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COBRAS

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Any scrypt python+ GPU for substract scalar from pub, multiply pub to scalar ?

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Quote from: j2002ba2 on October 11, 2022, 08:19:00 PM

Quote from: NotATether on October 10, 2022, 10:52:32 AM

A bit off-topic but...

SAGE seems to have represented these finite fields and curves & operations really well. It would be nice if this functionality could be had in other languages as well - especially C-C++ where there are many applications for this kind of thing because of its raw speed, but are hard to implement because all the crypto libraries for these languages are half-arsed or incomplete (libsecp256k1 is the closest that replicates SAGE stuff but a general-purpose curve and field library would be a nice to-have).

I have used PARI/GP C library
The following is with the provided gp shell (some empty lines omitted):

Code:

gp > ellgroup(ellinit([0,7]), 2^256 - 2^32 - 977)
%1 = [115792089237316195423570985008687907852837564279074904382605163141518161494337]
gp > factor(%1[1] - 1)
%2 =
[ 2 6]
[ 3 1]
[ 149 1]
[ 631 1]
[ 107361793816595537 1]
[ 174723607534414371449 1]
[341948486974166000522343609283189 1]

The easiest for me was doing pari_init_opts, then (after recording avma) using gp_read_str with corresponding string (instead of interfacing each and every function), and then pari_sprintf("%Ps",...) to get the result as text (then recovering avma), and parse it to something meaningful.

Couldn't find a function returning the multiplicative order of point though.

are you trying to find magic numbers, which part i mention here before a year
https://bitcointalksearch.org/topic/m.57373246
here is full list of numbers

Code:

1
2
3
4
6
8
12
16
24
32
48
64
96
149
192
298
447
596
631
894
1192
1262
1788
1893
2384
2524
3576
3786
4768
5048
7152
7572
9536
10096
14304
15144
20192
28608
30288
40384
60576
94019
121152
188038
282057
376076
564114
752152
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91752844086621390985396977027486456301773030332072031998894740999618194528
97141014460835734415747470644872405916810037146874919784064734179125974408
129521352614447645887663294193163207889080049529166559712086312238834632544
183505688173242781970793954054972912603546060664144063997789481999236389056
194282028921671468831494941289744811833620074293749839568129468358251948816
259042705228895291775326588386326415778160099058333119424172624477669265088
388564057843342937662989882579489623667240148587499679136258936716503897632
603083798111021851164432213586916186733528980620181793659401891362073757783
777128115686685875325979765158979247334480297174999358272517873433007795264
1206167596222043702328864427173832373467057961240363587318803782724147515566
1809251394333065553493296640760748560200586941860545380978205674086221273349
2412335192444087404657728854347664746934115922480727174637607565448295031132
3618502788666131106986593281521497120401173883721090761956411348172442546698
4824670384888174809315457708695329493868231844961454349275215130896590062264
7237005577332262213973186563042994240802347767442181523912822696344885093396
9649340769776349618630915417390658987736463689922908698550430261793180124528
14474011154664524427946373126085988481604695534884363047825645392689770186792
19298681539552699237261830834781317975472927379845817397100860523586360249056
28948022309329048855892746252171976963209391069768726095651290785379540373584
38597363079105398474523661669562635950945854759691634794201721047172720498112
57896044618658097711785492504343953926418782139537452191302581570759080747168
115792089237316195423570985008687907852837564279074904382605163141518161494336

NotATether

legendary

Activity: 1568

Merit: 6660

bitcoincleanup.com / bitmixlist.org

Quote from: j2002ba2 on October 11, 2022, 08:19:00 PM

I have used PARI/GP C library
The following is with the provided gp shell (some empty lines omitted):

Code:

gp > ellgroup(ellinit([0,7]), 2^256 - 2^32 - 977)
%1 = [115792089237316195423570985008687907852837564279074904382605163141518161494337]
gp > factor(%1[1] - 1)
%2 =
[ 2 6]
[ 3 1]
[ 149 1]
[ 631 1]
[ 107361793816595537 1]
[ 174723607534414371449 1]
[341948486974166000522343609283189 1]

The easiest for me was doing pari_init_opts, then (after recording avma) using gp_read_str with corresponding string (instead of interfacing each and every function), and then pari_sprintf("%Ps",...) to get the result as text (then recovering avma), and parse it to something meaningful.

Couldn't find a function returning the multiplicative order of point though.

Amazing stuff, I'll definitely check it out!

brainless

member

Activity: 313

Merit: 34

Quote from: CrunchyF on October 11, 2022, 01:02:14 PM

Quote from: brainless on October 11, 2022, 12:31:05 AM

Ok but a multiplication of what by what ?...sorry i d'ont understand

for multiplication or halve the point (50k loop)

Code:

from fastecdsa.curve import secp256k1
from fastecdsa.point import Point
from fastecdsa import keys, curve

def c2ux(point):

p_hex = 'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F'
p = int(p_hex, 16)
compressed_key_hex = point
x_hex = compressed_key_hex[2:66]
x = int(x_hex, 16)
prefix = compressed_key_hex[0:2]

y_square = (pow(x, 3, p) + 7) % p
y_square_square_root = pow(y_square, (p+1) * pow(4, p - 2, p) % p , p)
if (prefix == "02" and y_square_square_root & 1) or (prefix == "03" and not y_square_square_root & 1):
y = (-y_square_square_root) % p
else:
y = y_square_square_root

return x_hex

def c2uy(point):

p_hex = 'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F'
p = int(p_hex, 16)
compressed_key_hex = point
x_hex = compressed_key_hex[2:66]
x = int(x_hex, 16)
prefix = compressed_key_hex[0:2]

y_square = (pow(x, 3, p) + 7) % p
y_square_square_root = pow(y_square, (p+1) * pow(4, p - 2, p) % p , p)
if (prefix == "02" and y_square_square_root & 1) or (prefix == "03" and not y_square_square_root & 1):
y = (-y_square_square_root) % p
else:
y = y_square_square_root

computed_y_hex = format(y, '064x')

return computed_y_hex

def cpub(x,y):
prefix = '02' if y % 2 == 0 else '03'
c = prefix+ hex(x)[2:].zfill(64)
return c

with open('in.txt') as f:
for line in f:
line=line.strip()

xs = int(c2ux(line),16)
ys = int(c2uy(line),16)
S = Point(xs, ys, curve=secp256k1)

xsorg = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
ysorg = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
Sorg = Point(xsorg, ysorg, curve=secp256k1)
for i in range(0,50000):
S=S*57896044618658097711785492504343953926418782139537452191302581570759080747169
xx=S.x
yy=S.y
pub04=cpub(xx,yy)
print(pub04,file=open("out.txt", "a"))

j2002ba2

full member

Activity: 204

Merit: 437

Quote from: NotATether on October 10, 2022, 10:52:32 AM

A bit off-topic but...

SAGE seems to have represented these finite fields and curves & operations really well. It would be nice if this functionality could be had in other languages as well - especially C-C++ where there are many applications for this kind of thing because of its raw speed, but are hard to implement because all the crypto libraries for these languages are half-arsed or incomplete (libsecp256k1 is the closest that replicates SAGE stuff but a general-purpose curve and field library would be a nice to-have).

I have used PARI/GP C library
The following is with the provided gp shell (some empty lines omitted):

Code:

gp > ellgroup(ellinit([0,7]), 2^256 - 2^32 - 977)
%1 = [115792089237316195423570985008687907852837564279074904382605163141518161494337]
gp > factor(%1[1] - 1)
%2 =
[ 2 6]
[ 3 1]
[ 149 1]
[ 631 1]
[ 107361793816595537 1]
[ 174723607534414371449 1]
[341948486974166000522343609283189 1]

The easiest for me was doing pari_init_opts, then (after recording avma) using gp_read_str with corresponding string (instead of interfacing each and every function), and then pari_sprintf("%Ps",...) to get the result as text (then recovering avma), and parse it to something meaningful.

Couldn't find a function returning the multiplicative order of point though.

CrunchyF

jr. member

Activity: 54

Merit: 26

Quote from: brainless on October 11, 2022, 12:31:05 AM

Ok but a multiplication of what by what ?...sorry i d'ont understand

brainless

member

Activity: 313

Merit: 34

Quote from: CrunchyF on October 10, 2022, 04:19:16 PM

Quote from: brainless on October 10, 2022, 12:05:58 AM

Quote from: gmaxwell on October 09, 2022, 09:23:45 PM

Something is wrong here because the order of the group formed by multiplication of 2 mod n is much much larger than 20 million, so you can't generate all these addresses by going 20 million steps in either direction from any of them.

Code:

sage: F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
C = EllipticCurve ([F (0), F (7)])
G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
N = FiniteField (C.order())
sage: N(2).multiplicative_order()
1809251394333065553493296640760748560200586941860545380978205674086221273349

yes , will take time aprox 7 hours for 20m generate multiplication steps
but in my first message already tip
pick 1 pubkey from 1634 list, get pubkey
example
https://blockchain.info/q/pubkeyaddr/1121f21h1wyrnm2ipXiKaCULLopeBegt2s
result: 027262bdb402fe5ddc6b1e81cef02bcd673140e6a26857503459a4891920a6a5a9
it could be your starting point,
now take 50k steps by pubkey point * 2, ( you can create script here, same time generate next pubkey and convert address and verify from 1634 list, and can print results)
same 50k steps of pubkey point * 57896044618658097711785492504343953926418782139537452191302581570759080747169
(halv the point)
and same convert and verufy address, print)

up and down side 50k +50k, take few minutes

as for 20m halve required too much time, for this i create an other thread, for discus this issue, where i ask developer, just for basic add/sub/mul conversion creator/generator by pycuda or cuda tools , when said tools available, these job are for seconds for millions point
https://bitcointalksearch.org/topic/cuda-scripts-for-point-addition-multiplication-etc-5409721

this following python script (you need to have bit and gmpy2 installed) can do the work in 2 seconds...

Code:

from bit.format import public_key_to_address,public_key_to_coords,coords_to_public_key
from bit.utils import bytes_to_hex,hex_to_bytes
import gmpy2

def point_double_gmp(point):

x1, y1 = point

m = (3 *gmpy2.powmod(x1, 2,P)) * gmpy2.invert(2 * y1,P)
x3 = gmpy2.powmod(m, 2,P) - x1 - x1
y3 = y1 + m * (x3 - x1)
result = (int(x3%P),int(-y3%P))
return result

P=0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f

start_pubk='0398ce5d78ed1a3b121cbdbd62daecda243a43cf3f201c3599ee78a391d0190950'
start_coord=public_key_to_coords(hex_to_bytes(start_pubk))

pt=start_coord
for m in range(1,50001):
pt=point_double_gmp(pt)
x,y=pt
mulmod="2^%d mod P "%m
pubk=coords_to_public_key(x,y,compressed=True)
add=public_key_to_address(pubk)

print("pubk * %s ==> pubk:%s add:%s"%(mulmod,bytes_to_hex(pubk),add))

script about double point, could you post multiplication point script too ?

CrunchyF

jr. member

Activity: 54

Merit: 26

Quote from: brainless on October 10, 2022, 12:05:58 AM

Quote from: gmaxwell on October 09, 2022, 09:23:45 PM

Something is wrong here because the order of the group formed by multiplication of 2 mod n is much much larger than 20 million, so you can't generate all these addresses by going 20 million steps in either direction from any of them.

Code:

sage: F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
C = EllipticCurve ([F (0), F (7)])
G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
N = FiniteField (C.order())
sage: N(2).multiplicative_order()
1809251394333065553493296640760748560200586941860545380978205674086221273349

yes , will take time aprox 7 hours for 20m generate multiplication steps
but in my first message already tip
pick 1 pubkey from 1634 list, get pubkey
example
https://blockchain.info/q/pubkeyaddr/1121f21h1wyrnm2ipXiKaCULLopeBegt2s
result: 027262bdb402fe5ddc6b1e81cef02bcd673140e6a26857503459a4891920a6a5a9
it could be your starting point,
now take 50k steps by pubkey point * 2, ( you can create script here, same time generate next pubkey and convert address and verify from 1634 list, and can print results)
same 50k steps of pubkey point * 57896044618658097711785492504343953926418782139537452191302581570759080747169
(halv the point)
and same convert and verufy address, print)

up and down side 50k +50k, take few minutes

as for 20m halve required too much time, for this i create an other thread, for discus this issue, where i ask developer, just for basic add/sub/mul conversion creator/generator by pycuda or cuda tools , when said tools available, these job are for seconds for millions point
https://bitcointalksearch.org/topic/cuda-scripts-for-point-addition-multiplication-etc-5409721

this following python script (you need to have bit and gmpy2 installed) can do the work in 2 seconds...

Code:

from bit.format import public_key_to_address,public_key_to_coords,coords_to_public_key
from bit.utils import bytes_to_hex,hex_to_bytes
import gmpy2

def point_double_gmp(point):

x1, y1 = point

m = (3 *gmpy2.powmod(x1, 2,P)) * gmpy2.invert(2 * y1,P)
x3 = gmpy2.powmod(m, 2,P) - x1 - x1
y3 = y1 + m * (x3 - x1)
result = (int(x3%P),int(-y3%P))
return result

P=0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f

start_pubk='0398ce5d78ed1a3b121cbdbd62daecda243a43cf3f201c3599ee78a391d0190950'
start_coord=public_key_to_coords(hex_to_bytes(start_pubk))

pt=start_coord
for m in range(1,50001):
pt=point_double_gmp(pt)
x,y=pt
mulmod="2^%d mod P "%m
pubk=coords_to_public_key(x,y,compressed=True)
add=public_key_to_address(pubk)

print("pubk * %s ==> pubk:%s add:%s"%(mulmod,bytes_to_hex(pubk),add))

NotATether

legendary

Activity: 1568

Merit: 6660

bitcoincleanup.com / bitmixlist.org

A bit off-topic but...

SAGE seems to have represented these finite fields and curves & operations really well. It would be nice if this functionality could be had in other languages as well - especially C-C++ where there are many applications for this kind of thing because of its raw speed, but are hard to implement because all the crypto libraries for these languages are half-arsed or incomplete (libsecp256k1 is the closest that replicates SAGE stuff but a general-purpose curve and field library would be a nice to-have).

gmaxwell

staff

Activity: 4158

Merit: 8382

Quote from: brainless on October 07, 2022, 06:19:08 AM

pick pubkey of any address,
pubkey point * 2, and loop it to till 50000 pubkey generate, convert to address, you will get all these 1634 addresses,
same you can halve till 50000 pubkey too,

What am I failing to understand here, then? Because to me this clearly appears to saying that you can "pick any of the pubkeys" and double it to generate all 1634 addresses. Or, alternatively, you can do the same by repeated halving.

Because the order is ~2^250, that isn't possible.

Now, if it said that you could start at the first (in sequence rather than sorted order) and double to generate the reset or the last and halve to generate the reset-- sure, that is plausible.

brainless

member

Activity: 313

Merit: 34

Quote from: _Counselor on October 10, 2022, 04:59:13 AM

Quote from: gmaxwell on October 10, 2022, 04:17:57 AM

You can't do 1809251394333065553493296640760748560200586941860545380978205674086221273349 operations in several hours either.

I don't have any reason to doubt that you've listed a number of points related by doubling, but the claim that you were able to wrap around and enumerate all of them from any starting position and then moving in one direction (either doubling or halving) can't be true, AFAICT.

He doesn't talking about mapping all points, which can be generated by doubling/halving.
As I understand it, he found a sequence of keys that are generated in this way and leads to the used addresses.
It looks like a manual generation of something like HD wallet with bad realisation. Something like if you take first address key ("master key") and derive other wallet addresses just by doubling "master key" N times. It is obvious that such an algorithm, unlike a normal HD wallet, allows you to recover the keys to all addresses, if you know any one of them.

Agree

_Counselor

member

Activity: 107

Merit: 61

Quote from: gmaxwell on October 10, 2022, 04:17:57 AM

You can't do 1809251394333065553493296640760748560200586941860545380978205674086221273349 operations in several hours either.

I don't have any reason to doubt that you've listed a number of points related by doubling, but the claim that you were able to wrap around and enumerate all of them from any starting position and then moving in one direction (either doubling or halving) can't be true, AFAICT.

He doesn't talking about mapping all points, which can be generated by doubling/halving.
As I understand it, he found a sequence of keys that are generated in this way and leads to the used addresses.
It looks like a manual generation of something like HD wallet with bad realisation. Something like if you take first address key ("master key") and derive other wallet addresses just by doubling "master key" N times. It is obvious that such an algorithm, unlike a normal HD wallet, allows you to recover the keys to all addresses, if you know any one of them.

gmaxwell

staff

Activity: 4158

Merit: 8382

You can't do 1809251394333065553493296640760748560200586941860545380978205674086221273349 operations in several hours either.

I don't have any reason to doubt that you've listed a number of points related by doubling, but the claim that you were able to wrap around and enumerate all of them from any starting position and then moving in one direction (either doubling or halving) can't be true, AFAICT.

_Counselor

member

Activity: 107

Merit: 61

Quote from: brainless on October 10, 2022, 12:05:58 AM

as for 20m halve required too much time, for this i create an other thread, for discus this issue, where i ask developer, just for basic add/sub/mul conversion creator/generator by pycuda or cuda tools , when said tools available, these job are for seconds for millions point
https://bitcointalksearch.org/topic/cuda-scripts-for-point-addition-multiplication-etc-5409721

If you need 50k keys by sequential halving the original, why use expensive division on each step, you just can take "last" key (original / 2^50000), and then generate all keys by fast doubling.

brainless

member

Activity: 313

Merit: 34

Quote from: gmaxwell on October 09, 2022, 09:23:45 PM

Something is wrong here because the order of the group formed by multiplication of 2 mod n is much much larger than 20 million, so you can't generate all these addresses by going 20 million steps in either direction from any of them.

Code:

sage: F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
C = EllipticCurve ([F (0), F (7)])
G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
N = FiniteField (C.order())
sage: N(2).multiplicative_order()
1809251394333065553493296640760748560200586941860545380978205674086221273349

yes , will take time aprox 7 hours for 20m generate multiplication steps
but in my first message already tip
pick 1 pubkey from 1634 list, get pubkey
example
https://blockchain.info/q/pubkeyaddr/1121f21h1wyrnm2ipXiKaCULLopeBegt2s
result: 027262bdb402fe5ddc6b1e81cef02bcd673140e6a26857503459a4891920a6a5a9
it could be your starting point,
now take 50k steps by pubkey point * 2, ( you can create script here, same time generate next pubkey and convert address and verify from 1634 list, and can print results)
same 50k steps of pubkey point * 57896044618658097711785492504343953926418782139537452191302581570759080747169
(halv the point)
and same convert and verufy address, print)

up and down side 50k +50k, take few minutes

as for 20m halve required too much time, for this i create an other thread, for discus this issue, where i ask developer, just for basic add/sub/mul conversion creator/generator by pycuda or cuda tools , when said tools available, these job are for seconds for millions point
https://bitcointalksearch.org/topic/cuda-scripts-for-point-addition-multiplication-etc-5409721

gmaxwell

staff

Activity: 4158

Merit: 8382

Something is wrong here because the order of the group formed by multiplication of 2 mod n is much much larger than 20 million, so you can't generate all these addresses by going 20 million steps in either direction from any of them.

Code:

sage: F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
C = EllipticCurve ([F (0), F (7)])
G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
N = FiniteField (C.order())
sage: N(2).multiplicative_order()
1809251394333065553493296640760748560200586941860545380978205674086221273349

brainless

member

Activity: 313

Merit: 34

connection exist here too 26 dec 2020

https://bitcointalksearch.org/topic/--5303856

nc50lc

legendary

Activity: 2394

Merit: 5531

Self-proclaimed Genius

Quote from: NeuroticFish on October 07, 2022, 06:36:46 AM

I'm not sure I understand where's the problem (as in 2022);

I think he's presuming that there could be a centralized service or exchange that have a broken implementation of HD wallet which produces the child keys in series instead of the standard implementation.

In fact, all of the addresses he presented belong to a single wallet according to walletexplorer: walletexplorer.com/wallet/00113e9c26df0947/addresses
Having a total of 6,023 linked addresses suggests that it's indeed an exchange or service provider.

NeuroticFish

legendary

Activity: 3500

Merit: 6205

Looking for campaign manager? Contact icopress!

Quote from: brainless on October 07, 2022, 06:19:08 AM

if any one address prv key exposed, in series all addresses balances could be in high risk

I'm not sure I understand where's the problem (as in 2022); similarly with any modern HD wallet, it would be utterly stupid to an user to expose any of his private keys.
Did you manage to get private keys? I guess not. It is written everywhere nowadays that people should avoid brain wallets since they're unsafe. I think that all brain wallets got emptied years ago (the few addresses from your list I've checked were also emptied years ago).

brainless

member

Activity: 313

Merit: 34

Code:

1FC5Y4y7j9YJoeWvxK2p7mfve43YNFqzCS
1FcEi7F6VSrJr8WF566VA6HWP4VJLFjJaD
1FCWNedrk4vZTzqkKkahqHvnvFWr1Qw8vD
1FDePYFo7z4TLjESdiXmX9n1bKLdsJeZQg
1FdMf2QJx3do4U7mX2TqZ91bighmRcqn3S
1FdqRW8RXEAWCrLMZVcCDU3s5eVbvPPaiA
1Fehrh3rBLG87DqsJgDvMR4vrMzjYgsBJx
1FemCkkRWA2tmdZpGGMAxmB1ST2YxhGBEH
1FeQUSjCgBTJvZV9MuHdYxKLK65Y8GooeQ
1FESdQJwTy4Ve2iiadyHWBJomZp3QZH1Hm
1FFr1j74tiyrqD5mbW3styyrnC3c3ue4KN
1FG1YStGnBRc9y11Zb6MnA49TbpFht1DbZ
1Fg4pKoK3HC1abEkacZyLSruLZc1tp6EZR
1FGJLbWGqdv5UJApxhwWAUxP7VTcG51KPh
1FgmYX3cJ15ZYjpGHjyGQSAeDgqjV5oDJ3
1FgTAuErPmBs6nC7D4JStnRFR3WXN653FQ
1FgzkE1Yx1imJzb8UVxrajvqvmyuMAtX3f
1Fh437TXVycgP6Y8yCSu9dRwuutrWXxcYf
1FHmpbSi6hs4TTU4ejim256Q6BWf1avy4X
1FHuQkF1Bnk5wArTMn2SizBGK62qiwqYg1
1FiqrF5tZg6uJzBAt8By2xZn2Lbqo4BYXu
1Fjnq6opsugrZcNT4KXwfVaXtkcNMxEt5w
1Fjyhr23anEeNdTxd2qmMQn7KPLqjWPhq
1Fk3hBf4yrC2d2YkiMCuAaV6sB6YvZuRoT
1FkChoRsfTQRuZidumamS4C4z9syk5Fn6n
1FkkfckWiLC4bk5m98gtenzYskmYXMoPtf
1FkME4jMenXPc6rZ8RFMjwdxJ1UnoZgUqb
1FKmgg66BPYLA6DRS9si4vZ1XiG6NjHMdq
1FLPjtR2reT1C6Zzmv6JDZgiqKKEJTqZXv
1FLYbyfisxuis8LwaFtR5YfdjsVbBqFmHF
1FmvWKpjrNX6Eiwgm6gEBstLcFf9DcRjVW
1FnQXYkeeG2hBS48tMdZgQFinc8uwidpMu
1FnTsv9WMhRRFFcBBWMT8tJYiT9VHxUPmp
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Topic: Exposed ... Mistakes or ... (Read 542 times)