Re: SECP256K1 Bitcoin - Fully formed sequential group of blocks curve
There is also the possibility to form the entire block based on a single private key (0.2 BTC per block) or any single public key without private keys (0.05 BTC per block).
Demo (part of the block): ...
Demo (part of the block): ...
Why would one pay 50 BTC for a script that simply multiplies a scalar key by lambda endomorphism, and curve point field elements by beta endomorphism (for X) and subtracts Y from field prime / negates the key?
Sorry to ruin your secret.
Hi! Well, a full 50 BTC? That definitely wasn’t my offer )) I discovered Lambda myself without even realizing that it had already been discovered before me. )
I didn’t quite understand how you use the lambda endomorphism to obtain the entire group without private keys...
How about this kind of block (full with pk)?
Single block design:
pk gx gy
-------------------
A 27 K
B 27 L
C H K
D H L
E J K
F J L
-------------------
27+H+J=p
https://e.radikal.host/2025/03/06/2999bdf922e54c1d3.png
I also discovered it myself. but without private key. Uncompressed public key: 042f8bde4d1a07209355b4a7250a5c5128e88b84bddc619ab7cba8d569b240efe4d8ac222636e5e 3d6d4dba9dda6c9c426f788271bab0d6840dca87d3aa6ac62d6
Three x values:
x1 = 21505829891763648114329055987619236494102133314575206970830385799158076338148
x2 = 23285849548026170226712523888619559634478006467037872208296602441247713932904
x3 = 71000409797526377082529405132449111724689844884027484860330595767503044400611
Two y values:
y1 = 98003708678762621233683240503080860129026887322874138805529884920309963580118
y2 = 17788380558553574189887744505607047724243097342766425233927699087598871091545
Enter private key for (x1, y1) = (21505829891763648114329055987619236494102133314575206970830385799158076338148, 98003708678762621233683240503080860129026887322874138805529884920309963580118): 5
Six public keys with private keys:
Public key 1: 042f8bde4d1a07209355b4a7250a5c5128e88b84bddc619ab7cba8d569b240efe4d8ac222636e5e 3d6d4dba9dda6c9c426f788271bab0d6840dca87d3aa6ac62d6 [Private key: 5]
Validated: k1 matches
Public key 2: 04337b52e3acda49dff79f54fbccb94671a045693ee0d097cc138c694695a83668d8ac222636e5e 3d6d4dba9dda6c9c426f788271bab0d6840dca87d3aa6ac62d6 [Private key: 72798312578463789091060122408687194401800723498338030560477939572921828405753]
Validated: k2 matches
Public key 3: 049cf8cecf391e958cb2ac03df28ea6865772f120342cdcd7c20cac14eb816d5e3d8ac222636e5e 3d6d4dba9dda6c9c426f788271bab0d6840dca87d3aa6ac62d6 [Private key: 42993776658852406332510862600000713451036840780736873822127223568596333088579]
Validated: k3 matches
Public key 4: 042f8bde4d1a07209355b4a7250a5c5128e88b84bddc619ab7cba8d569b240efe42753ddd9c91a1 c292b24562259363bd90877d8e454f297bf235782c459539959 [Private key: 115792089237316195423570985008687907852837564279074904382605163141518161494332]
Validated: k4 matches
Public key 5: 04337b52e3acda49dff79f54fbccb94671a045693ee0d097cc138c694695a836682753ddd9c91a1 c292b24562259363bd90877d8e454f297bf235782c459539959 [Private key: 42993776658852406332510862600000713451036840780736873822127223568596333088584]
Validated: k5 matches
Public key 6: 049cf8cecf391e958cb2ac03df28ea6865772f120342cdcd7c20cac14eb816d5e32753ddd9c91a1 c292b24562259363bd90877d8e454f297bf235782c459539959 [Private key: 72798312578463789091060122408687194401800723498338030560477939572921828405758]
Validated: k6 matches