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.
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.
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