The formalization of Ideal Money
Bitcoin is said to be an implementation of 'bitgold' which was a reference to this blogpost by Nick Szabo: https://unenumerated.blogspot.com/2005/1...
In this writing szabo is aiming to design something that has the property of what he describes as, 'unforgeable scarcity due to the costliness of their creation.'
To create this setup he references his formalization of a proof-of-work implementation based on his formalization of Intrapolynomial Cryptography:
https://www.fon.hum.uva.nl/rob/Courses/I...
[QUOTE=Szabo]I propose the following formalization:
f: {0,1}* --> {0,1}* is called a strong k-benchmark function
for machine model M and k>=1 if the following hold:
1. f is computable in O(p(n)) time on M, where p is a polynomial.
2. f does not shrink the input more than q(n,k), where q(n,k)
is a polynomial of degree k.
3. For every randomized algorithm A running on M in time
less than q(n,k)p(n), there exists an N such that for n > N
Pr[A(f(x)) = f^-1(f(x))] < 1/q(n,k)p(n)
In other words, there is no algorithm running faster than q(n,k)p(n) which can invert f for more than a negligibly small number of values.[/QUOTE]
My proposal for bit gold is based on computing a string of bits from a string of challenge bits, using functions called variously "client puzzle function," "proof of work function," or "secure benchmark function.". The resulting string of bits is the proof of work. Where a one-way function is prohibitively difficult to compute backwards, a secure benchmark function ideally comes with a specific cost, measured in compute cycles, to compute backwards.
The implementation however has an issue in regard to setting the level of costliness for pseudo/effective (ie cost inefficient) unforgeable scarcity. That is, rapid advances in Application-specific integrated circuit's or ASIC'S could dramatically affect the cost to forge. Szabo makes an interesting observation on this:
[QUOTE=Szabo]However, since bit gold is timestamped, the time created as well as the mathematical difficulty of the work can be automatically proven. From this, it can usually be inferred what the cost of producing during that time period was.[/QUOTE]
The idea is that because there are periods, you can observe how many bitgold units were mined or created in a given period, and 'assay' the value each bitgold unit comparatively and accordingly. ie if double the units were produced in a certain period compared to a previous period, those units should be worth only half as much as that previous period.
This external observation or 'rule' would standardize the cost to forge.
Here I am noticing that Szabo has introduced sigma notation with his periodic based observation. I'd like to observe this formula with respect to Satoshi's implementation with bitcoin...and invite the scrutiny of this group on the mathiness of my math.
1 Reply
This is maybe one or two subjects i have no clue about. You lost me after the first sentence.
But im not back to work still. And i feel up for learning what you are talking about. brb
