If it works how I understand it does, getting the right combination of substances is probably just a matter of solving a linear programming problem.
As I understand the explanations, the basic measurement is obtained by illuminating the coin with light of wavelength λ_1, and measuring the intensity coming back of another wavelength λ_2 - let c be a putative coin, and I_c_{λ_1}_{λ_2} be the measurement. To detect a valid coin, the machine has a set of n standard values for a real coin 'C' at a range of (λ_1, λ_2) pairs I_C_{λ_1_i}_{λ_2_i} for i in [1, n].
To pass, a coin c has to match within a tolerance, i.e. for all i in [1, n], |I_C_{λ_1_i}_{λ_2_i} - I_c_{λ_1_i}_{λ_2_i}| < ε.
I am assuming that the set of I_C_{λ_1_i}_{λ_2_i}, and the (λ_1_i, λ_2_i) values will be public knowledge, because they are needed by privately manufactured machines working with coins.
The aim of a counterfeiter is to find substances s_j and the concentrations in which to mix in α_j for j in 1..l (to a base that has no fluorescence), so that the mixture c passes the intensity tests within tolerance. If we assume the substances do not affect each other significantly, then we can expect that
Using an off the shelf spectrofluorometer (or even a modified coin reader) a counterfeiter could obtain the I_s_{λ_1_i}_{λ_2_i} for a wide variety of substances s, which can be normalised to be per unit of concentration.
Given a bank of substances s_j for i in 1..l (the counterfeiter can choose an l that is large enough to make the attack work), with known I_{s_j}_{λ_1_i}_{λ_2_i} values, it is easy to solve for a least squares concentrations vector α. Let A be an l by n vector such that A_ij = I_norm_{s_j}_{λ_1_i}_{λ_2_i}. Let y be the column vector such that y_i = I_C_{λ_1_i}_{λ_2_i}.
Let t(A) denote the transpose of vector A. Using the simplex algorithm, solve t(A)y = t(A)A \hat{α}, subject to all concentrations being greater than or equal to zero, yielding the least squares solution \hat{α}. If the result is within tolerance, the counterfeiter has a viable solution, if not they need a larger or different pool of starting substances.
In practice, they might want to reduce the number or cost of substances they use. They could use an optimisation method such as a genetic algorithm to find the lowest cost set (taking into account set size and the price of substances) that results in an acceptable \hat{α} solution.
Of course, these coins are fairly low value, and in practice counterfeiting the coins might not be that profitable anyway given the low value of the coins and the amount of labour needed to get any significant amount of real currency in exchange for the coins without detection, so someone capable of making a counterfeit might be able to use their skills more profitably elsewhere.
I think the problem is chemistry, not math. If you don't start with phosphors with the right behavior, you can't combine them to get the result you want.
Specifically, the math breaks down at "subject to all concentrations being >= 0". This is exactly the same reason you can't generate all visible colors from RGB or CMY (http://en.wikipedia.org/wiki/Gamut) - there are colors outside the linear combination of the starting values. And the problem is much worse here, because the number of dimensions is much greater than three. (You also have to assume the mint will watch purchases of the necessary phosphors.)
However because this new coin is being touted as very secure and not falsifiable, people may not catch on to the fact that you are counterfeiting the coins, because they might just assume that they cannot be counterfeited. So perhaps counterfeiting the coins would actually end up being profitable in the end.
Also, it might even make counterfeit coin production cheaper if it replaces rather than supplements current detection methods - maybe a counterfeiter can make a plastic or wooden coin of roughly the right shape and paint it with a paint containing the appropriate mixture, and then trick a vending machine into giving them non-counterfeit change.
Usual weight, magnetic and maybe inductance tests apply.
I also wonder about someone's ability to take slices of the surface of a coin and spread that out over other cheaper coins. I guess you have to randomize the test, or make sure it covers more than just a couple predictable spots on the coin.
I would guess the I_C_{λ_1_i}_{λ_2_i} and (λ_1_i, λ_2_i) will be protected by some sort of security by obscurity, and coin reader manufacturers will only be given the info if they comply with some sort of security process and make it hard to extract the info from a coin reader. Probably just a way of making it harder to reverse engineer, not impossible.
The method of reading described in the patents is reading the emissions from the coin after the light source is turned off. So a counterfeit would have to match the specific absorption/emission profile of the original - I think this makes counterfeiting many levels of magnitude harder.
As I understand the explanations, the basic measurement is obtained by illuminating the coin with light of wavelength λ_1, and measuring the intensity coming back of another wavelength λ_2 - let c be a putative coin, and I_c_{λ_1}_{λ_2} be the measurement. To detect a valid coin, the machine has a set of n standard values for a real coin 'C' at a range of (λ_1, λ_2) pairs I_C_{λ_1_i}_{λ_2_i} for i in [1, n].
To pass, a coin c has to match within a tolerance, i.e. for all i in [1, n], |I_C_{λ_1_i}_{λ_2_i} - I_c_{λ_1_i}_{λ_2_i}| < ε.
I am assuming that the set of I_C_{λ_1_i}_{λ_2_i}, and the (λ_1_i, λ_2_i) values will be public knowledge, because they are needed by privately manufactured machines working with coins.
The aim of a counterfeiter is to find substances s_j and the concentrations in which to mix in α_j for j in 1..l (to a base that has no fluorescence), so that the mixture c passes the intensity tests within tolerance. If we assume the substances do not affect each other significantly, then we can expect that
I_c_{λ_1_i}_{λ_2_i} = Σ_{j=1}^l α_j I_norm_{s_j}_{λ_1_i}_{λ_2_i}.
Using an off the shelf spectrofluorometer (or even a modified coin reader) a counterfeiter could obtain the I_s_{λ_1_i}_{λ_2_i} for a wide variety of substances s, which can be normalised to be per unit of concentration.
Given a bank of substances s_j for i in 1..l (the counterfeiter can choose an l that is large enough to make the attack work), with known I_{s_j}_{λ_1_i}_{λ_2_i} values, it is easy to solve for a least squares concentrations vector α. Let A be an l by n vector such that A_ij = I_norm_{s_j}_{λ_1_i}_{λ_2_i}. Let y be the column vector such that y_i = I_C_{λ_1_i}_{λ_2_i}.
Let t(A) denote the transpose of vector A. Using the simplex algorithm, solve t(A)y = t(A)A \hat{α}, subject to all concentrations being greater than or equal to zero, yielding the least squares solution \hat{α}. If the result is within tolerance, the counterfeiter has a viable solution, if not they need a larger or different pool of starting substances.
In practice, they might want to reduce the number or cost of substances they use. They could use an optimisation method such as a genetic algorithm to find the lowest cost set (taking into account set size and the price of substances) that results in an acceptable \hat{α} solution.
Of course, these coins are fairly low value, and in practice counterfeiting the coins might not be that profitable anyway given the low value of the coins and the amount of labour needed to get any significant amount of real currency in exchange for the coins without detection, so someone capable of making a counterfeit might be able to use their skills more profitably elsewhere.