SECP256K1 Bitcoin - Fully formed sequential group of blocks curve

[kreosan]

A fully formed sequential group of blocks secp256k1 is for sale, where A...F are private keys (k), G...J are public keys part 1 (x), and K...L are public keys part 2 (y).  
Group of blocks are formed sequentially with odd 'A' at an interval of 1.
Total number of blocks: 50. Price: 1 BTC.  

There is also the possibility to form the entire block based on a single private key (0.02 BTC per block) or any single public key without private keys (0.01 BTC per block).  

Demo (part of the block):
k (C): 4BB7B36F21ECB0D1F022E94A4CBC0447FC8D38ECC2BCFEDFBB0074F3651641BB
x (H): BFB810DED91B7B6B7B75D16D77BDAEA9C058B2221581FEAEB7B0E709CBC79AE3
y (K): 6A07EB895682E6FDB724888516F6BF469D9159E5F1B76A33B404DD58DDBD3BD5

k (D): B4484C90DE134F2E0FDD16B5B343FBB6BE21A3F9EC8BA15C04D1E9996B1FFF86
x (H): BFB810DED91B7B6B7B75D16D77BDAEA9C058B2221581FEAEB7B0E709CBC79AE3
y (L): 95F81476A97D190248DB777AE90940B9626EA61A0E4895CC4BFB22A62242C05A

k (E): B369C959CDEE340A885C4C47EF198513537F28A32BE2C3799E3B42C4F5FAC1C1
x (J): F2E25C0854A08991BF91DAE028A38DBE4E35341AB8C037915F2BDD8529DF8299
y (K): 6A07EB895682E6FDB724888516F6BF469D9159E5F1B76A33B404DD58DDBD3BD5

k (F): 4C9636A63211CBF577A3B3B810E67AEB672FB4438365DCC221971BC7DA3B7F80
x (J): F2E25C0854A08991BF91DAE028A38DBE4E35341AB8C037915F2BDD8529DF8299
y (L): 95F81476A97D190248DB777AE90940B9626EA61A0E4895CC4BFB22A62242C05A

Single block design:
k      x      y
------------------
A      G      K
B      G      L
C      H      K
D      H      L
E      J       K
F      J       L
------------------

[kTimesG]

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): ...

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.

[ekstremista]

I have absolutely no idea what is being discussed here. Somebody break it down for me dummy-style 

[kreosan]

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): ...

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 private keys)?

Single block design:
k        x        y
-------------------
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

[kreosan]

New block with small scalars in a group

k (A): 000000000000000000000000000024E76D35C791FE725652FEF636EF9BE3C9E0
x (G): 8C1EC1FA62ACEDDEF7F56692CAA89258A59D0B35F11964CFE65A724EE623BB54
y (K): 62B197CFCDF317F02A66E397C23D4164EADCA6DCA7ED8263198585F608752CAA

k (B): FFFFFFFFFFFFFFFFFFFFFFFFFFFFDB174D791554B0D649E8C0DC279D34527761[/b]
x (G): 8C1EC1FA62ACEDDEF7F56692CAA89258A59D0B35F11964CFE65A724EE623BB54
y (L): 9D4E6830320CE80FD5991C683DC2BE9B1523592358127D9CE67A7A08F78ACF85

pk (C): 000000000000000000000000000042CB78C4E2A2A699BB6D5E7601EFDB714950
gx (H): 7554E357693B95B3825235CA10DCBE52E0BEC4A676C7EC2CFA850903809E6513
gy (K): 62B197CFCDF317F02A66E397C23D4164EADCA6DCA7ED8263198585F608752CAA

k (D): FFFFFFFFFFFFFFFFFFFFFFFFFFFFBD3341E9FA4408AEE4CE615C5C9CF4C4F7F1
x (H): 7554E357693B95B3825235CA10DCBE52E0BEC4A676C7EC2CFA850903809E6513
y (L): 9D4E6830320CE80FD5991C683DC2BE9B1523592358127D9CE67A7A08F78ACF85

k (E): 000000000000000000000000000067B2E5FAAA34A50C11C05D6C38DF77551330
x (J): FE8C5AAE34177C6D85B863A3247AAF5479A43023981EAF031F2084AB993DD7F7
y (L): 9D4E6830320CE80FD5991C683DC2BE9B1523592358127D9CE67A7A08F78ACF85

k (F): FFFFFFFFFFFFFFFFFFFFFFFFFFFF984BD4B432B20A3C8E7B626625AD58E12E11
x (J): FE8C5AAE34177C6D85B863A3247AAF5479A43023981EAF031F2084AB993DD7F7
y (K): 62B197CFCDF317F02A66E397C23D4164EADCA6DCA7ED8263198585F608752CAA

Single block design:
k      x      y
------------------
A      G      K
B      G      L
C      H      K
D      H      L
E      J       K
F      J       L
------------------

[JackMazzoni]

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): ...

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