brainless (OP)
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October 07, 2022, 10:19:08 AM Last edit: October 08, 2022, 10:26:10 PM by Mr. Big |
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Dear Friends 2009 after blockchain launch, first peoples found brain wallet mistakes, words or sentence from dic, easily found by hundreds peoples later some other strategies, where we listen in passed, some exchanges hacked and some wallets provider services were compromised still their is lot of strategies exist for pick addresses with balance here i am posting 1 strategy out of (17), maybe help full to exchanges or corporate or wallet provider, for their own analyzing mistakes, where they maybe could get better secure their services No Begging - Mod----------------- more then 1634 addresses are in used from 2013 to 2021 these addresses are maybe under use of exchange or wallet service provider or maybe hardware wallets whats mistake inside is all addresses, from owner side, every privatekey is looks difrent from each other but reality is every private key for those addresses are very close and in series if any one address prv key exposed, in series all addresses balances could be in high risk these addresses are in series like 2 ,6, 10, 20, 26 etc checking...... 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, Result ... if some one found privatekey 1 of these addresses, can get all addresses private keys by privatekey * 2 mod n, and loop to .. Exposed here posting 1 pubkey, those who want tough experiment, can halve this pubkey in loop to 20m pubkeys, then to address, you will find all 1634 addresses their and post your experience here, after see how much peoples have experiment mode, i will post easy solution to check after 24 hours halve to 20 million pubkey from here 0398ce5d78ed1a3b121cbdbd62daecda243a43cf3f201c3599ee78a391d0190950 1121f21h1wyrnm2ipXiKaCULLopeBegt2s 112fPaBsEHcXw5J3JbDeHX8vngBGdmatbQ 116F4u8GZq7WuHeeGyvaV3jGLq79CCHcRx 121DZih4HdiNVDDnF4HKFNFca3cMUwFGc9 122HrXBgNywq1jc8SvTK4xwPPK2xdrpNa5 122Kxx8duGrq2BphDRMvnfiiDr6S6R9U9Y 123jyDqTL7ZFYdfn8MXXXUADd161WzJfdT 126buMUzPKWqauQD2k7DNDWeNhG7s2HH7k 126zWtHexYNsMaFJeufAf2aY2DadbiCzbc 1272zrR8XXNK5HxitEYqA7AuhcfmVgfzyH 127ZukxwEE6JruuptnCXjiooM5PTsFWeCd 12bYvCV4MfpSPNxL7uSWNs8QmtARMCm6pp 12CJ63AjGG2So2GG1bPHPu9XtK8wwaSJyW 12CL24SVqoTyjgdUu5EFPyKejbvGfzPcaA 12CMoczj8Dmz7AsGp2UwwR8EiTNmaz37JZ 12CoAy9BUNCJ5qCHa4xEzpCqxTEbqZRDYJ 12ddGqfuwHzeER61FJNngswMkCuHQieKx7 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13sXkWqtivcMtNGQpskD78iqsgVy9hcHLF
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brainless (OP)
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Activity: 316
Merit: 34
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October 07, 2022, 10:20:00 AM |
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1PLSimrqgtcmCcqh7dsRWbk5wwNXCc2Frc 1PLsNo2huXQztY9jtmxpD7sChfztismUih 1Pm39rzxVT5fv2D7UrN33Jyg3npdofyVSK 1PmdQHbEwuHFTNFa15orbF6rrJWhbkBMer 1PMNd7canw5Tbv9JxJyGiQ2idYBpVMmGJw 1PmosdsieYxcT2NzvUScyF6YiA6L1yvcCq 1PoioCvTFS3kLBUiUMcLXUMG7qWygyhxY9 1PP1oEeHDCRvdQVX1LkCXLCUjZjWz1Q7cm 1Pp4FAsHfkP5X6P9iK1kHGgxdh38ZfSYLy 1PPh3nGjzg6A77p5CU7QJ64jnWS2fV3qFi 1PPuM2unu3dmEqXLcNPbEGBNB9EKo7Sits 1Ppxw3J1NYYHhSKtQ3iFs11ZQfb3km58D5 1PQ426uyYw2JPhD9T6KWrEgrx6wbN5LPYq 1PQdfWgjt7epy5imRe7w5Ad1UmXrpyt96g 1PRBVraqrCZ6pkuNyzXEmpAdaUACRUYe86 1PRKtzzzpG4qBmJxhjWLLhZ1kp3CMZxB4C 1Ps5NzxSRUTWfnNPUxNFnPpfH9vBAXVJuQ 1PsDKb7AE6Bb4g6sc64CmZ4h8EXzs6gW4f 1PSdQoPY3aRi1umpT5zQH6RYUbd3r9PMKf 1PSyox4tQ9CJYAeB2ojXiRcDmubHnCDofa 1PTSUQL2BwmALbkXRiTcX4MTFmWDaXczbu 1PTViQUvnR6o579ccShqbFtLLJbbrARd5S 1PuCcMcTN5SdkWA7qPFoXpoUryv56tsQWt 1Pudn2KtcjT5b33pEZ3sjzjiPt1TXEjzUN 1PUUWUqrP4NHiT4mxPQNbyJpsDU1XWSDo5 1PuZEgRiTiP5rjU8J1WyrktKchaTFfpkrU 1PuZN4v6zPA3oE9bKnG9gxbA7uJd8wub8P 1PV3jM1fFA5kN1dEbqLmCYob2UJNGNzhek 1PV9wAtbgWfoh9vVNkwgJ3Ed5Bn4fMmpNy 1PvkSvvhYMbT7SCTeqJFzP27XzxE8QBoNj 1PVLGf9V3gv5r112RfDxqujfPxQoMz5oDT 1PWgghxAtEp7ohp4F1jTmiQLTG5BKnNTys 1PwrB3ZwmknPXnmnafqkLUJxQ6nPuNg8Mn 1PykZFokPhjXTqUVLbzsrayFWwudtmNsHZ 1PYPws5kZe3VhTmCoj8SPxRmzQRD2Xe4YT 1PYvUMBS7YEH5VSCQnvsFRyrMzBxtVyiZv 1Pz4zqwUry9JzGUXHmUsHZSbCmCDamaf6q 1Q1ftoVqXKxSYgTNRWrLsxCizYxvqrjM2n 1Q1LuTdtBQ7QM7YZD66Up2ZB7qPBuKLMe4 1Q2LoRseD63WLRa2isVmYhz8s4Jyww2XRX 1Q2TFFB1AYygrMDkTn1pkzF1behPSjUYFh 1Q33tTdmfMyGZ4iNVnuJdGGuDzzv4VJNtX 1Q3ZgqBVCzxhEMmysu3AyBHPajcjxtaJ9B 1Q4GehasksU9nYmgqYF5qofQZLPUgeoC1S 1Q5aj2cytusjbGfafrYE17kF6eLEda5T5s 1Q5auRZi4PkHxyaQmHgrJrVyETk7ikhfFH 1Q66dQju3BfNFT4MPWP29fLfivCYG4ayCp 1Q6jKKpHU7U71A8bPtkJAKyFHscY6BjpA5 1Q6PdYiPjZP1Zic9pZMN4SQkptZ27RgJZF 1Q71Azbu2bgZ59TNYbHhm9aLwUzrXLanm7 1Q8KTb7KUC4NBB7RiNoKwmtAiyz86a8r4D 1Q98hLM3eG9gS2keBdtxV6SkyfdSG1WgJd 1QAPFXGmkGuQADURQ4ujShFdGHM6sfikKo 1QCEKaFEC2zY54J3zcjyNKYHKy8Zyk9mGS 1QEE5eXFkdhVxftt7cZefgXNuvrxLWdHz9 1QEydB97SWHxkMEqr61zPe1b1CoTEqCFjW 1QEZsq6BkvY4zRYtyLsgvoAhy7dLQnXspF 1QFQ784hwTdhtjbjBACjbYfpPHGGZYegLf 1QGekdnozM7xAB1ADwMStQh2iTBpm6Q3Cz 1QH3mdRa7P3ZED6DWvfktPXSiUtq7GXR5G 1QHocc13M9GmVj79gJmo98Q9Dc59tw5gqJ 1qiuQMceBXBJ5WhyBLLDAAh9kHXBHWnWa 1QJDQGCN3mQy22WbMdqPhuRNs6QWNZt7jG 1QKAoiXrrg66U2BWgcQW2XdSNnAcgZNfrP 1QLKgoCMyo61eqjNwbJ3sh581FzVFN6md8 1RCodGSapmgV5msNPepfrjTJGearvVaC1 1s9Fd7tFfo2MeoSyFQhuBBPDpjF77iLh8 1saS33EB9gxhs8UDCrUTWQcZ23YWP6Yon 1SxuyCJtqn91QtgD94bxXXjUhdGJcURf3 1TMJz39r9CcD9oain8rwYpu6DzM1HZb6Z 1TU8fuKFQsGRySvVJK4YbdF3krZrP637V 1TVceQyXvL8Umx4jR93jaEDcTQWsYzV6A 1uDUg5ZrTEpoY12Rwgnb8DaJrB7XZyqdX 1uVtgw8htsgNw4D9sn2iwJBxK32fGgxUV 1VrsicphfMLHaPNoQoVwwu1UEuBB6DSsA 1w2NfYF2tACtvS9FWKccepCSzjQzyRF91 1X1hXPN54jBiUhkdYFR52GA4CzvFVBU4A 1x6xxjAU5b2YRoLjJcWjD4tukweeVmATP 1X8EnoA77xUXre44tXFwnnNevfeYhtMJd 1xwTMrvQobLjsN87PbBdcTELRV8Hq7wys 1Y5C1M5Sucb9oJLpJ6MyNhRYDtpzFfyVa 1YFBGE1aA956piwVkvCmdKkmDWnzJEvkg 1ypbxfDwwz6KYxJeCeovvDHto7dpfJP5R 1YSmMYYWHNY3bDEDbWm6veoQJf78U7FHV 1ySWXWDr688a4fFRHGBmZ15a8gRcadpWc 1ZeG1Q12mcNMAyPtCiGmRLz9gKtMyDLsa 1ZirAw442wKnhZWgXw4M1f5zRRMrn19MG 1zJk882hsRqyyk8HFbT2BYYYwcuG9Bzgb
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13sXkWqtivcMtNGQpskD78iqsgVy9hcHLF
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NeuroticFish
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October 07, 2022, 10:36:46 AM |
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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).
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nc50lc
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October 07, 2022, 11:11:49 AM |
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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/addressesHaving a total of 6,023 linked addresses suggests that it's indeed an exchange or service provider.
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brainless (OP)
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October 08, 2022, 12:19:28 PM |
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13sXkWqtivcMtNGQpskD78iqsgVy9hcHLF
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gmaxwell
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October 10, 2022, 01:23:45 AM |
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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. 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
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brainless (OP)
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October 10, 2022, 04:05:58 AM |
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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. 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/1121f21h1wyrnm2ipXiKaCULLopeBegt2sresult: 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://bitcointalk.org/index.php?topic=5409721.0
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13sXkWqtivcMtNGQpskD78iqsgVy9hcHLF
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_Counselor
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October 10, 2022, 05:33:06 AM |
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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://bitcointalk.org/index.php?topic=5409721.0If 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.
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gmaxwell
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October 10, 2022, 08:17:57 AM |
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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.
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_Counselor
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October 10, 2022, 08:59:13 AM Merited by vapourminer (2) |
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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.
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brainless (OP)
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October 10, 2022, 12:37:02 PM |
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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
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13sXkWqtivcMtNGQpskD78iqsgVy9hcHLF
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gmaxwell
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October 10, 2022, 02:43:37 PM |
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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.
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NotATether
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October 10, 2022, 02:52:32 PM |
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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).
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. .BLACKJACK ♠ FUN. | | | ███▄██████ ██████████████▀ ████████████ █████████████████ ████████████████▄▄ ░█████████████▀░▀▀ ██████████████████ ░██████████████ █████████████████▄ ░██████████████▀ ████████████ ███████████████░██ ██████████ | | CRYPTO CASINO & SPORTS BETTING | | │ | | │ | ▄▄███████▄▄ ▄███████████████▄ ███████████████████ █████████████████████ ███████████████████████ █████████████████████████ █████████████████████████ █████████████████████████ ███████████████████████ █████████████████████ ███████████████████ ▀███████████████▀ ███████████████████ | | .
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CrunchyF
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October 10, 2022, 08:19:16 PM |
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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. 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/1121f21h1wyrnm2ipXiKaCULLopeBegt2sresult: 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://bitcointalk.org/index.php?topic=5409721.0this following python script (you need to have bit and gmpy2 installed) can do the work in 2 seconds...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))
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brainless (OP)
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October 11, 2022, 04:31:05 AM |
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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. 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/1121f21h1wyrnm2ipXiKaCULLopeBegt2sresult: 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://bitcointalk.org/index.php?topic=5409721.0this following python script (you need to have bit and gmpy2 installed) can do the work in 2 seconds...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 ?
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13sXkWqtivcMtNGQpskD78iqsgVy9hcHLF
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CrunchyF
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October 11, 2022, 05:02:14 PM |
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Ok but a multiplication of what by what ?...sorry i d'ont understand
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j2002ba2
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October 12, 2022, 12:19:00 AM |
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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): 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.
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brainless (OP)
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October 12, 2022, 01:11:23 PM |
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Ok but a multiplication of what by what ?...sorry i d'ont understand for multiplication or halve the point (50k loop) 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"))
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13sXkWqtivcMtNGQpskD78iqsgVy9hcHLF
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NotATether
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In memory of o_e_l_e_o
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October 12, 2022, 04:01:45 PM |
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I have used PARI/GP C library The following is with the provided gp shell (some empty lines omitted): 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!
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. .BLACKJACK ♠ FUN. | | | ███▄██████ ██████████████▀ ████████████ █████████████████ ████████████████▄▄ ░█████████████▀░▀▀ ██████████████████ ░██████████████ █████████████████▄ ░██████████████▀ ████████████ ███████████████░██ ██████████ | | CRYPTO CASINO & SPORTS BETTING | | │ | | │ | ▄▄███████▄▄ ▄███████████████▄ ███████████████████ █████████████████████ ███████████████████████ █████████████████████████ █████████████████████████ █████████████████████████ ███████████████████████ █████████████████████ ███████████████████ ▀███████████████▀ ███████████████████ | | .
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brainless (OP)
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October 12, 2022, 06:10:51 PM |
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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): 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://bitcointalk.org/index.php?topic=5244940.msg57373246#msg57373246here is full list of numbers 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 1128228 1504304 2256456 3008608 4512912 6017216 9025824 18051648 107361793816595537 214723587633191074 322085381449786611 429447175266382148 644170762899573222 858894350532764296 1288341525799146444 1717788701065528592 2576683051598292888 3435577402131057184 5153366103196585776 6871154804262114368 10306732206393171552 15996907278672735013 20613464412786343104 31993814557345470026 47990721836018205039 63987629114690940052 67745291898271783847 95981443672036410078 127975258229381880104 135490583796543567694 174723607534414371449 191962887344072820156 203235875694815351541 255950516458763760208 270981167593087135388 349447215068828742898 383925774688145640312 406471751389630703082 511901032917527520416 524170822603243114347 541962335186174270776 698894430137657485796 767851549376291280624 812943502779261406164 1023802065835055040832 1048341645206486228694 1083924670372348541552 1397788860275314971592 1535703098752582561248 1625887005558522812328 2096683290412972457388 2167849340744697083104 2795577720550629943184 3071406197505165122496 3251774011117045624656 4193366580825944914776 4335698681489394166208 5591155441101259886368 6503548022234091249312 8386733161651889829552 10094048492842495793203 11182310882202519772736 13007096044468182498624 16773466323303779659104 20188096985684991586406 26033817522627741345901 30282145478527487379609 33546932646607559318208 40376193971369983172812 52067635045255482691802 60564290957054974759218 78101452567883224037703 80752387942739966345624 104135270090510965383604 110250596354215468384319 121128581914109949518436 156202905135766448075406 161504775885479932691248 208270540181021930767208 220501192708430936768638 242257163828219899036872 312405810271532896150812 323009551770959865382496 330751789062646405152957 416541080362043861534416 441002385416861873537276 484514327656439798073744 624811620543065792301624 646019103541919730764992 661503578125292810305914 833082160724087723068832 882004770833723747074552 969028655312879596147488 1249623241086131584603248 1323007156250585620611828 1666164321448175446137664 1764009541667447494149104 1938057310625759192294976 2499246482172263169206496 2646014312501171241223656 3528019083334894988298208 4998492964344526338412992 5292028625002342482447312 7056038166669789976596416 10584057250004684964894624 16427338856778104789263531 21168114500009369929789248 32854677713556209578527062 49282016570334314367790593 65709355427112419157054124 98564033140668628735581186 131418710854224838314108248 197128066281337257471162372 262837421708449676628216496 394256132562674514942324744 525674843416899353256432992 788512265125349029884649488 1051349686833798706512865984 1577024530250698059769298976 3154049060501396119538597952 341948486974166000522343609283189 683896973948332001044687218566378 1025845460922498001567030827849567 1367793947896664002089374437132756 2051690921844996003134061655699134 2735587895793328004178748874265512 4103381843689992006268123311398268 5471175791586656008357497748531024 8206763687379984012536246622796536 10942351583173312016714995497062048 16413527374759968025072493245593072 21884703166346624033429990994124096 32827054749519936050144986491186144 50950324559150734077829197783195161 65654109499039872100289972982372288 101900649118301468155658395566390322 152850973677452202233487593349585483 203801298236602936311316791132780644 215769495280698746329598817457692259 305701947354904404466975186699170966 407602596473205872622633582265561288 431538990561397492659197634915384518 611403894709808808933950373398341932 647308485842096238988796452373076777 815205192946411745245267164531122576 863077981122794985318395269830769036 1222807789419617617867900746796683864 1294616971684192477977592904746153554 1630410385892823490490534329062245152 1726155962245589970636790539661538072 2445615578839235235735801493593367728 2589233943368384955955185809492307108 3260820771785646980981068658124490304 3452311924491179941273581079323076144 4891231157678470471471602987186735456 5178467886736769911910371618984614216 6904623848982359882547162158646152288 9782462315356940942943205974373470912 10356935773473539823820743237969228432 13809247697964719765094324317292304576 18758639927001554244874997690913623113 20713871546947079647641486475938456864 32149654796824113203110223801196146591 37517279854003108489749995381827246226 41427743093894159295282972951876913728 56275919781004662734624993072740869339 64299309593648226406220447602392293182 75034559708006216979499990763654492452 96448964390472339609330671403588439773 112551839562009325469249986145481738678 128598619187296452812440895204784586364 150069119416012433958999981527308984904 192897928780944679218661342807176879546 225103679124018650938499972290963477356 257197238374592905624881790409569172728 300138238832024867917999963054617969808 385795857561889358437322685614353759092 450207358248037301876999944581926954712 514394476749185811249763580819138345456 600276477664049735835999926109235939616 771591715123778716874645371228707518184 900414716496074603753999889163853909424 1028788953498371622499527161638276690912 1200552955328099471671999852218471879232 1543183430247557433749290742457415036368 1800829432992149207507999778327707818848 2057577906996743244999054323276553381824 2795037349123231582486374655946129843837 3086366860495114867498581484914830072736 3601658865984298415015999556655415637696 5590074698246463164972749311892259687674 6172733720990229734997162969829660145472 8385112047369694747459123967838389531511 11180149396492926329945498623784519375348 11836701793937980728516123542966496184303 16770224094739389494918247935676779063022 22360298792985852659890997247569038750696 23673403587875961457032247085932992368606 33540448189478778989836495871353558126044 35510105381813942185548370628899488552909 44720597585971705319781994495138077501392 47346807175751922914064494171865984737212 67080896378957557979672991742707116252088 71020210763627884371096741257798977105818 89441195171943410639563988990276155002784 94693614351503845828128988343731969474424 134161792757915115959345983485414232504176 142040421527255768742193482515597954211636 178882390343886821279127977980552310005568 189387228703007691656257976687463938948848 268323585515830231918691966970828465008352 284080843054511537484386965031195908423272 378774457406015383312515953374927877897696 536647171031660463837383933941656930016704 568161686109023074968773930062391816846544 757548914812030766625031906749855755795392 1136323372218046149937547860124783633693088 1763668567296759128548902407902007931461147 2272646744436092299875095720249567267386176 3527337134593518257097804815804015862922294 5291005701890277385646707223706023794383441 7054674269187036514195609631608031725844588 10582011403780554771293414447412047588766882 14109348538374073028391219263216063451689176 21164022807561109542586828894824095177533764 28218697076748146056782438526432126903378352 42328045615122219085173657789648190355067528 56437394153496292113564877052864253806756704 84656091230244438170347315579296380710135056 112874788306992584227129754105728507613513408 169312182460488876340694631158592761420270112 338624364920977752681389262317185522840540224 36712202954417214842724336778420075919000906527493 73424405908834429685448673556840151838001813054986 110136608863251644528173010335260227757002719582479 146848811817668859370897347113680303676003626109972 220273217726503289056346020670520455514005439164958 293697623635337718741794694227360607352007252219944 440546435453006578112692041341040911028010878329916 587395247270675437483589388454721214704014504439888 881092870906013156225384082682081822056021756659832 1174790494541350874967178776909442429408029008879776 1762185741812026312450768165364163644112043513319664 2349580989082701749934357553818884858816058017759552 3524371483624052624901536330728327288224087026639328 5470118240208165011565926179984591311931135072596457 7048742967248105249803072661456654576448174053278656 10940236480416330023131852359969182623862270145192914 16410354720624495034697778539953773935793405217789371 21880472960832660046263704719938365247724540290385828 23165400064237262565759056507183067904889572018848083 32820709441248990069395557079907547871586810435578742 43760945921665320092527409439876730495449080580771656 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