Quote from: 247casino on November 26, 2014, 09:27:06 PM

Quote from: Addition on November 26, 2014, 01:56:12 PM

Quote from: Vessko on November 26, 2014, 09:31:34 AM

This is conspiracy theory bullshit written by somebody with no clue in mathematics, number theory, primality testing, cryptography and so on.

Yes, the prime numbers distribution is not random and Ulam spirals are real but they are nothing more than a curious pattern with no practical applications. There is no magic formula that will yield simultaneously a) only primes, b) all primes and c) different primes every time without some kind of brute force testing.

There are many polynomials that yield primes more often than usual - but they yield composites too and the primes they yield are not unique. One of the best known ones was invented by Euler: k ^ 2 + k + 17; it yields 16 different primes as k takes values from 0 to 15 inclusive. An even better one is 36 * k ^ 2 - 810 * k + 2763; it yields 45 different primes when k takes values from 0 to 44 inclusive. The existence of such polynomials is the reason why primes form "patterns" when put in a grid on a plane - because in analytical geometry, lines and curves on the plane are expressed with polynomials.

If you relax the requirement to get only primes, it is trivial to come up with a polynomial that would yield all possible primes. For instance 6 * k +/- 1 yields every prime greater than 3.

The sieve of Eratosthenes is a rather inefficient algorithm for primality testing and prime number generation; it is useless for anything but relatively small numbers and it does use brute force. It is just better than trial division - but only clueless idiots use trial division for primality testing. From what I can see in the PyPrimes code, Croft spirals (or Adoni spirals or whatever) is just a variant of the formula I've given above, only it sieves out the multiples of 2, 3, 5, 7, 11, 13, 17, 19 and 29, instead of just 2 and 3 as the formula above does. It might be marginally faster than Eratosthenes's sieve for small numbers but is utterly useless for sufficiently large primes.

The author obviously is too clueless to understand the much more complex algorithms like Miller-Rabin, or NFS.

That said, how exactly the NIST elliptic curves are picked is a concern and I personally don't trust Elliptic Curve Encryption - but that's only because I don't have a sufficiently good understanding of it (while I do understand and prefer RSA encryption). But nobody forces you to use the NIST curves. You can easily pick different ones and still use EC-based cryptography.

And, of course, all this has nothing to do with Bitcoin or with the cryptographic hash functions in general.

...as per opening statement?

I'm not a mathematician, I'm a geologist. Just posted this simply as topical subject matter, that's what these forums are for, right?

Been a supporter of Blockchain technology for almost 2 years, and fortunately may have more BTC than most. With that, there are also many other investors that visit these forums. Personally I do fear at times for the security of private keys and just wanted to know if there was any mathematical premise for PNC, as to decryption?

Apologies, as it appears to have summoned emotive negativity for some of you folk.

I'm just after an explanation that confirms that this is impossible and why.

Dude you're talking to NSA shills here, you know that right.

haha

NSA created bitcoin and it is back doored

ECC is backed doored by using seed keys created on the same prime spiral that was exposed in 1995 by Dr. Sol Adoni

So listen to the NSA bots here, they give you bogus info, the seeds are corrupt as the Snowden docs revealed

CORRUPT KEYS destroyed ECC

Bitcoin uses ECC

Any ECC can be back doored due to understanding how the seed keys lie on the same spiral, so that relationship is what they use to create bad seed keys

DUH

Appreciate everyone's input, so thanks - but I sincerely hope you are wrong on this one!!

Thus far, no one has given me any proof. What I would need to see in order to believe is;

- Someone finding a Wallet on the Blockchain with say 50BTC;

- Then hitting the "Request Funds" button;

- Running their Software "backdoor" (prime-base, 8 prime spiral based) decryption program;

- Withdrawing the funds to another Wallet.

Until I see that, I say SHA256 Bitcoin is secure/unhackable