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1  Bitcoin / Development & Technical Discussion / Re: BASE58 (P2SH) vs BECH32 (P2WPKH) on: January 04, 2020, 06:14:26 PM
Sorry I have been offline for a while....

Just my humble visual summary:

best regars
2  Bitcoin / Development & Technical Discussion / Re: SHA256 output as mathematical function of input? on: November 04, 2019, 06:32:32 PM
Thanks for replies, suggestions, and @aliashraf for the "merit".. really appreciated

and sorry for me being late, but I'm involved in a lot of stuff lately

I was thinking that -as underlined by aliashraf- the general problem for sure is huge (stated it seems to still rest unsolved), but I'm in some way confident "that reduction" perhaps could be less impossible Tongue if we consider the mining problem...

I mean, if -for sake of simplicity- we consider:

  • a fixed order of transactions in the block (so fixed merkle root)
  • no misuse of timestamp and version fields from their original meaning

then the only remaining  freedom degrees are the nonce's 32 bits.. still many but not the whole 640 bit header

Ok ok, I know the block hash is the SHA256 applied TWO TIMES to the block header, nevertheless the "whole function" would still apply to just 32 bits input...

And for the PoW we "only" need the beginning 0s, so we would not be interested in all the 256 bits outputs (so we would handle a smaller vector function/system)

When I'll have time I'll try to write a symbolic SHA256 able to mill the numbers and to pass-through variables.. just to check what happen....

..but it won't be soon , for sure  Sad  Grin
3  Bitcoin / Development & Technical Discussion / Re: SHA256 output as mathematical function of input? on: October 25, 2019, 05:14:59 PM
If I understand correctly your question, what you are asking is if it is actually possible to break the POW Bitcoin algorithm, using a mathematical function to find the nonce to be used in the block header, instead of random guesses, to get the desidered hash value. 
Then I second your request, as a bitcoin enthusiast (and might be investor), but I have a very strong feeling the answer is NO.

Well "to break" maybe is too strong  Grin  let's say I'm interested in SHA256 analysis:

- to understand what makes an HASH effective against collisions

- to understand if its computation can be optimized in particular circumstances.. a sort of new ASICboost-like optimization let's say

I think the first step is to write SHA256 in an alternative form.. algebraical? over which field? as set of relations in graph-db? I don't' know.. I just wanted to explore if someone has already thought about it too
4  Bitcoin / Development & Technical Discussion / Re: SHA256 output as mathematical function of input? on: October 23, 2019, 03:02:41 PM
interesting replies, thank you very much

So, you have restated the problem as:

"per-output-bit" mathematical formula/equation could exist (maybe in the form of a vectorial function to calculate all the output bits at the same time as well), but it would be as long and difficult to be expressed as the number of inputs increase (aka length of hashed string)

and that as... as... wouldn't be polynomial, but exponential  at least...

from an algorithmic point of view this complexity explosion comes from the recursive nature of SHA256 over unbound input... that's why I'm wondering if in your opinion (but I guess the answer is "no"  Sad ) any in-some-way-cyclic mathematical operator like Series or Infinite Products (or something else, maybe in a superset of binary field) could introduce any reduction in formulas, or if you know if this idea has ever been explored.

5  Bitcoin / Development & Technical Discussion / Re: SHA256 output as mathematical function of input? on: October 20, 2019, 09:44:41 AM
Thank you everybody replying, and sorry to:

- have originally posted in the wrong forum section (Mining)

- haven't been clear enough

what I was trying to say was:

given SHA256 output bits: O_1, O_2, ..., O_256
and input bits: I_1, I_2, ..., I_n

is it possible to obtain:

O_1 = f1(I_1, I_2, ..., I_n)
O_2 = f2(I_1, I_2, ..., I_n)
O_256 = f256(I_1, I_2, ..., I_n)

where the f* functions are math equations and not algorithms?
I mean, for example, given x,y belonging to [0,1]:

XOR = x(1-y)+y(1-x)
AND = xy
OR = x+y-xy
NOT = 1-x

but I don't know for shifts, rotations, mod-additions...

I'm also thinking if recursive structure of SHA256 (deriving from input being unbounded) can -in some way- be substituted by Series, Infinite Product, or other math stuff like that

And maybe considering operators working on binary field is not the best choice, in the same sense complex numbers are sometimes easier to work with than real numbers even when both math function domain and codomain are real.

I'm thinking about those things because I wonder if this "mapping" of SHA256 algorithm into math objects with more workable properties could permit easier hash analysis and optimizations in its computation

Thanks everybody

6  Bitcoin / Development & Technical Discussion / SHA256 output as mathematical function of input? on: October 17, 2019, 03:26:34 PM
Hi everybody! Is it possible to express SHA256 output bits as MATHEMATICAL function of input bits?
If so, which is the minimum subset of needed mathematical operators? Over which numeric set (e.g. Real or Complex field instead of binary to exploit more freedom degrees)?  Any news about it already out there on the Internet?

7  Bitcoin / Development & Technical Discussion / Re: Difference between SegWit addresses on: October 14, 2019, 10:05:19 PM
Hi everybody!

while studying addresses types and locking/unlocking scripts I ended up with an hand-written messy cheatsheet... I've gotten a PDF from it, hope it can helps!
8  Other / Meta / Re: Stake your Bitcoin address here on: October 13, 2019, 03:30:57 PM
This is baro77 from bitcointalk and today is October 13, 2019
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