Topic: Why can't a private key be calculated from its address? - page 2. (Read 3059 times)

If you watch a video on a pen and paper SHA256 hash, it might become more clear. It's pretty neat.

Basically they did.  (although no one has been able to mathematically PROVE the
existence of one way functions). 

Hashing is a non reversible function.   Think of like this:  You can turn a cow into
hamburgers, but you cannot turn hamburgers into a cow.

Nope, that does explain Bitcoin. Each address represents around 2^96 possible private keys. It is believed to be computationally infeasible to generate a collision.

I hear the young ones like video, so Ill add this: http://media.ccc.de/browse/congress/2014/31c3_-_6369_-_en_-_saal_1_-_201412272145_-_ecchacks_-_djb_-_tanja_lange.html#video

http://arstechnica.com/security/2013/10/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/1/

The first few explanations gave me a conceptual idea, this explained everything. 

The examples given here are wrong and misleading.

The problem is not that it is not possible to compute the private key, because there is more than one solution (like in the case of abs() or the sum of numbers). The problem is that it is possible, in theory, to compute it, but the computation is so hard that it is practically infeasible.

Do not confuse asymmetrical cryptography with hashes. A hash is impossible to reverse, because many different inputs can result in the same output. (It's just that there is no easy way of finding all of them - or even any one of them.) A private key can be computed from the public one - but it is very, very hard - hard enough to be practically impossible.

For instance, if I ask you what is the product of 31 and 37, the answer is easy - 1147. But if I ask you what are the prime factors of 1147, that's a hard question. The easiest way to answer it is by trial and error - you try to divide 1147 by every prime number smaller than the integer part of its square root until you find a number that divides it exactly (the first such number is 31). When the numbers involved are very large it becomes practically impossible to answer such questions. (With large numbers there are faster methods than trial division, but they are still too slow to be practical.)

In his example, it is extremely easy to calculate not just one, but many and all the possible private keys of an address, with nearly the same difficulty of the reverse, it surely doesn't explain bitcoin at all.

His example does explain a lot to be honest , I personally got it
Thanks for the information Kazimir , really helpful

~ Madness

Any number of which the digits' sum is 43?

I don' think your example really explains why a btc private key (actually, as far as I know each address has something like 2^100 private keys), can't be calculated from the address.

Thanks for the response. I like mathematics but never studied too much of it. I would like to understand in more detail both about functions that can't be reversed and the ones which reversion is much harder than the original, where can I read about that?

And if it's possible to create a non-reversible function, then why didn't they do that with bitcoin?

Not all calculations are reversible. Suppose private keys and address work like this: private keys are long numbers, and addresses are the sum of all digits. Obviously a simplification, but just as an example.

So if you have private key = 134505719542, then you can easily calculate the address: 1+3+4+5+0+5+7+1+9+5+4+2 = 46.

Now I have another address: 43. What's the private key?

Because the "trapdoor" functions used in public key cryptography are designed with exactly that property.
In your question, the first implicit assumption is already wrong. If a function can be calculated, it does not necessarily follow that its inverse can be calculated with similar effort or can be calculated at all.
For example, the function "abs" returns the absolute value of its argument. Naturally, its inverse cannot be computed, because you don't know whether the original argument was positive or negative.
Other functions have a defined inverse but it's much harder to compute the inverse than computing the original function. Elliptic curve functions as used in bitcoin belong to this class, as well as the operations on large primes that are used in RSA public key crypto (Pretty Good Privacy).
"Much harder" in this case does not mean "requires a faster computer" but "impossible given the natural laws and available ressources of humankind."

Onkel Paul

If computers can calculate an address from its private key, then why can't they do the reverse and calculate a private key from an address?