Tuesday, June 29, 2010
JSH: Integer factorization IS the short-cut
Intriguingly enough my research results studying the simple system of:
f_1 = a_1*k mod N thru f_m = a_m*k mod N
indicate that integer factorization IS itself the key to modular arithmetic, so what I called surrogate factoring is in retrospect the way modular arithmetic operates.
The result I recently posted showing a way to solve discrete logarithms is amazing for its compactness but also for what it may indicate about the power of knowledge: not knowing how modular arithmetic works at a deep level, certain things that may be easy, appear hard.
That result actually may eliminate the value of a large m, with k^m = q mod N, allowing one to easily handle it by simply cancelling out much of m with a simple technique equivalent to having a certain number of the a's equal to k^{-1} mod N.
I'll be looking at replies with interest. One of the problems with knowledge is when people reject it because, well, because they don't like it!!!
That creates huge problems on a world-wide scale.
Quite simply, people refuse solutions to problems, bad things happen, people get upset, but, they refuse solutions to problems!
It's a HUGE issue. So far the problem has been intractable.
Human beings seem to love misery. I'm not sure why. But make no mistake, the human animal often works very hard to NOT solve its problems, preferring often instead to whine about them, but refusing to solve them.
That may be built into the human genome. The reasons are complex.
f_1 = a_1*k mod N thru f_m = a_m*k mod N
indicate that integer factorization IS itself the key to modular arithmetic, so what I called surrogate factoring is in retrospect the way modular arithmetic operates.
The result I recently posted showing a way to solve discrete logarithms is amazing for its compactness but also for what it may indicate about the power of knowledge: not knowing how modular arithmetic works at a deep level, certain things that may be easy, appear hard.
That result actually may eliminate the value of a large m, with k^m = q mod N, allowing one to easily handle it by simply cancelling out much of m with a simple technique equivalent to having a certain number of the a's equal to k^{-1} mod N.
I'll be looking at replies with interest. One of the problems with knowledge is when people reject it because, well, because they don't like it!!!
That creates huge problems on a world-wide scale.
Quite simply, people refuse solutions to problems, bad things happen, people get upset, but, they refuse solutions to problems!
It's a HUGE issue. So far the problem has been intractable.
Human beings seem to love misery. I'm not sure why. But make no mistake, the human animal often works very hard to NOT solve its problems, preferring often instead to whine about them, but refusing to solve them.
That may be built into the human genome. The reasons are complex.
# posted by James Harris @ 23:35 
