Quote from: divine_core on January 30, 2014, 05:57:44 AM

I don't understand. SHA-256 has nothing to do with computing Euler's totient function, and neither does computing the GCD (well, you can use it to compute the totient function, but it's not the most efficient way). And I'm not sure how you'd use the totient function as a proof-of-work.

I was reading an article on entropy problems concerning public keys and was wondering if the algorithm would work better with RSA. Eurler's totient fuction came to mind as I have been looking more into phi's relationship to scalar and vector fields and had an idea is all. Clip from the article is below.

"If the initial seed to the pseudorandom number generator is generated with low entropy, this could result in multiple devices generating different moduli which share the prime factor p and have different second factors q. Then both moduli can be easily factored by computing their GCD: p = gcd(N1, N2).

OpenSSLs RSA key generation functions this way: each time random bits are produced from the entropy pool to generate the primes p and q, the current time in seconds is added to the entropy pool. Many, but not all, of the vulnerable keys were generated by OpenSSL and OpenSSH, which calls OpenSSLs RSA key generation code.

Computing the GCDs of all pairs of keys

If any pair of RSA moduli N1 and N2 share, say, the same prime factor p in common, but have different second factors q1 and q2, then we can easily factor the moduli by computing their greatest common divisor. On my desktop computer, computing the GCD of two 1024-bit RSA moduli took about 17µs.

For the mathematically inclined, Ill explain how we were able to use this idea to factor a large collection of keys.

The simplest way that one might try to factor keys is by computing the GCD of each pair of RSA moduli. A back of the envelope calculation shows that doing a GCD computation for all pairs of moduli in our data sets would take 24 years of computation time on my computer."

Here is a link that explains in part why i brought up the subject http://en.reddit.com/r/crypto/comments/1l886l/some_thoughts_on_proofofwork_systems/