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Showing 7 of 7 results by Pythagoras33
Why waste so much electricity with the brute force attack when you just need to solve a simple mathematical problem? 
https://decrypt.co/59340/ancient-bitcoin-whale-just-moved-5-million
https://decrypt.co/59340/ancient-bitcoin-whale-just-moved-5-million
But isn't he the seller of this video? I remember when he sold me 10 bitcoins for 2 euros and 50 cents
https://www.youtube.com/watch?v=YmPg4V-YE0k
https://www.youtube.com/watch?v=YmPg4V-YE0k
Re: One Trillion dollars maektcap: How dose it escalates technical challenges.
What kind of technological challenges are you referring to?
Those hundreds of millions with of value spread out in a block's transactions are unmodifiable by the miner who mines it, because they do not have the private keys to them...
Those hundreds of millions with of value spread out in a block's transactions are unmodifiable by the miner who mines it, because they do not have the private keys to them...
The private key is becoming less and less private...
https://billatnapier.medium.com/ecdsa-revealing-the-private-key-from-four-signed-message-two-keys-and-shared-nonces-secp256k1-5758f1258b1d
Re: Elliptic Curve Cryptography and Government Backdoors
This is to highlight the fact that compared to 10 years ago the ECC algorithm presents worrying vulnerabilities.
nonsense.
this is not a vulnerability in elliptic curve cryptography. it is a weakness in some of the bad implementations of it created by bad developers. it is not even about ECC, it is about RNG.
it also has nothing to do with what your title suggests.
the standard for ECC clearly states that k must be chosen randomly. when an implantation like blockchain.info decides to use a weak one or use a crazy option such as random.org that's not the algorithm's flaw!
Dual_EC_DBRG, the random number generator OP is talking about, isn't even used by default by anyone except for some obscure RSA corp library (and that's only because NSA bribed them to do it). Not that it means anything because everybody else is either using a hash-based, HMAC-based or the block cipher based RNG, none of which have the flaw.
In Satoshi Nakamoto's day there were no vulnerabilities like the MOV Attack
https://asecuritysite.com/encryption/mir_mov
https://asecuritysite.com/encryption/mir_mov
This only works if you have a second point from a generator point different from G that has the same group order as secp256k1. Since bitcoin doesn't bother with using different generator points this attack can't be done.
If you create such a backdoor then it is likely that the encryption algorithm you have chosen is a backdor as well. I am not a mathematician but the solution to the problem of the elliptic curve can be solved even by a student in the first year of high school.
https://www.aimath.org/news/congruentnumbers/ecconnection.html#:~:text=Congruent%20numbers%20naturally%20lead%20to,%2Bb2%3D%20c2.&text=It%20is%20possible%20to%20describe%20all%20Pythagorean%20triples%20by%20a%20formula.
Re: Elliptic Curve Cryptography and Government Backdoors
This is to highlight the fact that compared to 10 years ago the ECC algorithm presents worrying vulnerabilities.
nonsense.
this is not a vulnerability in elliptic curve cryptography. it is a weakness in some of the bad implementations of it created by bad developers. it is not even about ECC, it is about RNG.
it also has nothing to do with what your title suggests.
the standard for ECC clearly states that k must be chosen randomly. when an implantation like blockchain.info decides to use a weak one or use a crazy option such as random.org that's not the algorithm's flaw!
In Satoshi Nakamoto's day there were no vulnerabilities like the MOV Attack
https://asecuritysite.com/encryption/mir_mov
Re: Elliptic Curve Cryptography and Government Backdoors
Assuming that the attacker generated the constants used in Dual EC pseudorandom number generator it has been known for several years that an attacker generating these constants and seeing a long enough stretch of Dual EC output bits can predict all future outputs. This could be a problem since in the very early days of Bitcoin it was common to pay to public keys (P2PK) directly?
References
https://projectbullrun.org/dual-ec/documents/dual-ec-20150731.pdf
https://services.math.duke.edu/~bray/Courses/89s-MOU/2016/Papers/BAS_Paper3_EllipticCurveCryptography.pdf
https://www.youtube.com/watch?v=-UcCMjQab4w
References
https://projectbullrun.org/dual-ec/documents/dual-ec-20150731.pdf
https://services.math.duke.edu/~bray/Courses/89s-MOU/2016/Papers/BAS_Paper3_EllipticCurveCryptography.pdf
https://www.youtube.com/watch?v=-UcCMjQab4w
@Pythagoras33 for what purpose did you publish it?
This is to highlight the fact that compared to 10 years ago the ECC algorithm presents worrying vulnerabilities.
https://github.com/tintinweb/ecdsa-private-key-recovery
Assuming that the attacker generated the constants used in Dual EC pseudorandom number generator it has been known for several years that an attacker generating these constants and seeing a long enough stretch of Dual EC output bits can predict all future outputs. This could be a problem since in the very early days of Bitcoin it was common to pay to public keys (P2PK) directly?
References
https://projectbullrun.org/dual-ec/documents/dual-ec-20150731.pdf
https://services.math.duke.edu/~bray/Courses/89s-MOU/2016/Papers/BAS_Paper3_EllipticCurveCryptography.pdf
https://www.youtube.com/watch?v=-UcCMjQab4w
References
https://projectbullrun.org/dual-ec/documents/dual-ec-20150731.pdf
https://services.math.duke.edu/~bray/Courses/89s-MOU/2016/Papers/BAS_Paper3_EllipticCurveCryptography.pdf
https://www.youtube.com/watch?v=-UcCMjQab4w