lightweight database, for brute force using publickeys-32Mk =3.81MB(secp256k1)

[mcdouglasx]

There are many options when we work with bits:
could use this with bits

PUBKEY - RANDOM NUMBER = CREATE -1024 Pubs, as my publication (1 bit per key).

Repeat 1 million times.

We save a database that we will call "A"
where all pubs and random number are saved from the random subtractions.

We save a database that we will call "B"
where only the bits obtained are saved.

We scan

64 -bit collision margin

If there is match
We identify the pub found counting the bits in the DB using the % 1024  to calculate the PK found (because each operation is different and 1024 was the number of sequential keys for each pub).

We would basically have 1 million mini dB of 1024 keys stored in 1 1000000*1024 bits database.
With the difference that they would not be in sequences and could cover the target range randomly. .

Then that match (pub) we will find in database "A" and add to the RANDOM NUMBER to obtain pk from the main target

[WanderingPhilospher]

There are many options when we work with bits:
could use this with bits

PUBKEY - RANDOM NUMBER = CREATE -1024 Pubs, as my publication (1 bit per key).

Repeat 1 million times.

We save a database that we will call "A"
where all pubs and random number are saved from the random subtractions.

We save a database that we will call "B"
where only the bits obtained are saved.

We scan

64 -bit collision margin

If there is match
We identify the pub found counting the bits in the DB using the % 1024  to calculate the PK found (because each operation is different and 1024 was the number of sequential keys for each pub).

We would basically have 1 million mini dB of 1024 keys stored in 1 1000000*1024 bits database.
With the difference that they would not be in sequences and could cover the target range randomly. .

Then that match (pub) we will find in database "A" and add to the RANDOM NUMBER to obtain pk from the main target

Did you ever tinker or mess with your multi-pub binary and search scripts?
That would work as well.
Generate pubs and offsets (random number subtracted by of original pubkey) and save in a file and load the new gen pubs in another and run the multi pub script against the pub only file.

[ecdsa123]

@WanderingPhilospher

can you publish your version?

[whanau]

Ah, I uploaded a version of create_database that doesn't match with that version of the search_pk script
Now it should work:

It works for me up to 0x81 and after that it does not seem to find any keys.
I tried deleting and recreating the database from 0x80 but still nothing found.

[mcdouglasx]

There are many options when we work with bits:
could use this with bits

PUBKEY - RANDOM NUMBER = CREATE -1024 Pubs, as my publication (1 bit per key).

Repeat 1 million times.

We save a database that we will call "A"
where all pubs and random number are saved from the random subtractions.

We save a database that we will call "B"
where only the bits obtained are saved.

We scan

64 -bit collision margin

If there is match
We identify the pub found counting the bits in the DB using the % 1024  to calculate the PK found (because each operation is different and 1024 was the number of sequential keys for each pub).

We would basically have 1 million mini dB of 1024 keys stored in 1 1000000*1024 bits database.
With the difference that they would not be in sequences and could cover the target range randomly. .

Then that match (pub) we will find in database "A" and add to the RANDOM NUMBER to obtain pk from the main target

Did you ever tinker or mess with your multi-pub binary and search scripts?
That would work as well.
Generate pubs and offsets (random number subtracted by of original pubkey) and save in a file and load the new gen pubs in another and run the multi pub script against the pub only file.

added binary version.

[COBRAS]

There are many options when we work with bits:
could use this with bits

PUBKEY - RANDOM NUMBER = CREATE -1024 Pubs, as my publication (1 bit per key).

Repeat 1 million times.

We save a database that we will call "A"
where all pubs and random number are saved from the random subtractions.

We save a database that we will call "B"
where only the bits obtained are saved.

We scan

64 -bit collision margin

If there is match
We identify the pub found counting the bits in the DB using the % 1024  to calculate the PK found (because each operation is different and 1024 was the number of sequential keys for each pub).

We would basically have 1 million mini dB of 1024 keys stored in 1 1000000*1024 bits database.
With the difference that they would not be in sequences and could cover the target range randomly. .

Then that match (pub) we will find in database "A" and add to the RANDOM NUMBER to obtain pk from the main target

Did you ever tinker or mess with your multi-pub binary and search scripts?
That would work as well.
Generate pubs and offsets (random number subtracted by of original pubkey) and save in a file and load the new gen pubs in another and run the multi pub script against the pub only file.

added binary version.

Thank you very much, Mister ;!)

[sssergy2705]

The first version of the script worked, the second does not find matches.
There may be an error in the code.

On my PC, 100 keys found out of 100, ....  

Did you set the same parameters in both scripts?

About an hour and a half ago, I copied both scripts, created a database and launched the search script. I didn't change anything in the parameters.

Ah, I uploaded a version of create_database that doesn't match with that version of the search_pk script

Now it should work:

To perform multiple search, for linux:

time for i in {1..100}; do python3 search_pk_arulbero.py; done

Code:

This is the public key: f5c03157f4a489ed71c0df0f37799431b3f432654a9bd6efdbb79ba767b62e81
I need to find this private key: 821480591424854

Private key found!!!
Collision!
258530638003543
604085cce892dbb8bf9e70959ef178bc78fb123caaa4e9b1f3521139542da57f

For example, I got a collision, how to calculate the private key?

[arulbero]

Code:

This is the public key: f5c03157f4a489ed71c0df0f37799431b3f432654a9bd6efdbb79ba767b62e81
I need to find this private key: 821480591424854

Private key found!!!
Collision!
258530638003543
604085cce892dbb8bf9e70959ef178bc78fb123caaa4e9b1f3521139542da57f

For example, I got a collision, how to calculate the private key?

The key 821480591424854 is in the range 2^49 - 2^50

Try with these parameters:

Code:

start_key = 1
num_public_keys = 2**50 
bits_to_store = 64
bytes_to_store = bits_to_store//8
rate_of_key_to_generate = 2**24

Did you use bits_to_store = 64? And the other parameters?

[arulbero]

Ah, I uploaded a version of create_database that doesn't match with that version of the search_pk script
Now it should work:

It works for me up to 0x81 and after that it does not seem to find any keys.
I tried deleting and recreating the database from 0x80 but still nothing found.

0x80 = 128

What are you parameters?

Like these?

Code:

start_key = 1
num_public_keys = 2**32
bits_to_store = 64
bytes_to_store = bits_to_store//8
rate_of_key_to_generate = 2**20

[sssergy2705]

Code:

This is the public key: f5c03157f4a489ed71c0df0f37799431b3f432654a9bd6efdbb79ba767b62e81
I need to find this private key: 821480591424854

Private key found!!!
Collision!
258530638003543
604085cce892dbb8bf9e70959ef178bc78fb123caaa4e9b1f3521139542da57f

For example, I got a collision, how to calculate the private key?

The key 821480591424854 is in the range 2^49 - 2^50

Try with these parameters:

Code:

start_key = 1
num_public_keys = 2**50 
bits_to_store = 64
bytes_to_store = bits_to_store//8
rate_of_key_to_generate = 2**24

Did you use bits_to_store = 64? And the other parameters?

Code:

start_key = 2**49
num_public_keys = 2**50
bits_to_store = 64
bytes_to_store = bits_to_store//8
rate_of_key_to_generate = 2**20

In general, I already figured it out, the difference is 2**49).

By the way, how to calculate this parameter? Calculate the golden mean.
When you set it above 2**26, the search script eats up all the RAM.
If you decrease it, the size of the database increases.
rate_of_key_to_generate = 2**20

[arulbero]

Code:

start_key = 2**49
num_public_keys = 2**50
bits_to_store = 64
bytes_to_store = bits_to_store//8
rate_of_key_to_generate = 2**20

Actually, I already figured it out, the difference is just 2**49)

2**49 / 2**20 = 2**29 keys stored in DB.   2**20 keys generated in search script against 2**29 keys generated in create_database script  = 2**49 couples.

I presume that the probability of collision is not low with these numbers.

The script is not optimized, it is only a proof of concept. It needs some work.  

Try with bits_to_store = 96, in this way the probability of collision is lower.

[whanau]

0x80 = 128

What are you parameters?

Like these?

Code:

start_key = 1
num_public_keys = 2**32
bits_to_store = 64
bytes_to_store = bits_to_store//8
rate_of_key_to_generate = 2**20

No I had 128 as per your original script instead of 2**20. I think I am not understanding how all these variables interact or  when to change them.

I changed to 2**20 and  0x82 (130) works.
I will study some more. Thank you 

[Kpot87]

Code:

start_key = 2**49
num_public_keys = 2**50
bits_to_store = 64
bytes_to_store = bits_to_store//8
rate_of_key_to_generate = 2**20

Actually, I already figured it out, the difference is just 2**49)

2**49 / 2**20 = 2**29 keys stored in DB.   2**20 keys generated in search script against 2**29 keys generated in create_database script  = 2**49 couples.

I presume that the probability of collision is not low with these numbers.

The script is not optimized, it is only a proof of concept. It needs some work.  

Try with bits_to_store = 96, in this way the probability of collision is lower.

Ok but how you image to work with bigger size of range, the nearest 2**130…? How much ram do you need to generate such equation ?

[arulbero]

Ok but how you image to work with bigger size of range, the nearest 2**130…? How much ram do you need to generate such equation ?

I don't image to work with bigger size of range.
At this level the problem in my opinion is to shrink the size of database. That's all.

To "cover" a 2**130 space, you need 2**65 keys with distance 2**65.

2**65 keys with 128 bits (at least) for each key means 2**73 bit = 2**70 bytes,  1 Billions of TB.

If you use the script of the OP,  2**65 keys = 2**65 bits = 2**62 bytes = 4 Millions of TB.

These are the numbers.

These script are made for fun, not to become rich.

[Kpot87]

Ok but how you image to work with bigger size of range, the nearest 2**130…? How much ram do you need to generate such equation ?

I don't image to work with bigger size of range.
At this level the problem in my opinion is to shrink the size of database. That's all.

To "cover" a 2**130 space, you need 2**65 keys with distance 2**65.

2**65 keys with 128 bits (at least) for each key means 2**73 bit = 2**70 bytes,  1 Billions of TB.

If you use the script of the OP,  2**65 keys = 2**65 bits = 2**62 bytes = 4 Millions of TB.

These are the numbers.

These script are made for fun, not to become rich.

Nobody talk about to be reach, the question is like you told to shrink DB. But on big intervals … that’s all

[mcdouglasx]

Ok but how you image to work with bigger size of range, the nearest 2**130…? How much ram do you need to generate such equation ?

I don't image to work with bigger size of range.
At this level the problem in my opinion is to shrink the size of database. That's all.

To "cover" a 2**130 space, you need 2**65 keys with distance 2**65.

2**65 keys with 128 bits (at least) for each key means 2**73 bit = 2**70 bytes,  1 Billions of TB.

If you use the script of the OP,  2**65 keys = 2**65 bits = 2**62 bytes = 4 Millions of TB.

These are the numbers.

These script are made for fun, not to become rich.

Although your numbers are correct, you forget about statistics and probabilities.

because when you involve chance, the larger your sample, the larger your probabilities are, so when you sacrifice your sample size for speed, it can serve you well in small ranges but in high ranges the number of probable objects you can hit is always better.

An example in the real world is rain, if the speed at which the water fell to the ground was double, it would wet less space on the earth, the drops would be larger.
The fewer raindrops = the greater the proportion of dry soil.

It's just the big problem with bsgs.

[COBRAS]

From start to finish. But it's not the speed, it's the size of the DB, only 121kb
Well I mean the speed is good for a single core. DB creation and search for the key and find it in under 9 seconds, 100% of the time.

I modified slightly the OP's 'create_database' script (1 bit for key, 128 kB), now it is a bit faster

I tried with the search script too, but it is still slow (using bits, not bytes)

Results:

Code:

Making Binary Data-Base
Keys generated: 1048576
Space covered by the keys spread with distance 16 in the database : 16777216

real	0m1,548s
user	0m1,548s
sys	0m0,000s

create_database.py

Code:

#@mcdouglasx modified by arulbero
import secp256k1 as ice
import bitcoin
import random
from bitstring import BitArray


print("Making Binary Data-Base")


#pk = 25 498 121 788 = 0x5efce763c   between 2**34 and 2**35, between 16 billions and 32 billions
target_public_key = "029016f6bb53c86cbb410462bb01abdc258f5b9fb1e5528f19bc383685e1874391"
target = ice.pub2upub(target_public_key)

numb = 2**20 # 1 million of keys.
sustract= 2**4 #amount to subtract each time, If you modify this, use the same amount to scan.
space_covered = numb*sustract  #2**24 = 16 millions, space covered from the database
print("Keys generated: " + str(numb))
print("Space covered by the keys spread with distance " +  str(sustract) + " in the database : " + str(space_covered)) 

Low_m= 2**6
lm= numb // Low_m
sustract_pub= ice.scalar_multiplication(sustract)


res= ice.point_loop_subtraction(lm, target, sustract_pub)
my_str= BitArray(res[t*65+64]%2 for t in range(lm))  #0 if even, 1 if odd
       
with open('data-base.bin', 'wb') as binary_file:
   my_str.tofile(binary_file)        


for i in range (1,Low_m):
    lm_upub=ice.scalar_multiplication((lm*i)*sustract)

    A1= ice.point_subtraction(target, lm_upub)

    res=ice.point_loop_subtraction(lm, A1, sustract_pub)
    my_str= BitArray(res[t*65+64]%2 for t in range(lm))  #0 if even, 1 if odd

    with open('data-base.bin', 'ab') as binary_file:
        my_str.tofile(binary_file)

Can you provide your BSGS scrypt ?

[Kpot87]

@macduglasx hi, how you provide working with mulpubs, about ram it’s clear and what about threads ? 1pub=1th? Tnx

[arulbero]

I modified slightly the OP's 'create_database' script (1 bit for key, 128 kB, distance between 2 keys = 1)

it takes about 111 minutes (less than 2 hours) to generate 2**32 keys (4 billions), size of the DB = 512 MB

The script search takes less than 1 second to retrieve a key in this space.

create_database.py

Code:

#@mcdouglasx modified by arulbero
import secp256k1 as ice
from bitstring import BitArray


#########################DATABASE PARAMETERS#########################
prefix = '32_0'
data_base_name = 'data-base'+prefix+'.bin'

num_public_keys = 2**32 # 4 billions of keys
num_bytes_db = num_public_keys//8 # 1 bit for each key
sustract= 2**0 #amount to subtract each time, If you modify this, use the same amount to scan.
sustract_pub= ice.scalar_multiplication(sustract)
space_covered = num_public_keys*sustract  #2**32 = 4 billions, space covered


#pk = 32 294 923 307 823 = 0x1d5f3f6e8b2f between 2**44 and 2**45
target_public_key = "03f760d768600e639758836fda5da546c10b1d84886165a5a1a4586192518aaf77"
target = ice.pub2upub(target_public_key)


Low_m= 2**8  #to save ram
lm= num_public_keys // Low_m
###################################################################

print("Making Binary Data-Base")
print()

res= ice.point_loop_subtraction(lm, target, sustract_pub)
my_str= BitArray(res[t*65+64]%2 for t in range(lm)) #0 if even, 1 if odd     

with open(data_base_name, 'wb') as binary_file:
    my_str.tofile(binary_file)      


for i in range (1,Low_m):
    lm_upub=ice.scalar_multiplication((lm*i)*sustract)

    A1= ice.point_subtraction(target, lm_upub)

    res=ice.point_loop_subtraction(lm, A1, sustract_pub)
    my_str=BitArray(res[t*65+64]%2 for t in range(lm))

    with open(data_base_name, 'ab') as binary_file:
        my_str.tofile(binary_file)

print("Keys generated: " + str(num_public_keys))
print("Space covered by the keys spread with distance " +  str(sustract) + " in the database : " + str(space_covered)) 

search_pk.py

Code:

#@mcdouglasx modified by arulbero
import secp256k1 as ice
from bitstring import BitArray
import random
import sys


#########################DATABASE PARAMETERS#########################
prefix = '32_0'
data_base_name = 'data-base'+prefix+'.bin'

num_public_keys = 2**32 # 4 billions of keys
num_bytes_db = num_public_keys//8 # 1 bit for each key
sustract= 2**0 #amount to subtract each time, If you modify this, use the same amount to scan.
sustract_pub= ice.scalar_multiplication(sustract)
space_covered = num_public_keys*sustract  #2**32 = 4 billions, space covered


#pk = 32 294 923 307 823 = 0x1d5f3f6e8b2f between 2**44 and 2**45
target_public_key = "03f760d768600e639758836fda5da546c10b1d84886165a5a1a4586192518aaf77"
target = ice.pub2upub(target_public_key)
###################################################################

########################SEARCH PARAMATERS##########################
num = 1024+1024# collision margin in bits
total_search_keys_to_generate = sustract
split_total_keys = 1 #> 1 only if sustract > 1
multiple_search_keys_at_once = total_search_keys_to_generate//split_total_keys
bytes_for_key = num//8

split_database = 2**9 #read only a fraction of the database to speedup the finding of the string and save RAM
size_partial_db = num_bytes_db//split_database

pk_orig = 32294923307823
#pk = 32 294 923 307 823 = 0x1d5f3f6e8b2f between 2**44 and 2**45 
space_search_start =  pk_orig  - space_covered  #I'm assuming that the space search contains for sure the pk 
space_search_end   =  pk_orig  + space_covered   
                   

#####################################################################
print("Keys generated in DB: " + str(num_public_keys))
print("Space covered by the keys in DB (the keys are distributed in this space with distance " + str(sustract) + ") : " + str(space_covered)) 
print()
print("This is the public key: " + target_public_key[2:])
print("I need to find this private key: " + str(pk_orig))
print()
print("Scanning Binary Sequence")       
print("Looking in the range: "+str(space_search_start)+" " +str(space_search_end))
print()


while True:
     
    #pk0=random.randint(space_search_start, space_search_end)
    for t in range(split_total_keys):
        
        pk0=random.randint(space_search_start, space_search_end)
        b=BitArray()
        
        for r in range(multiple_search_keys_at_once): #how many different consecutive keys are generated at once against the keys in DB


            target2 = ice.scalar_multiplication(pk0-t*multiple_search_keys_at_once-r)
            res=ice.point_loop_subtraction(2*num, target2, sustract_pub)   
            b = b + (res[t*65+64]%2 for t in range(2*num))  #0 if even, 1 if odd 
            #2*num -> means we utilize double size of collision margin for each key, in this way we can shift and obtain num windows of num bits 
            
        b2 = ()
        for r in range(multiple_search_keys_at_once):
            for j in range(num):
                b2 = b2 + b[(r*2*num)+j:(r*2*num)+j+num]  #64 strings of 64 bits
        b3 = bytes(b2) 
        b2_i = [ b3[j*bytes_for_key:j*bytes_for_key+bytes_for_key] for j in range(len(b3)//bytes_for_key)]
        set_search_keys = set(b2_i)
  
        with open(data_base_name, 'r+b') as f: 
            for k in range(split_database):
	    
                f.seek(0,1)
                partial_db = f.read(size_partial_db)
                
                dat_i = [partial_db[j*bytes_for_key:j*bytes_for_key+bytes_for_key] for j in range(size_partial_db//bytes_for_key)]
                set_database = set(dat_i) 
                        
                a = list(set_database & set_search_keys)

                if(len(a) > 0): 
                    s = b2_i
                    f = dat_i
                    inx = f.index(a[0])
                    r_ind = s.index(a[0])
                    Pk = (pk0 - r_ind//num - (r_ind%num)*sustract - t*multiple_search_keys_at_once) + (k*size_partial_db*8 +(inx*num))*sustract    
                    print("Found!")
                    if(Pk == pk_orig):
                        print("The private key " + str(Pk)+ " was recovered successfully!")
                    data = open("win.txt","a")
                    data.write("Pk:"+" "+str(Pk)+"\n")
                    data.close()
                    sys.exit()  

[COBRAS]

I modified slightly the OP's 'create_database' script (1 bit for key, 128 kB, distance between 2 keys = 1)

it takes about 111 minutes (less than 2 hours) to generate 2**32 keys (4 billions), size of the DB = 512 MB

The script search takes less than 1 second to retrieve a key in this space.

create_database.py

Code:

#@mcdouglasx modified by arulbero
import secp256k1 as ice
from bitstring import BitArray


#########################DATABASE PARAMETERS#########################
prefix = '28_0'
data_base_name = 'data-base'+prefix+'.bin'

num_public_keys = 2**28 # 4 billions of keys
num_bytes_db = num_public_keys//8 # 1 bit for each key
sustract= 2**0 #amount to subtract each time, If you modify this, use the same amount to scan.
sustract_pub= ice.scalar_multiplication(sustract)
space_covered = num_public_keys*sustract  #2**32 = 4 billions, space covered


#pk = 32 294 923 307 823 = 0x1d5f3f6e8b2f between 2**44 and 2**45
target_public_key = "03f760d768600e639758836fda5da546c10b1d84886165a5a1a4586192518aaf77"
target = ice.pub2upub(target_public_key)


Low_m= 2**8  #to save ram
lm= num_public_keys // Low_m
###################################################################

print("Making Binary Data-Base")
print()

res= ice.point_loop_subtraction(lm, target, sustract_pub)
my_str= BitArray(res[t*65+64]%2 for t in range(lm)) #0 if even, 1 if odd     

with open(data_base_name, 'ab') as binary_file:
        my_str.tofile(binary_file)      


for i in range (1,Low_m):
    lm_upub=ice.scalar_multiplication((lm*i)*sustract)

    A1= ice.point_subtraction(target, lm_upub)

    res=ice.point_loop_subtraction(lm, A1, sustract_pub)
    my_str=BitArray(res[t*65+64]%2 for t in range(lm))

    with open(data_base_name, 'ab') as binary_file:
        my_str.tofile(binary_file)

print("Keys generated: " + str(num_public_keys))
print("Space covered by the keys spread with distance " +  str(sustract) + " in the database : " + str(space_covered)) 

search_pk.py

Code:

#@mcdouglasx modified by arulbero
import secp256k1 as ice
from bitstring import BitArray
import random
import sys


#########################DATABASE PARAMETERS#########################
prefix = '32_0'
data_base_name = 'data-base'+prefix+'.bin'

num_public_keys = 2**32 # 4 billions of keys
num_bytes_db = num_public_keys//8 # 1 bit for each key
sustract= 2**0 #amount to subtract each time, If you modify this, use the same amount to scan.
sustract_pub= ice.scalar_multiplication(sustract)
space_covered = num_public_keys*sustract  #2**32 = 4 billions, space covered


#pk = 32 294 923 307 823 = 0x1d5f3f6e8b2f between 2**44 and 2**45
target_public_key = "03f760d768600e639758836fda5da546c10b1d84886165a5a1a4586192518aaf77"
target = ice.pub2upub(target_public_key)
###################################################################

########################SEARCH PARAMATERS##########################
num = 1024+512# collision margin in bits
total_search_keys_to_generate = sustract
split_total_keys = 2**0 #> 1 only if sustract > 1
multiple_search_keys_at_once = total_search_keys_to_generate//split_total_keys
bytes_for_key = num//8

split_database = 2**3 #read only a fraction of the database to speedup the finding of the string and save RAM
size_partial_db = num_bytes_db//split_database

pk_orig = 32294923307823
#pk = 32 294 923 307 823 = 0x1d5f3f6e8b2f between 2**44 and 2**45 
space_search_start =  pk_orig  - space_covered  #I'm assuming that all the space search is covered by keys in DB, 
space_search_end   =  pk_orig                   #otherwise we have to generate more than 'total_search_keys_to_generate = sustract' search_keys
                   

#####################################################################
print("Keys generated in DB: " + str(num_public_keys))
print("Space covered by the keys in DB (the keys are distributed in this space with distance " + str(sustract) + ") : " + str(space_covered)) 
print()
print("This is the public key: " + target_public_key[2:])
print("I need to find this private key: " + str(pk_orig))
print()
print("Scanning Binary Sequence")       
print("Looking in the range: "+str(space_search_start)+" " +str(space_search_end))
print()


while True:
     
   
    for t in range(split_total_keys):
        
        pk0=random.randint(space_search_start, space_search_end)
        b=BitArray()
        
        for r in range(multiple_search_keys_at_once): #how many different consecutive keys are generated at once against the keys in DB


            target2 = ice.scalar_multiplication(pk0-t*multiple_search_keys_at_once-r)
            res=ice.point_loop_subtraction(2*num, target2, sustract_pub)   
            b = b + (res[t*65+64]%2 for t in range(2*num))  #0 if even, 1 if odd 
            #2*num -> means we utilize double size of collision margin for each key, in this way we can shift and obtain num windows of num bits 
            
        b2 = ()
        for r in range(multiple_search_keys_at_once):
            for j in range(num):
                b2 = b2 + b[(r*2*num)+j:(r*2*num)+j+num]  #64 strings of 64 bits
        b3 = bytes(b2) 
        b2_i = [ b3[j*bytes_for_key:j*bytes_for_key+bytes_for_key] for j in range(len(b3)//bytes_for_key)]
        set_search_keys = set(b2_i)
  
        with open(data_base_name, 'r+b') as f: 
            for k in range(split_database):
	    
                f.seek(0,1)
                partial_db = f.read(size_partial_db)
                
                dat_i = [partial_db[j*bytes_for_key:j*bytes_for_key+bytes_for_key] for j in range(size_partial_db//bytes_for_key)]
                set_database = set(dat_i) 
                        
                a = list(set_database & set_search_keys)

                if(len(a) > 0): 
                    s = b2_i
                    f = dat_i
                    inx = f.index(a[0])
                    r_ind = s.index(a[0])
                    Pk = (pk0 - r_ind//num - (r_ind%num)*sustract - t*multiple_search_keys_at_once) + (k*size_partial_db*8 +(inx*num))*sustract    
                    print("Found!")
                    if(Pk == pk_orig):
                        print("The private key " + str(Pk)+ " was recovered successfully!")
                    data = open("win.txt","a")
                    data.write("Pk:"+" "+str(Pk)+"\n")
                    data.close()
                    sys.exit()  

Good day, what about 2^65 range, posible or not ?