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    Author Topic: Pollard's kangaroo ECDLP solver  (Read 62728 times)

    • WanderingPhilospher
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    June 11, 2020, 03:52:13 PM
     #781
    Quote from: WanderingPhilospher on June 10, 2020, 08:44:54 PM
    If any of you are working on #115 or #120 or # any above that, by yourself, you're just wasting power.

    Jean Luc's knowledge, with Zielar's unlimited GPUs through his work...YOU can't compete. Especially if Jean Luc is making changes to increase chances of Zielar finding the puzzle.

    You can't compete. Not with Kangaroo. You'll have to get creative and try random other options.

    It's like everyone has GPU power but no one wants to link up and send DPs to common server, or get together and agree on a specific DP to share work files, etc.

    I'd rather have 10% of 1.15 BTC versus 0%.

    I'm still in the chase, but not strictly with Kangaroo. I offered up my work files, at DP 30 or 31. They are just sitting in file, no longer being used. I'm down to DP 12, with creative works.



    Quote
    We also get lots of troubles handling large workfiles (above 200GB) so I created a partitioned work file system (available on github) , an integrity workfile checker.

    Told you  Cool

  • WanderingPhilospher
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    June 11, 2020, 03:55:35 PM
     #782
    Quote from: Jean_Luc on June 11, 2020, 03:44:33 PM
    Quote from: MrFreeDragon on June 10, 2020, 08:25:13 PM

    How long are your GPUs working on #115?

    If #110 was solved for 2 days, so with the same speed and the same luck you need 2days * sqrt(2^5) = 2 days * 5.66 ~ 11.3 days for #115. So, yes, if you started on 1 June, the estimated completion date 11-12 June  Cheesy

    For #110 you was very close to sqrt(n) operations, but not the average 2*sqrt(n). That means that probably you should wait another 11-12 days to be close to the average and 50% probability to find the key.

    EDIT:
    I doubt you will find the #115 key tomorrow. Much more likely at the end of June, or mid July. But not tomorrow.

    We almost reached 50% probability yesterday (~8 days of run, ~2^33 DP, DP25) but unfortunately everything was shutdown due to a storm Sad
    Fortunately the workfiles has been preserved but we have to restart clients and servers to recover from crash.
    As there was no kangaroo backup we will get a DP overhead by restarting the work.
    I don't know if Zielar restarted the GPUs, yesterday he was a bit nervous Cheesy
    We also get lots of troubles handling large workfiles (above 200GB) so I created a partitioned work file system (available on github) , an integrity workfile checker. We manage to re-merge all worfiles in ~24H.
    The current release is tagged 1.10(unstable) but should work.
    Hope it will go better now...

    I've told you...build a comparer. No issues with overhead or large workfiles or 24 hour merging. I've built a homemade one and am able to run any DP without any RAM or merging issues. But I'm not a programmer and know a better one can be built.

  • Etar
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    June 11, 2020, 05:40:56 PM
     #783
    Anybody think about using bsgs algo but with DP?
    bsgs  fast but have a problem due to memory usage. maybe using DP can solve this issues?

  • WanderingPhilospher
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    June 11, 2020, 06:00:01 PM
     #784
    Quote from: Etar on June 11, 2020, 05:40:56 PM
    Anybody think about using bsgs algo but with DP?
    bsgs  fast but have a problem due to memory usage. maybe using DP can solve this issues?
    Extremely fast, it gets through a FFFFFFFFFFF range in 2 seconds total. Including step build time. Only uses 600Mb.

    I thought about how to implement it differently. Use DP or build the table on harddrive and when giants start stepping compare back to the saved table. After so long, save the giant file with previously created file, and continue with giant step.

  • arulbero
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    June 11, 2020, 06:35:59 PM
     #785
    Quote from: WanderingPhilospher on June 11, 2020, 06:00:01 PM
    Quote from: Etar on June 11, 2020, 05:40:56 PM
    Anybody think about using bsgs algo but with DP?
    bsgs  fast but have a problem due to memory usage. maybe using DP can solve this issues?
    Extremely fast, it gets through a FFFFFFFFFFF range in 2 seconds total. Including step build time. Only uses 600Mb.

    I thought about how to implement it differently. Use DP or build the table on harddrive and when giants start stepping compare back to the saved table. After so long, save the giant file with previously created file, and continue with giant step.

    How do you use DPs with BSGS?

  • WanderingPhilospher
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    June 11, 2020, 06:48:03 PM
     #786
    Quote from: arulbero on June 11, 2020, 06:35:59 PM
    Quote from: WanderingPhilospher on June 11, 2020, 06:00:01 PM
    Quote from: Etar on June 11, 2020, 05:40:56 PM
    Anybody think about using bsgs algo but with DP?
    bsgs  fast but have a problem due to memory usage. maybe using DP can solve this issues?
    Extremely fast, it gets through a FFFFFFFFFFF range in 2 seconds total. Including step build time. Only uses 600Mb.

    I thought about how to implement it differently. Use DP or build the table on harddrive and when giants start stepping compare back to the saved table. After so long, save the giant file with previously created file, and continue with giant step.

    How do you use DPs with BSGS?
    I don't...Etar was pondering if it could be done. I just added some of the thoughts I have had because the speed is insane and it's a 100% solver.

  • WanderingPhilospher
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    June 11, 2020, 07:06:48 PM
     #787
    What are your thoughts...

    For this Kangaroo ECDLP solver, if RAM was not an issue, what is the optimal DP setting?

    Would lower always be better? Small DP means you have to find more DPs.

    Expected group operations remains the same no matter how you adjust the DP, right?

    So what is the optimal DP setting if RAM is not an issue?

  • Etar
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    June 11, 2020, 07:46:32 PM
    Last edit: June 11, 2020, 08:29:19 PM by Etar
     #788
    Quote from: arulbero on June 11, 2020, 06:35:59 PM
    -snip-
    How do you use DPs with BSGS?
    First fill baby steps, but not each point put to table but only DP and distance
    when you reach last DP you will get final distance.
    Doubled distance it will be Giant steps.
    Before GS you need to find 2 DP (+/-) for known pubkey, compare with hashtable this DP
    if not success sub GS from pubkey and repeat..

    In ex. i generate random pubkey b305a37bdbf60a2ba47fc0d134b2ce3646ab7d1236d0e29c73dc27da311dba82bbfbb9d25748a27 92fcac6ec1b892db592556534f1b6155a37804522d1ff2194
    private key is 0xA0300879 in range 2^32
    I set DPsize=8, and maxDP in table around 262144
    when i fill baby steps i get 262346 DPs
    It is very small hashtable ofcourse it is just for test..
    In this case i should make 20 giant steps to find key.
    Total add point op was 6981.
    Code:
    DPSIZE   :8
    MASK     :ff00000000000000000000000000000000000000000000000000000000000000
    TOTAL DPs:262144
    STARTx:79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
    STARTy:483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
    FINDx :b305a37bdbf60a2ba47fc0d134b2ce3646ab7d1236d0e29c73dc27da311dba82
    FINDy :bbfbb9d25748a2792fcac6ec1b892db592556534f1b6155a37804522d1ff2194
    100.1%
    TOTAL DPs  :262346
    AVEDIST    :256
    TABLE SIZE :0000000000000000000000000000000000000000000000000000000004000001
    SUB POINTx:930224dc7b052d55216cd197b65997a703e4864ed12ef2f65018a5c8d815dde7
    SUB POINTy:392b293eb3eb8d6597f659938411eb241d9ebb59209eeddb308e09b7dd5bf9ea
    JUMP..20
    +FIND!!!>>00000000000000000000000000000000000000000000000000000000A0300879
    HASH DISTANCE:3147960
    PRE DISTANCE:2684354600
    DISTANCE:103
    POINTx:b305a37bdbf60a2ba47fc0d134b2ce3646ab7d1236d0e29c73dc27da311dba82
    POINTy:bbfbb9d25748a2792fcac6ec1b892db592556534f1b6155a37804522d1ff2194
    op 6981

    the same with 2^40 range
    Code:
    DPSIZE   :8
    MASK     :ff00000000000000000000000000000000000000000000000000000000000000
    TOTAL DPs:1048576
    STARTx:79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
    STARTy:483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
    FINDx :d25841ae281aad4c516463fe69553b6f9526ef39692b7a5a483d30fee7a3bc22
    FINDy :0ab386a9f0985ba4718c827250789cc5e7fc0852800521bb725e05dddc9a4bc2
    100.0%
    TOTAL DPs  :1048354
    AVEDIST    :256
    TABLE SIZE :0000000000000000000000000000000000000000000000000000000010000001
    SUB POINTx:2d0ea198923cdaf6c8e38f2f7595912a19efb1e78a6c0ce793863da8b4312e3c
    SUB POINTy:f61fb584f1753d923951f4af8b26d9e96b572283c3f12c15971f6699bc74362b
    JUMP..1315
    +FIND!!!>>000000000000000000000000000000000000000000000000000000A4530846E5
    HASH DISTANCE:217563888
    PRE DISTANCE:705985251910
    DISTANCE:113
    POINTx:d25841ae281aad4c516463fe69553b6f9526ef39692b7a5a483d30fee7a3bc22
    POINTy:0ab386a9f0985ba4718c827250789cc5e7fc0852800521bb725e05dddc9a4bc2
    op 530970

  • arulbero
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    June 11, 2020, 08:16:10 PM
     #789
    Quote from: WanderingPhilospher on June 11, 2020, 07:06:48 PM
    For this Kangaroo ECDLP solver, if RAM was not an issue, what is the optimal DP setting?

    Would lower always be better? Small DP means you have to find more DPs.

    Expected group operations remains the same no matter how you adjust the DP, right?

    So what is the optimal DP setting if RAM is not an issue?

    If the RAM was not a issue, it would be better to use a low DP, because high DP means long time between a collision and its detection, especially if you use many kangaroos in parallel.  

    But not too low, with DP = 0 ** you would have the minimum number of steps, but the generation of the the start points is much slower than the generation of the other points of the path. Let's say that the cost of generating a start point is about x50 the cost of generating the next point with a single jump, with an average length of 10k points (about 2^13) you should have a good value. Then DP = 12 13 14, not more.

    ** A note: if you use equivalence classes with DP = 0, you need only sqrt(2).sqrt(N) steps, this is the expected group operations.

  • arulbero
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    June 11, 2020, 08:26:46 PM
    Last edit: June 11, 2020, 08:39:08 PM by arulbero
     #790
    Quote from: Etar on June 11, 2020, 07:46:32 PM
    Quote from: arulbero on June 11, 2020, 06:35:59 PM
    -snip-
    How do you use DPs with BSGS?
    First fill baby steps, but not each point put to table but only DP and distance
    when you reach last DP you will get final distance.
    Doubled distance it will be Giant steps.
    Before GS you need to find 2 DP (+/-) for known pubkey, compare with hashtable this DP
    if not success sub GS from pubkey and repeat..

    But in this way you find the private key at 100%?

    EDIT:

    Quote from: Etar on June 11, 2020, 07:46:32 PM
    In ex. i generate random pubkey b305a37bdbf60a2ba47fc0d134b2ce3646ab7d1236d0e29c73dc27da311dba82bbfbb9d25748a27 92fcac6ec1b892db592556534f1b6155a37804522d1ff2194
    private key is 0xA0300879 in range 2^32
    I set DPsize=8, and maxDP in table around 262144
    when i fill baby steps i get 262346 DPs
    It is very small hashtable ofcourse it is just for test..
    In this case i should make 20 giant steps to find key.
    Total add point op was 6981.

    With the classic BSGS, for a range of 2^32 you need only 2^16 = 65536 baby steps, you use instead 262346 DPs, you use more RAM, not less.

  • Etar
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    June 11, 2020, 08:46:29 PM
     #791
    Quote from: arulbero on June 11, 2020, 08:26:46 PM
    -snip-
    With the classic BSGS, for a range of 2^32 you need only 2^16 = 65536 baby steps, you use instead 262346 DPs, you use more RAM, not less.
    you can use what ever you want amount of DPs, but less amount of DP then more GS you need.
    here is 16k DPs
    Code:
    DPSIZE   :8
    MASK     :ff00000000000000000000000000000000000000000000000000000000000000
    TOTAL DPs:16384
    STARTx:79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
    STARTy:483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
    FINDx :225e0e43997fb77b83ef7e61a7be88d2851b09da3e36615c0a2d7e06f06b4517
    FINDy :cb488adc7c5ba9f4bf0ccf48e0adc7bd2fb2b1488ed42c9cd14a5762be5017dd
    101.1%
    TOTAL DPs  :16567
    AVEDIST    :253
    TABLE SIZE :00000000000000000000000000000000000000000000000000000000003fffff
    SUB POINTx:045685b52a932ee1f2638b9ea3b075f8be2ecd902e14bb7eb1ff0c24c22bbcc5
    SUB POINTy:672f0bb37150ac5427d93df317fcb2b2798251581f4966f067f59291b1413b5c
    JUMP..142
    HASH DISTANCE:3177180
    PRE DISTANCE:1191182052
    DISTANCE:159
    POINTx:225e0e43997fb77b83ef7e61a7be88d2851b09da3e36615c0a2d7e06f06b4517
    POINTy:cb488adc7c5ba9f4bf0ccf48e0adc7bd2fb2b1488ed42c9cd14a5762be5017dd
    +FIND!!!>>0000000000000000000000000000000000000000000000000000000046CF8369
    op 57909

  • arulbero
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    June 11, 2020, 09:10:52 PM
     #792
    Quote from: Etar on June 11, 2020, 08:46:29 PM
    Quote from: arulbero on June 11, 2020, 08:26:46 PM
    -snip-
    With the classic BSGS, for a range of 2^32 you need only 2^16 = 65536 baby steps, you use instead 262346 DPs, you use more RAM, not less.
    you can use what ever you want amount of DPs, but less amount of DP then more GS you need.
    here is 16k DPs

    The goal is to use less RAM than classic BSGS.

    Let's say we want to find a key in 120 bit range.
    With the classic BSGS you need 2^60 BS (huge amount of RAM) and 2^60 GS.

    With BSGS + (DP = 10):

    2^50 BABYSTEPS  + on average 2^59 GIANTSTEPS * 2^10 = 2^69 steps.

    Then less RAM but more steps.

    With BSGS + (DP = 10):

    if you want to use more BABYSTEPS:

    2^80 BABYSTEPS  + on average 2^29 GIANTSTEPS * 2^10 = 2^80 steps + 2^39 GIANTSTEPS.

    The advantage is that you can precompute this 2^80 BABYSTEPS, but you don't have space to store them.

  • COBRAS
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    June 11, 2020, 10:37:13 PM
    Last edit: June 11, 2020, 10:52:34 PM by COBRAS
     #793
    Quote from: arulbero on June 11, 2020, 09:10:52 PM
    Quote from: Etar on June 11, 2020, 08:46:29 PM
    Quote from: arulbero on June 11, 2020, 08:26:46 PM
    -snip-
    With the classic BSGS, for a range of 2^32 you need only 2^16 = 65536 baby steps, you use instead 262346 DPs, you use more RAM, not less.
    you can use what ever you want amount of DPs, but less amount of DP then more GS you need.
    here is 16k DPs

    The goal is to use less RAM than classic BSGS.

    Let's say we want to find a key in 120 bit range.
    With the classic BSGS you need 2^60 BS (huge amount of RAM) and 2^60 GS.

    With BSGS + (DP = 10):

    2^50 BABYSTEPS  + on average 2^59 GIANTSTEPS * 2^10 = 2^69 steps.

    Then less RAM but more steps.

    With BSGS + (DP = 10):

    if you want to use more BABYSTEPS:

    2^80 BABYSTEPS  + on average 2^29 GIANTSTEPS * 2^10 = 2^80 steps + 2^39 GIANTSTEPS.

    The advantage is that you can precompute this 2^80 BABYSTEPS, but you don't have space to store them.

    Jean_Luc BSGS support only 2^32 max BABYSTEP
    [

  • Jean_Luc (OP)
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    June 12, 2020, 06:57:27 AM
     #794
    New release 1.10 available:

        Added -wcheck option (Check workfile integrity)
        Added partitioned work file
        Merger performance increase

    https://github.com/JeanLucPons/Kangaroo/releases

    Thanks for testing Wink

  • Etar
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    June 12, 2020, 12:18:28 PM
     #795
    Interesting thing this elliptic curve..
    I didn’t think that there are even fractional points on the curve
    For ex. if 7/2=3.5
    Code:
    (5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc,6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264da)
    /2=
    (592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b031,72dd2e1d26c233337760c49122a1df67d0aa792b453f97bd29765c83b47ba01d)

    and if double this point it will be again 7
    (592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b031,72dd2e1d26c233337760c49122a1df67d0aa792b453f97bd29765c83b47ba01d)
    +
    (592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b031,72dd2e1d26c233337760c49122a1df67d0aa792b453f97bd29765c83b47ba01d)
    =
    (5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc,6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264da)

  • brainless
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    June 12, 2020, 12:24:32 PM
     #796
    Quote from: Etar on June 12, 2020, 12:18:28 PM
    Interesting thing this elliptic curve..
    I didn’t think that there are even fractional points on the curve
    For ex. if 7/2=3.5
    Code:
    (5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc,6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264da)
    /2=
    (592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b031,72dd2e1d26c233337760c49122a1df67d0aa792b453f97bd29765c83b47ba01d)

    and if double this point it will be again 7
    (592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b031,72dd2e1d26c233337760c49122a1df67d0aa792b453f97bd29765c83b47ba01d)
    +
    (592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b031,72dd2e1d26c233337760c49122a1df67d0aa792b453f97bd29765c83b47ba01d)
    =
    (5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc,6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264da)

    3.5 would be in real figure
    57896044618658097711785492504343953926418782139537452191302581570759080747172
    hex:  7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A4
    pubkey: 04592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b03172dd2e1d26c23 3337760c49122a1df67d0aa792b453f97bd29765c83b47ba01d

    its common practice
    13sXkWqtivcMtNGQpskD78iqsgVy9hcHLF

  • brainless
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    June 12, 2020, 12:28:54 PM
     #797
    Quote from: brainless on June 12, 2020, 12:24:32 PM
    Quote from: Etar on June 12, 2020, 12:18:28 PM
    Interesting thing this elliptic curve..
    I didn’t think that there are even fractional points on the curve
    For ex. if 7/2=3.5
    Code:
    (5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc,6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264da)
    /2=
    (592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b031,72dd2e1d26c233337760c49122a1df67d0aa792b453f97bd29765c83b47ba01d)

    and if double this point it will be again 7
    (592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b031,72dd2e1d26c233337760c49122a1df67d0aa792b453f97bd29765c83b47ba01d)
    +
    (592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b031,72dd2e1d26c233337760c49122a1df67d0aa792b453f97bd29765c83b47ba01d)
    =
    (5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc,6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264da)

    3.5 would be in real figure
    57896044618658097711785492504343953926418782139537452191302581570759080747172
    hex:  7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A4
    pubkey: 04592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b03172dd2e1d26c23 3337760c49122a1df67d0aa792b453f97bd29765c83b47ba01d

    its common practice
    both odd and even fractional points are exist, you only need to calc it, as i can do it Smiley
    13sXkWqtivcMtNGQpskD78iqsgVy9hcHLF

  • Etar
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    June 12, 2020, 12:34:11 PM
    Last edit: June 12, 2020, 12:49:10 PM by Etar
     #798
    Quote from: brainless on June 12, 2020, 12:28:54 PM
    -snip-
    both odd and even fractional points are exist, you only need to calc it, as i can do it Smiley
    Can you explain  how you calculate 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A4 ?
    edit: solved (n+7)/2

  • mrxtraf
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    June 12, 2020, 12:40:01 PM
     #799
    Try calculate real for 0.1 or 0.001 or 0.0000000000000000000000001  Smiley

  • brainless
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    June 12, 2020, 12:41:56 PM
     #800
    Quote from: mrxtraf on June 12, 2020, 12:40:01 PM
    Try calculate real for 0.1 or 0.001 or 0.0000000000000000000000001  Smiley

    for 0.1
    a = 1/3
    b = a/2
    result = 0.1
    13sXkWqtivcMtNGQpskD78iqsgVy9hcHLF
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