Pollard's kangaroo ECDLP solver - page 38.

WanderingPhilospher

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Shooters Shoot...

Quote from: dextronomous on September 07, 2021, 06:49:12 PM

wich publickey's private key you need, what range.?
@DESKTOP-EAVG3O8:/mnt/d/bsgs-development$ python3.9 bsgs_hybrid_dll_secp256k1.py -n 20000000000000000 -pfile puzzle_pubs.txt -b bPfile.bin -bl bloomfile.bin -keyspace 800000000000000000000000000000:FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF -rand

Starting Program : BSGS mode with hybrid algo using bloom dll and secp256k1 dll Version [ 13072021 ]
Loading 75 Public Keys to search
Search Mode: Random Start after every n sequential key search
Reading bloom filter from file complete in : 350.20511 sec
Reading Baby table from file complete in : 0.13070 sec
seq value: 20000000000000000 m value : 20000000000
Search Range: 0x1 to 0xffffffffffffffffffffffffffffffff
k1: 0x38b63a35d47e0ca8b7dd83abeb1c3177
PVK not found. 20000.00000 Trillion scanned in 12.01 sec. New range
k1: 0xca5da4b0e249fc9673b61fa0576ca7a1

and right now the terakeys is doing 2200 tera /s Kang 23552 / Elapsed 20 sec. /ram 24.6MB / 45.7MB

Again, key/s is all in how the coder, coded their program.
Long discussion, especially concerning BSGS.

Jean Luc's version, if this program counts like the other BSGS program did, would be considered to get 14.6 PKey/s...that is 14,600 TKey/s. People get caught up with dazzling numbers without running the same exact tests to compare such claims, or speeds of programs. I don't know about this program as I have not used it but again, a similiar discussion already exists and at the end of the day, JLPs version was faster and when comparing times and speeds of what was going on under the hood, if JLP wanted to, he could have changed the speed read out to 14.6 Petakeys/s.
https://bitcointalksearch.org/topic/m.54243367 Read from the 1st post if need be.

dextronomous

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wich publickey's private key you need, what range.?
@DESKTOP-EAVG3O8:/mnt/d/bsgs-development$ python3.9 bsgs_hybrid_dll_secp256k1.py -n 20000000000000000 -pfile puzzle_pubs.txt -b bPfile.bin -bl bloomfile.bin -keyspace 800000000000000000000000000000:FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF -rand

Starting Program : BSGS mode with hybrid algo using bloom dll and secp256k1 dll Version [ 13072021 ]
Loading 75 Public Keys to search
Search Mode: Random Start after every n sequential key search
Reading bloom filter from file complete in : 350.20511 sec
Reading Baby table from file complete in : 0.13070 sec
seq value: 20000000000000000 m value : 20000000000
Search Range: 0x800000000000000000000000000000 to 0xffffffffffffffffffffffffffffffff
k1: 0x38b63a35d47e0ca8b7dd83abeb1c3177
PVK not found. 20000.00000 Trillion scanned in 12.01 sec. New range
k1: 0xca5da4b0e249fc9673b61fa0576ca7a1

and right now the terakeys is doing 2200 tera /s Kang 23552 / Elapsed 20 sec. /ram 24.6MB / 45.7MB

COBRAS

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Quote from: WanderingPhilospher on September 07, 2021, 05:26:26 PM

Quote from: a.a on September 07, 2021, 03:51:03 PM

I think WP is just trolling. As I said, there is no way to calculate that much despite having an empty loop.

I was trying out a new KangaGSDPQuadro...Kangaroo that mimics baby steps, then running giant steps through those while setting a DP...but I do not think it works as designed. I found the private key to Cobra's pubkey several times but it did not match #120s address: 17s2b9ksz5y7abUm92cHwG8jEPCzK3dLnT

But I will reengineer from scratch.

Yes !! Ofcause !!!! You cant use finded privkey directly, you need send me this privkey, I will make from what you give me, PRIVATE KEY FOR 17s2b9ksz5y7abUm92cHwG8jEPCzK3dLnT !!! WP, PROVIDE KEYS, AND LETS GO SHARE 1.2 BTC !!!! ?? DO NOT GO CRASY PLEASY WP Grin

If you realy find privkey, you find PART of privkey WP!!! Part of privkey is absolutely normal and your software if is find a privkey, possibly works absolutely fine. But you not need try making from this privkey adress of 120 puzle, this is need mach more calculus additionally Bro.... Wink

Please Bro !!!
Huh

I waiting privkey from you....

p.s. In PM you answer me what you not find a privkey, whats why I some misunderstand you.

WanderingPhilospher

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Shooters Shoot...

Quote from: COBRAS on September 07, 2021, 04:13:19 PM

p.s. This is a real keyreyt for this day -

1,5 QADRILION/SEC

This is BSGS program. It's all in how the keyrate is measured. I remember a post long ago that had this same discussion...

WanderingPhilospher

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Shooters Shoot...

Quote from: a.a on September 07, 2021, 03:51:03 PM

I think WP is just trolling. As I said, there is no way to calculate that much despite having an empty loop.

I was trying out a new KangaGSDPQuadro...Kangaroo that mimics baby steps, then running giant steps through those while setting a DP...but I do not think it works as designed. I found the private key to Cobra's pubkey several times but it did not match #120s address: 17s2b9ksz5y7abUm92cHwG8jEPCzK3dLnT

But I will reengineer from scratch.

dextronomous

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iceland github search will do.
this is a great programmer,
https://github.com/iceland2k14?tab=repositories

share speed and if succeeded..

a.a

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LOL, provide the code

?

COBRAS

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$$P2P BTC BRUTE.JOIN NOW ! https://uclck.me/SQPJk

p.s. This is a real keyreyt for this day -

1,5 QADRILION/SEC

dextronomous

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in 10sec. with 20 cores i get range 120 2^26.00/2^29.10 2200000000000000000 x 22fffffffffffffffff
in 60sec. with 3 cores i get range 120 2^26.00/2^29.10 2200000000000000 x 22ffffffffffffff

Scanning Range 0xa10000000000003700000000000000 : 0xa100000000000037ffffffffffffff
[158.47 TeraKeys/s][Kang 3072][Count 2^26.65/2^29.06][Elapsed 12s][Dead 0][RAM 14.4MB/44.7MB]

and hey right now it is not xpoints searching just plain old pubkey compressed or uc. so will make it even go faster by factor ?

(the gpu version should be released mr wandering) t.i.a. m.i.a. r.i.p. if not.

a.a

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I think WP is just trolling. As I said, there is no way to calculate that much despite having an empty loop.

dextronomous

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Quote from: COBRAS on September 07, 2021, 03:20:04 PM

Quote from: dextronomous on September 07, 2021, 02:47:38 PM

Quote from: COBRAS on September 07, 2021, 10:07:13 AM

Quote from: COBRAS on September 05, 2021, 09:43:45 PM

This is a 120 bit puzzle publick key !!!

If someone find a privkey for this pubkey in a range:

1:1124bff742a76f92fa3a76f8f6552f (decimal only 89014422443240977657631574972585263 !!! ) Range is mach less then origginal 120 Puzle range !!!

pubkey:

03c95ba9e6a637e739d13a6d036507ecc37a70c26e68ac7e5f157268311c6c3938
02c95ba9e6a637e739d13a6d036507ecc37a70c26e68ac7e5f157268311c6c3938

search in pubkey what start with 02 some faster than 03.

you can try any of this pubkeys.

Proof of my succes tests with another ranges and same pubkeys one what start with 03, and anower start with 02:

Working on Pubkey: 049fa3ea651e72c5f0a660c7ae509ad180860477283f539c918a2e43514c29da92237c8751b32e5 90883aa8bd617c60aa6b388aa78381cc7adb10046a33b038598
Using [Number of CPU Threads: 3] [DP size: 10] [MaxStep: 1]
............................................
Scanning Range 0x1 : 0x100000000000000
[55.22 TeraKeys/s][Kang 3072][Count 2^27.92/2^29.06][Elapsed 48s][Dead 0][RAM 25.8MB/44.7MB]
============== KEYFOUND ==============
Kangaroo FOUND PrivateKey : 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbf59aefd71d64b15
Working on Pubkey: 049fa3ea651e72c5f0a660c7ae509ad180860477283f539c918a2e43514c29da92dc8378ae4cd1a 6f77c557429e839f5594c775587c7e338524effb95bc4fc7697
Using [Number of CPU Threads: 3] [DP size: 10] [MaxStep: 1]
............................................
Scanning Range 0x1 : 0x100000000000000
[42.05 TeraKeys/s][Kang 3072][Count 2^28.68/2^29.06][Elapsed 01:26][Dead 0][RAM 37.7MB/44.7MB]
============== KEYFOUND ==============
Kangaroo FOUND PrivateKey : 0x0000000000000000000000000000000000000000000000000078af8f5e5ff62c
======================================

We are spit 1.2 btc 50/50 after with someone who publication in this thread privkey first, all others member sorry... !!!

Lets DO IT !!! ?

actual ! WanderPhilosofer stop search on his prototipe softwsre and nothing found !!! Any one try hack Huh

Privkey exact in key range !!!

getting 2.5 petakeys with this one on 1 system, only cpu, guess them wrote the gpu version of this same piece. Wandering you share it in your git.

His prototipe maybe wrang calculate keyrate, so,his prototype real prototype, because 1,5 Mkeys on 200 000 pubkeys is a not something special... Tongue

don't know wich version this is, or who's program, but it states them got the gpu programming skills, 1:1124bff742a76f92fa3a76f8f6552f
for current software it is waaaay to large.
Scanning Range 0x1 : 0x1124bff742a76f92fa3a76f8f6552f
[2714579271.01 TeraKeys/s] [Elapsed 4:26][RAM n/a]

btw how is this ok

--
Proof of my succes tests with another ranges and same pubkeys one what start with 03, and anower start with 02:

Working on Pubkey: 049fa3ea651e72c5f0a660c7ae509ad180860477283f539c918a2e43514c29da92237c8751b32e5 90883aa8bd617c60aa6b388aa78381cc7adb10046a33b038598
Using [Number of CPU Threads: 3] [DP size: 10] [MaxStep: 1]
............................................
this line range Scanning Range 0x1 : 0x100000000000000 quite the opposite?
[55.22 TeraKeys/s][Kang 3072][Count 2^27.92/2^29.06][Elapsed 48s][Dead 0][RAM 25.8MB/44.7MB]
============== KEYFOUND ==============
this line range Kangaroo FOUND PrivateKey : 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbf59aefd71d64b15 quite the opposite?
--

COBRAS

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Quote from: dextronomous on September 07, 2021, 02:47:38 PM

Quote from: COBRAS on September 07, 2021, 10:07:13 AM

Quote from: COBRAS on September 05, 2021, 09:43:45 PM

This is a 120 bit puzzle publick key !!!

If someone find a privkey for this pubkey in a range:

1:1124bff742a76f92fa3a76f8f6552f (decimal only 89014422443240977657631574972585263 !!! ) Range is mach less then origginal 120 Puzle range !!!

pubkey:

03c95ba9e6a637e739d13a6d036507ecc37a70c26e68ac7e5f157268311c6c3938
02c95ba9e6a637e739d13a6d036507ecc37a70c26e68ac7e5f157268311c6c3938

search in pubkey what start with 02 some faster than 03.

you can try any of this pubkeys.

Proof of my succes tests with another ranges and same pubkeys one what start with 03, and anower start with 02:

Working on Pubkey: 049fa3ea651e72c5f0a660c7ae509ad180860477283f539c918a2e43514c29da92237c8751b32e5 90883aa8bd617c60aa6b388aa78381cc7adb10046a33b038598
Using [Number of CPU Threads: 3] [DP size: 10] [MaxStep: 1]
............................................
Scanning Range 0x1 : 0x100000000000000
[55.22 TeraKeys/s][Kang 3072][Count 2^27.92/2^29.06][Elapsed 48s][Dead 0][RAM 25.8MB/44.7MB]
============== KEYFOUND ==============
Kangaroo FOUND PrivateKey : 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbf59aefd71d64b15
Working on Pubkey: 049fa3ea651e72c5f0a660c7ae509ad180860477283f539c918a2e43514c29da92dc8378ae4cd1a 6f77c557429e839f5594c775587c7e338524effb95bc4fc7697
Using [Number of CPU Threads: 3] [DP size: 10] [MaxStep: 1]
............................................
Scanning Range 0x1 : 0x100000000000000
[42.05 TeraKeys/s][Kang 3072][Count 2^28.68/2^29.06][Elapsed 01:26][Dead 0][RAM 37.7MB/44.7MB]
============== KEYFOUND ==============
Kangaroo FOUND PrivateKey : 0x0000000000000000000000000000000000000000000000000078af8f5e5ff62c
======================================

We are spit 1.2 btc 50/50 after with someone who publication in this thread privkey first, all others member sorry... !!!

Lets DO IT !!! ?

actual ! WanderPhilosofer stop search on his prototipe softwsre and nothing found !!! Any one try hack Huh

Privkey exact in key range !!!

getting 2.5 petakeys with this one on 1 system, only cpu, guess them wrote the gpu version of this same piece. Wandering you share it in your git.

His prototipe maybe wrang calculate keyrate, so,his prototype real prototype, because 1,5 Mkeys on 200 000 pubkeys is a not something special... Tongue

dextronomous

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Activity: 431

Merit: 105

Quote from: COBRAS on September 07, 2021, 10:07:13 AM

Quote from: COBRAS on September 05, 2021, 09:43:45 PM

This is a 120 bit puzzle publick key !!!

If someone find a privkey for this pubkey in a range:

1:1124bff742a76f92fa3a76f8f6552f (decimal only 89014422443240977657631574972585263 !!! ) Range is mach less then origginal 120 Puzle range !!!

pubkey:

03c95ba9e6a637e739d13a6d036507ecc37a70c26e68ac7e5f157268311c6c3938
02c95ba9e6a637e739d13a6d036507ecc37a70c26e68ac7e5f157268311c6c3938

search in pubkey what start with 02 some faster than 03.

you can try any of this pubkeys.

Proof of my succes tests with another ranges and same pubkeys one what start with 03, and anower start with 02:

Working on Pubkey: 049fa3ea651e72c5f0a660c7ae509ad180860477283f539c918a2e43514c29da92237c8751b32e5 90883aa8bd617c60aa6b388aa78381cc7adb10046a33b038598
Using [Number of CPU Threads: 3] [DP size: 10] [MaxStep: 1]
............................................
Scanning Range 0x1 : 0x100000000000000
[55.22 TeraKeys/s][Kang 3072][Count 2^27.92/2^29.06][Elapsed 48s][Dead 0][RAM 25.8MB/44.7MB]
============== KEYFOUND ==============
Kangaroo FOUND PrivateKey : 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbf59aefd71d64b15
Working on Pubkey: 049fa3ea651e72c5f0a660c7ae509ad180860477283f539c918a2e43514c29da92dc8378ae4cd1a 6f77c557429e839f5594c775587c7e338524effb95bc4fc7697
Using [Number of CPU Threads: 3] [DP size: 10] [MaxStep: 1]
............................................
Scanning Range 0x1 : 0x100000000000000
[42.05 TeraKeys/s][Kang 3072][Count 2^28.68/2^29.06][Elapsed 01:26][Dead 0][RAM 37.7MB/44.7MB]
============== KEYFOUND ==============
Kangaroo FOUND PrivateKey : 0x0000000000000000000000000000000000000000000000000078af8f5e5ff62c
======================================

We are spit 1.2 btc 50/50 after with someone who publication in this thread privkey first, all others member sorry... !!!

Lets DO IT !!! ?

actual ! WanderPhilosofer stop search on his prototipe softwsre and nothing found !!! Any one try hack Huh

Privkey exact in key range !!!

getting 2.5 petakeys with this one on 1 system, only cpu, guess them wrote the gpu version of this same piece. Wandering you share it in your git.

COBRAS

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Activity: 873

Merit: 22

$$P2P BTC BRUTE.JOIN NOW ! https://uclck.me/SQPJk

Quote from: COBRAS on September 05, 2021, 09:43:45 PM

This is a 120 bit puzzle publick key !!!

If someone find a privkey for this pubkey in a range:

1:1124bff742a76f92fa3a76f8f6552f (decimal only 89014422443240977657631574972585263 !!! ) Range is mach less then origginal 120 Puzle range !!!

pubkey:

03c95ba9e6a637e739d13a6d036507ecc37a70c26e68ac7e5f157268311c6c3938
02c95ba9e6a637e739d13a6d036507ecc37a70c26e68ac7e5f157268311c6c3938

search in pubkey what start with 02 some faster than 03.

you can try any of this pubkeys.

Proof of my succes tests with another ranges and same pubkeys one what start with 03, and anower start with 02:

Working on Pubkey: 049fa3ea651e72c5f0a660c7ae509ad180860477283f539c918a2e43514c29da92237c8751b32e5 90883aa8bd617c60aa6b388aa78381cc7adb10046a33b038598
Using [Number of CPU Threads: 3] [DP size: 10] [MaxStep: 1]
............................................
Scanning Range 0x1 : 0x100000000000000
[55.22 TeraKeys/s][Kang 3072][Count 2^27.92/2^29.06][Elapsed 48s][Dead 0][RAM 25.8MB/44.7MB]
============== KEYFOUND ==============
Kangaroo FOUND PrivateKey : 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbf59aefd71d64b15
Working on Pubkey: 049fa3ea651e72c5f0a660c7ae509ad180860477283f539c918a2e43514c29da92dc8378ae4cd1a 6f77c557429e839f5594c775587c7e338524effb95bc4fc7697
Using [Number of CPU Threads: 3] [DP size: 10] [MaxStep: 1]
............................................
Scanning Range 0x1 : 0x100000000000000
[42.05 TeraKeys/s][Kang 3072][Count 2^28.68/2^29.06][Elapsed 01:26][Dead 0][RAM 37.7MB/44.7MB]
============== KEYFOUND ==============
Kangaroo FOUND PrivateKey : 0x0000000000000000000000000000000000000000000000000078af8f5e5ff62c
======================================

We are spit 1.2 btc 50/50 after with someone who publication in this thread privkey first, all others member sorry... !!!

Lets DO IT !!! ?

actual ! WanderPhilosofer stop search on his prototipe softwsre and nothing found !!! Any one try hack Huh

Privkey exact in key range !!!

wedom

jr. member

Activity: 48

Merit: 11

Quote from: NotATether on September 07, 2021, 07:27:30 AM

...
Here's the thing about multiplication. It does not work between two public keys, which means you cannot multiply a public key by another public key, and that causes the whole method to fall apart. Sure, you end up with a lot of keys, but there is little to nothing else you can do with them.

I've been helping someone about this (trying to do exactly what you are saying is possible) by email for days before we reached this conclusion and try to use another attack method.
...

Until the moment we multiply the number by the point, we work with numbers. Perhaps he first generates all keys 1024^2 and 1024^3 in numbers and this allows him to multiply them. Only at the last step does he multiply by a point and get the public keys

wedom

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Quote from: ssxb on September 07, 2021, 06:38:08 AM

guys good news today i find 2 more ranges and where they are on the curve , today is celebration day for me , as i know total 3 ranges inside divisor , need to figure out other 29 ranges Grin

math is beautiful Kiss

Is this what you are looking for?

N=115792089237316195423570985008687907852837564279074904382605163141518161494337
for i in range(32):
print(i, hex((((N-1)//32)*i+1)%N))

Code:

0 0x1
1 0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20b
2 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd036415
3 0x17ffffffffffffffffffffffffffffffe18064b5a06ecf0599fbb8dd3385161f
4 0x1fffffffffffffffffffffffffffffffd755db9cd5e9140777fa4bd19a06c829
5 0x27ffffffffffffffffffffffffffffffcd2b52840b63590955f8dec600887a33
6 0x2fffffffffffffffffffffffffffffffc300c96b40dd9e0b33f771ba670a2c3d
7 0x37ffffffffffffffffffffffffffffffb8d640527657e30d11f604aecd8bde47
8 0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3340d9051
9 0x47ffffffffffffffffffffffffffffffa4812e20e14c6d10cdf32a979a8f425b
10 0x4fffffffffffffffffffffffffffffff9a56a50816c6b212abf1bd8c0110f465
11 0x57ffffffffffffffffffffffffffffff902c1bef4c40f71489f050806792a66f
12 0x5fffffffffffffffffffffffffffffff860192d681bb3c1667eee374ce145879
13 0x67ffffffffffffffffffffffffffffff7bd709bdb735811845ed766934960a83
14 0x6fffffffffffffffffffffffffffffff71ac80a4ecafc61a23ec095d9b17bc8d
15 0x77ffffffffffffffffffffffffffffff6781f78c222a0b1c01ea9c5201996e97
16 0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1
17 0x87ffffffffffffffffffffffffffffff532ce55a8d1e951fbde7c23ace9cd2ab
18 0x8fffffffffffffffffffffffffffffff49025c41c298da219be6552f351e84b5
19 0x97ffffffffffffffffffffffffffffff3ed7d328f8131f2379e4e8239ba036bf
20 0x9fffffffffffffffffffffffffffffff34ad4a102d8d642557e37b180221e8c9
21 0xa7ffffffffffffffffffffffffffffff2a82c0f76307a92735e20e0c68a39ad3
22 0xafffffffffffffffffffffffffffffff205837de9881ee2913e0a100cf254cdd
23 0xb7ffffffffffffffffffffffffffffff162daec5cdfc332af1df33f535a6fee7
24 0xbfffffffffffffffffffffffffffffff0c0325ad0376782ccfddc6e99c28b0f1
25 0xc7ffffffffffffffffffffffffffffff01d89c9438f0bd2eaddc59de02aa62fb
26 0xcffffffffffffffffffffffffffffffef7ae137b6e6b02308bdaecd2692c1505
27 0xd7fffffffffffffffffffffffffffffeed838a62a3e5473269d97fc6cfadc70f
28 0xdffffffffffffffffffffffffffffffee3590149d95f8c3447d812bb362f7919
29 0xe7fffffffffffffffffffffffffffffed92e78310ed9d13625d6a5af9cb12b23
30 0xeffffffffffffffffffffffffffffffecf03ef184454163803d538a40332dd2d
31 0xf7fffffffffffffffffffffffffffffec4d965ff79ce5b39e1d3cb9869b48f37

a.a

member

Activity: 126

Merit: 36

This is "just" a memory - cpu tradeoff.

Its like: If you generate all privatekeys and the corresponding public key to a lookup table, which would be a database with 2^256 entries, than you have a runtime of O(x) = 1.

Here you halve the potential processing time by 2 per bitshift. So yeah... bit shifting 10x results in 10 times (2^10 times?) faster pollard rho. But you need 2^10 more memory. Like you need 1kb ram for 1 pubkey, but need 2^10 kb = 1024 kb for shifting 10 bits.

NotATether

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Quote from: ssxb on September 07, 2021, 07:10:50 AM

i guess not useless , as he told

use 1024 divisor = A
than 1024*1024 divisor =B

than addition , multiplication of A and B with each other will give you significantly low number of keys , i guess this make sense but he need to explain more or perhaps some script

Here's the thing about multiplication. It does not work between two public keys, which means you cannot multiply a public key by another public key, and that causes the whole method to fall apart. Sure, you end up with a lot of keys, but there is little to nothing else you can do with them.

I've been helping someone about this (trying to do exactly what you are saying is possible) by email for days before we reached this conclusion and try to use another attack method.

ssxb

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Activity: 81

Merit: 2

Quote from: NotATether on September 07, 2021, 06:48:17 AM

Quote from: ssxb on September 07, 2021, 06:27:16 AM

brainless talked about reducing the number of keys but he never shared how can we (working script) , perhaps i will figure out something better soon Grin

IA

As I wrote earlier, that method is useless, because it increases the range of the generated keys.

i guess not useless , as he told

use 1024 divisor = A
than 1024*1024 divisor =B

than addition , multiplication of A and B with each other will give you significantly low number of keys , i guess this make sense but he need to explain more or perhaps some script

NotATether

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Activity: 1568

Merit: 6660

bitcoincleanup.com / bitmixlist.org

Quote from: ssxb on September 07, 2021, 06:27:16 AM

brainless talked about reducing the number of keys but he never shared how can we (working script) , perhaps i will figure out something better soon Grin

IA

As I wrote earlier, that method is useless, because it increases the range of the generated keys.

Topic: Pollard's kangaroo ECDLP solver - page 38. (Read 59389 times)