43ed4a124d8909a8a3362f91f1d20abaaf7e917b36 - 046caad634382d34691e3bef43ed4a124d8909a8a3362f91f1d20abaaf7e917b36f5c907aad14e4457181ce6be0f0206a1a22d2730d14edf5d50630ad30d63baf4
30 - 1LHtnpd8nU5VHEMkG2TMYYNUjjLc992bps - 030d282cf2ff536d2c42f105d0b8588821a915dc3f9a05bd98bb23af67a2e92a5b - 040d282cf2ff536d2c42f105d0b8588821a915dc3f9a05bd98bb23af67a2e92a5bb0ca8ab2bfb595a48a19d4faecd863697762a74e1e889de825accfee9895790d
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36 - 1Be2UF9NLfyLFbtm3TCbmuocc9N1Kduci1 - 02b3e772216695845fa9dda419fb5daca28154d8aa59ea302f05e916635e47b9f6 - 04b3e772216695845fa9dda419fb5daca28154d8aa59ea302f05e916635e47b9f66e1ad5a30b9c99a0ce54247314bd60f6a8c4af66c2672b1a9d7bfebbd8f9340c
37 - 14iXhn8bGajVWegZHJ18vJLHhntcpL4dex - 027d2c03c3ef0aec70f2c7e1e75454a5dfdd0e1adea670c1b3a4643c48ad0f1255 - 047d2c03c3ef0aec70f2c7e1e75454a5dfdd0e1adea670c1b3a4643c48ad0f12556144da0f5d8070b5cbfc25541705394c22b83d0c90f3f6fb1fe5b20dac02a940
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42 - 1E32GPWgDyeyQac4aJxm9HVoLrrEYPnM4N - 03eec88385be9da803a0d6579798d977a5d0c7f80917dab49cb73c9e3927142cb6 - 04eec88385be9da803a0d6579798d977a5d0c7f80917dab49cb73c9e3927142cb628afea598588ea50a6b11e552f8574e0b93abd5595f5aa17ea3be5304103d255
43 - 1PiFuqGpG8yGM5v6rNHWS3TjsG6awgEGA1 - 02a631f9ba0f28511614904df80d7f97a4f43f02249c8909dac92276ccf0bcdaed - 04a631f9ba0f28511614904df80d7f97a4f43f02249c8909dac92276ccf0bcdaedc69d75bbc4ec87b7d7616b7a197fa0ab25814fb551d292aa70b54979e21cbc64
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BurtW
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August 06, 2019, 01:24:59 AM
 #116

Thanks to JDScreesh and almightyruler, merit sent.

Our family was terrorized by Homeland Security.  Read all about it here:  http://www.jmwagner.com/ and http://www.burtw.com/  Any donations to help us recover from the $300,000 in legal fees and forced donations to the Federal Asset Forfeiture slush fund are greatly appreciated!
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August 06, 2019, 12:48:01 PM
 #117

Some Admin could you please delete the satoshidisk links with the ID C74Tfg from the posts of this tread? We don't what that people get scammed. Thanks!
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August 06, 2019, 10:04:09 PM
Last edit: August 06, 2019, 10:47:58 PM by BurtW
 #118

We made progress today and got our first positive test results.  Thanks for the help in posting the public keys.  That saved us some time.

Code:
bits  = 30
a     = 0x20000000
b     = 0x40000000
P     = 0x30D282CF2FF536D2C42F105D0B8588821A915DC3F9A05BD98BB23AF67A2E92A5B
s     = 0x3D94CD64

bits  = 31
a     = 0x40000000
b     = 0x80000000
P     = 0x387DC70DB1806CD9A9A76637412EC11DD998BE666584849B3185F7F9313C8FD28
s     = 0x7D4FE747

bits  = 32
a     = 0x80000000
b     = 0x100000000
P     = 0x209C58240E50E3BA3F833C82655E8725C037A2294E14CF5D73A5DF8D56159DE69
s     = 0xB862A62E

Written in C using OpenSSL, very slow, we will work on efficiency later...

bits is the number of bits of entropy in the private key
a is the lower bound of the private key
b is the upper bound of the private key
P is the public key
s is the private key found

Still to do: add the CPU cycle timers

Our family was terrorized by Homeland Security.  Read all about it here:  http://www.jmwagner.com/ and http://www.burtw.com/  Any donations to help us recover from the $300,000 in legal fees and forced donations to the Federal Asset Forfeiture slush fund are greatly appreciated!
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August 06, 2019, 10:08:58 PM
 #119

@drotika
I have faith and I purchased from https://github.com/Saadinr/Pollard-s FULL Code: https://satoshidisk.com/pay/C74Tfg and I received the file   :
Pollard_s kangaroo-Windows 10 -Ubuntu 18.04.zip
but the zip file is password protected, I hope is not fake.
please if you could send me the password.
Thanks

She's Not Me
sorry but someone is having fun  Undecided
Github / Saadinr file: 1034.12KB (fake)
my file: 1194.3KB
see it on my profile
sory

Lol the moderators and admins here are totally worthless.
Firebox
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August 07, 2019, 12:29:59 AM
 #120

We made progress today and got our first positive test results.  Thanks for the help in posting the public keys.  That saved us some time.

You are genius, guys.
If you need testers please consider me.
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