Public Key or RIPEMD160, which has more relation

[WanderingPhilospher]

Just a silly question, because that's what I do.

Below examples are abbreviated for brevity.  All 4 examples are different private keys.

Let's say you have pubkeys (minus the 04, 02, or 03):

d769fa21825b....  priv key w
d769fa21a104....  priv key x

and two RIPEs:

f037a6296d81...  priv key y
f037a6291034...  priv key z

Which two have more ec math properties, or more relational to each other?

The pubkeys because they are directly related to k*G, or the RIPES which are a result of k*G, a sha256, and then RIPEMD'd?

Since both pubkeys start with d769fa21, what relation is there, if any?

Same for the RIPEs, any relation?

Maybe nothing, zero relation. What say you?

[1714619234]

1714619234

[1714619234]

1714619234

[1714619234]

1714619234

[1714619234]

1714619234

[pooya87]

There is no relationships between any of them and they all have the same security. There is a massive space of 256 bit for private/public keys and a 160-bit space for HASH160 digests that can have some equal bits at some positions (like fist dozen bits being equal).

Take these 2 addresses for example, they have the same initial 13 bits

Code:

1Kr72ToFFj8sa6GwSnNWeJMfDjDPGepSLv (cebbad02e5441f3385e6ef9fe8679cfd6a75fa0c)
1Kr7USMAgMo7fcPSWsQ7kGL12V3u4sNtjV (cebc0cb7035c895abc286af83595f191e67c44d3)

[WanderingPhilospher]

There is no relationships between any of them and they all have the same security. There is a massive space of 256 bit for private/public keys and a 160-bit space for HASH160 digests that can have some equal bits at some positions (like fist dozen bits being equal).

Ok, what about the pubkeys?  Any of the bits have to be equal to get first 10 or so digits to be the same?

[NotATether]

Ok, what about the pubkeys?  Any of the bits have to be equal to get first 10 or so digits to be the same?

The very act of hashing destroys any relation there could have been with inputs, no matter what the hashing algorithm is.

As for the public keys, if you write them in hex format (nobody really writes pubkeys in base10), then the relevant bits being the same will make that particular hex char the same, but base16 and binary don't translate well into decimal so trying to find mathematical relations between the two using bitwise operations alone is futile.

[o_e_l_e_o]

There is no relation between private keys which have similar characters, public keys which have similar characters, addresses which have similar characters, or any subset thereof.

Here are two random private keys which differ by only 1:

Code:

02D615E2968401894AB0704E3B71E3C125F9B9A0C7ED3EDC204E1A0954B3E5C0
02D615E2968401894AB0704E3B71E3C125F9B9A0C7ED3EDC204E1A0954B3E5C1

And here are the two compressed public keys they generate:

Code:

029b438064a9e91a868390ed5cb9a66a6141141bc365f9cc064a8d1313426aa7a6
033bc0203bf01ccd77477a14aded37b489ca66d959bec40b90b3ec408a95a3db0c

As you can see, even a tiny different in the private keys results in such a difference in the public keys that they might as well be any two public keys - there is no clear link between them whatsoever.

Now, let's take the first public key from above, and a second public key which is simply n+1 of that public key:

Code:

029b438064a9e91a868390ed5cb9a66a6141141bc365f9cc064a8d1313426aa7a6
029b438064a9e91a868390ed5cb9a66a6141141bc365f9cc064a8d1313426aa7a7

And let's derive the two addresses these public keys generate:

Code:

1A4dJjJH3LYX6HZwujjQXCWpni2p3ZNRSr
1NUhDqSFqwkLFcZfdaCaB366J5KY7b842n

So again, as you can see, a tiny change in the public key results in two addresses which are completely different.

And the reverse is similarly true - any addresses which do happen to have several characters the same will have public and private keys with no obvious relation to each other.

[WanderingPhilospher]

Understood. I was just curious, without having to dig to deep and do a bunch of math. I asked because in my trips around the curve, I have found keys with some leading matching pubkey and RIPE bits.  Pubs had like 20 or 24 matching bits and RIPEs had 8 or 12 matching bits. I found it interesting and was curious. Thanks for the replies.