Pollard's kangaroo ECDLP solver

[Etar]

If pubkey appear "under zero" after shifting it is not a matter you any way will found key.

Don`t use this method yet.
For test range is 80000000000000000000:ffffffffffffffffffff
I generate random key very close to begin range.
0x9000000f000000300001
without shifting key was found. with shifting - no. I don`t understand why..

[1714986011]

1714986011

[1714986011]

1714986011

[1714986011]

1714986011

[1714986011]

1714986011

[WanderingPhilospher]

If pubkey appear "under zero" after shifting it is not a matter you any way will found key.

Don`t use this method yet.
For test range is 80000000000000000000:ffffffffffffffffffff
I generate random key very close to begin range.
0x9000000f000000300001
without shifting key was found. with shifting - no. I don`t understand why..

I don't understand how it's helpful since you must know the private key in advance. Example, for puzzle 115, you have to know it's private key before shifting it down, but if you already have the private key, why shift down?

[Etar]

how are you subtracting 80000.... from 037e.... and getting 033aeb....
edit: I guess you meant 80000...from the priv key

037e....  - 80000....*G = 033aeb....
(7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc,625c7118f1c29cb92d28ce0dfd0dc58144fe5572effebc7fee54c4fce3333a6b)
-
(769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be,4bf817362fe783bac8dce4cef73f5d4741a177767b7873add5920bffb0d9685f)
=
3aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256de f6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9

[WanderingPhilospher]

how are you subtracting 80000.... from 037e.... and getting 033aeb....
edit: I guess you meant 80000...from the priv key

037e....  - 80000....*G = 033aeb....
(7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc,625c7118f1c29cb92d28ce0dfd0dc58144fe5572effebc7fee54c4fce3333a6b)
-
(769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be,4bf817362fe783bac8dce4cef73f5d4741a177767b7873add5920bffb0d9685f)
=
3aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256de f6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9

Sorry, I'm still not tracking. Where is *G in the above?

[sssergy2705]

how are you subtracting 80000.... from 037e.... and getting 033aeb....
edit: I guess you meant 80000...from the priv key

037e....  - 80000....*G = 033aeb....
(7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc,625c7118f1c29cb92d28ce0dfd0dc58144fe5572effebc7fee54c4fce3333a6b)
-
(769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be,4bf817362fe783bac8dce4cef73f5d4741a177767b7873add5920bffb0d9685f)
=
3aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256de f6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9

What tool do you use to subtract coordinates? Share the code please.

[sssergy2705]

how are you subtracting 80000.... from 037e.... and getting 033aeb....
edit: I guess you meant 80000...from the priv key

037e....  - 80000....*G = 033aeb....
(7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc,625c7118f1c29cb92d28ce0dfd0dc58144fe5572effebc7fee54c4fce3333a6b)
-
(769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be,4bf817362fe783bac8dce4cef73f5d4741a177767b7873add5920bffb0d9685f)
=
3aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256de f6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9

Sorry, I'm still not tracking. Where is *G in the above?

037e....  - (80000....*G) = 033aeb....

[WanderingPhilospher]

how are you subtracting 80000.... from 037e.... and getting 033aeb....
edit: I guess you meant 80000...from the priv key

037e....  - 80000....*G = 033aeb....
(7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc,65c7118f1c29cb92d28ce0dfd0dc58144fe5572effebc7fee54c4fce3333a6b2)
-
(769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be,4bf817362fe783bac8dce4cef73f5d4741a177767b7873add5920bffb0d9685f)
=
3aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256de f6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9

Sorry, I'm still not tracking. Where is *G in the above?

037e....  - (80000....*G) = 033aeb....

what are these?

[mrxtraf]

-snip-
interesting solution, but it won’t work if only public keys are known, let's say there is a public key theoretically with private key 1, how to divide the public key by 10 to get public key with 0.1 without knowing the private keys?

i think that not all points have private key, maybe i am wrong
For example simple 7/5 it is (3ef1f322847965ee7f8d745af562e6507568fea5316b199f7349a2717021661d,b9a20bc3783777d2681f64d92740817f95b2c169c5db92ce0bab00efb36c0d74)
i don`t know if this result have private key.. (n+7)/5 give the same result as for ex. (n+3)/5 = 0x33333333333333333333333333333332f222f8faefdb533f265d461c29a47374
but 0x33333333333333333333333333333332f222f8faefdb533f265d461c29a47374 for (n+3)/5 is correct.
becouse if 1 have the same x-coordinate as n-1 so there only 2^255 points with unique x-coordinate. So there can be around 2^255 points that not have private key.(maybe  )

Mathematical working according to the rules of mathematics of public keys (addition, subtraction, division, multiplication), you will always get the coordinates (public key) at the output, which will have the corresponding private key.

Another thing is that one public key can have several private keys. But this collision has not yet been proven.

[brainless]

how are you subtracting 80000.... from 037e.... and getting 033aeb....
edit: I guess you meant 80000...from the priv key

037e....  - 80000....*G = 033aeb....
(7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc,65c7118f1c29cb92d28ce0dfd0dc58144fe5572effebc7fee54c4fce3333a6b2)
-
(769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be,4bf817362fe783bac8dce4cef73f5d4741a177767b7873add5920bffb0d9685f)
=
3aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256de f6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9

Sorry, I'm still not tracking. Where is *G in the above?

037e....  - (80000....*G) = 033aeb....

what are these?

hex: 80000000000000000000
dec: 604462909807314587353088
pubkey: 03769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be

[mrxtraf]

interesting solution, but it won’t work if only public keys are known, let's say there is a public key theoretically with private key 1, how to divide the public key by 10 to get public key with 0.1 without knowing the private keys?

You can't.

Let P be a public key with unknown private key k (that means P = k*G)
 
By definition, you can get a public key Q such that 10*Q = P in this way:

Q = inv(10)*P = inv(10)*k*G

that's all you can have (if you don't know k, you don't know inv(10)*k neither)

But it’s really possible to divide any public key into 10 without knowing the private one. But to divide by 3, 6, 7, 9, 14 .... is already more difficult.

[brainless]

how are you subtracting 80000.... from 037e.... and getting 033aeb....
edit: I guess you meant 80000...from the priv key

037e....  - 80000....*G = 033aeb....
(7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc,65c7118f1c29cb92d28ce0dfd0dc58144fe5572effebc7fee54c4fce3333a6b2)
-
(769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be,4bf817362fe783bac8dce4cef73f5d4741a177767b7873add5920bffb0d9685f)
=
3aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256de f6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9

Sorry, I'm still not tracking. Where is *G in the above?

037e....  - (80000....*G) = 033aeb....

what are these?

hex: 80000000000000000000
dec: 604462909807314587353088
pubkey: 03769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be

let me clear you more
if pubkey in 80 bit, he is doing minus 79bit, and thinking next key will be in 79 bit, but its not exact, its probability
next could be in 79 bit, or 78 bit, depand on 80 bit key location, which you all dont know, location mean 80bit start, middle, or in near last area of under 80 bit, you love to play try it again and again
btw staudy my 8 month old post and 
my exact down bit proof here
https://bitcointalk.org/index.php?topic=5244940.msg54531996#msg54531996

[WanderingPhilospher]

how are you subtracting 80000.... from 037e.... and getting 033aeb....
edit: I guess you meant 80000...from the priv key

037e....  - 80000....*G = 033aeb....
(7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc,65c7118f1c29cb92d28ce0dfd0dc58144fe5572effebc7fee54c4fce3333a6b2)
-
(769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be,4bf817362fe783bac8dce4cef73f5d4741a177767b7873add5920bffb0d9685f)
=
3aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256de f6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9

Sorry, I'm still not tracking. Where is *G in the above?

037e....  - (80000....*G) = 033aeb....

what are these?

hex: 80000000000000000000
dec: 604462909807314587353088
pubkey: 03769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be

let me clear you more
if pubkey in 80 bit, he is doing minus 79bit, and thinking next key will be in 79 bit, but its not exact, its probability
next could be in 79 bit, or 78 bit, depand on 80 bit key location, which you all dont know, location mean 80bit start, middle, or in near last area of under 80 bit, you love to play try it again and again
btw staudy my 8 month old post and 
my exact down bit proof here
https://bitcointalk.org/index.php?topic=5244940.msg54531996#msg54531996

just trying to understand the math a little better.
pub - start range * G(generator point) = new pub key
in his first example
(pub)7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc - (start range) 80000000000000000000 * G = (pub) 3aeb....

[brainless]

how are you subtracting 80000.... from 037e.... and getting 033aeb....
edit: I guess you meant 80000...from the priv key

037e....  - 80000....*G = 033aeb....
(7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc,65c7118f1c29cb92d28ce0dfd0dc58144fe5572effebc7fee54c4fce3333a6b2)
-
(769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be,4bf817362fe783bac8dce4cef73f5d4741a177767b7873add5920bffb0d9685f)
=
3aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256de f6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9

Sorry, I'm still not tracking. Where is *G in the above?

037e....  - (80000....*G) = 033aeb....

what are these?

hex: 80000000000000000000
dec: 604462909807314587353088
pubkey: 03769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be

let me clear you more
if pubkey in 80 bit, he is doing minus 79bit, and thinking next key will be in 79 bit, but its not exact, its probability
next could be in 79 bit, or 78 bit, depand on 80 bit key location, which you all dont know, location mean 80bit start, middle, or in near last area of under 80 bit, you love to play try it again and again
btw staudy my 8 month old post and 
my exact down bit proof here
https://bitcointalk.org/index.php?topic=5244940.msg54531996#msg54531996

just trying to understand the math a little better.
pub - start range * G(generator point) = new pub key
in his first example
(pub)7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc - (start range) 80000000000000000000 * G = (pub) 3aeb....

real: (pub)  7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc
G = 1 or in point pubkey is 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
hex 80000000000000000000 = pub 03769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be

now play in 2 forms
Real - G(pub)*hex =
Real - hex(pub) =
point to point minus
clear ??

[sssergy2705]

how are you subtracting 80000.... from 037e.... and getting 033aeb....
edit: I guess you meant 80000...from the priv key

037e....  - 80000....*G = 033aeb....
(7e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc,65c7118f1c29cb92d28ce0dfd0dc58144fe5572effebc7fee54c4fce3333a6b2)
-
(769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be,4bf817362fe783bac8dce4cef73f5d4741a177767b7873add5920bffb0d9685f)
=
3aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256de f6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9

Sorry, I'm still not tracking. Where is *G in the above?

037e....  - (80000....*G) = 033aeb....

what are these?

pubkey compressed     03769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be
pubkey uncompressed 04769bc75842bff58edc8366ecd78f8950ee4ab2e81359d90f9921fa3d2c4561be65c7118f1c29cb92d28ce0dfd0dc58144fe5572effebc7fee54c4fce3333a6b2

[PrivatePerson]

Please explain what is DP?

[COBRAS]

Please explain what is DP?

This is like the lucky. You can choose more or less.But every day you because of the no lack of results you will begin to understand that this is something like a game that can only be played by its developer mostly and no one else. You don't know what parameters to use... you can try with a big bet like Zelar or use the free spins provided by the test servers. I think all members of this branch are 60% gamblers. Welcome to roulette.

[arulbero]

interesting solution, but it won’t work if only public keys are known, let's say there is a public key theoretically with private key 1, how to divide the public key by 10 to get public key with 0.1 without knowing the private keys?

You can't.

Let P be a public key with unknown private key k (that means P = k*G)
 
By definition, you can get a public key Q such that 10*Q = P in this way:

Q = inv(10)*P = inv(10)*k*G

that's all you can have (if you don't know k, you don't know inv(10)*k neither)

But it’s really possible to divide any public key into 10 without knowing the private one. But to divide by 3, 6, 7, 9, 14 .... is already more difficult.

It is the same thing. Inv(10) or inv(3), where is the difference?

[arulbero]

For a change, this is current progress

To recap (and to return in topic):

#115 -> 114 bit

steps needed to have 50% chance of a collision: about (114/2)+1 = 58 bit -> 2^58

DP = 25

steps performed: 2**25 * 2**33.14 = 2**58.14, then you are close to the result?

[Etar]

Here is shematic why shifting should work.




In example above(few post ago) pub key after shifting was under "zero" and key was found.
I don`t understant why solution not find when pubkey is close to begin of range..
Any DP no matter "positive" or "negative" have the same X-coordinate, so collission should be any way..
If for ex. Wild DP -40 and Tame DP is 40 so there must be collision.

[COBRAS]

Here is shematic why shifting should work.




In example above(few post ago) pub key after shifting was under "zero" and key was found.
I don`t understant why solution not find when pubkey is close to begin of range..
Any DP no matter "positive" or "negative" have the same X-coordinate, so collission should be any way..

Please, someone make a scrypt for automatic shifting pubkey to "zero" ? I was try many times and not found any keys I think because of this. Manualy shift all pubkeys to "zero" is f**ing work, trust me please.

p.s. Jean_Luc insert in you code not shutdoun then something happen in yours kangaroo or BSGS, but power on "PAUSE" because of no pause I was 2 times lost result of 2-5 day's work.

Why we not deducted from pubkey (fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 - OUR RANGE) ? but OUR RANGE ONLY ?