Quote from: MrFreeDragon on September 28, 2019, 04:52:31 PM

Quote from: 57fe on September 28, 2019, 12:27:48 PM

Quote from: MrFreeDragon on September 27, 2019, 05:51:15 PM

By the way, where is the key for #105? It was released by 57fe 3 weeks ago (8Sep 19), but the key has not been published yet Huh

Not 3 weeks ago, 23th Sep 19 only.
#105 key is:
DEC: 29083230144918045706788529192435
HEX: 16f14fc2054cd87ee6396b33df3
WIFc: KwDiBf89QgGbjEhKnhXJuH7Lrcim5eBMkFQwQtRbW6wxT1ajoNqE

Thank you! I was wrong with the date. On the 8th of Sep there was release of #62 key.

57fe, how do you think, are there other possible private keys for the same #105? Have you any ideas how to find these "other" private keys?

There are two answers to your question.
1. No other private keys, if you mean the same public key (256 bits of X-coordinate plus one byte for parity of Y-coordinate and pubkey format). This is guaranteed by elliptic curve group structure. Each public point and corresponding coordinates are unique. It's true also for compressed pubkey.
2. Yes, huge amount of private keys, if you mean the same public address (160 bits, wallet address). Approximately there is must be 2^96 different private keys for each public address. This is provided by good statistical properties of SHA256 hash function, which was accurately tested by many cryptographers before this hash function was standardized, i'm sure. We must have unavoidable collisions for 256 bits space of input at rounding of SHA256 output to 160 bits. It is the reason for the creator of the puzzle to cancel problems from #161 to #255 some years ago, because if you can solve #160 by brute force means you can reveal privkey for any address in same time. It is not true for ECDLP, but ECDLP-race started only 4 month ago.

Nice question, thanks.
PS: nobody found collisions with known public address for secp256k1+SHA256 and similar schemes, it's equivalent to solving #160 by brute force. You can also found random, but useless collision by Pollard's rho or kangaroo methods, that equivalent to solve #255 with kangaroos. Yes, here is Pollard again. When the first case will be happened, BTC and all similar cryptocurrencies will be broken. Hopefully, we have only #63 solved right now, and no practical chances for #159 (#160 is occupied by kangaroos) without superquantum computer, which complexity growths even faster with each new qubit than the complexity of brute force, or we need something like Almanach from "Back to the Future" movie with published privkeys. Who knows what is more realistic.