So Bitcoin has 21,000,000.00000000 in existence. How does someone determine how many zeros are placed behind it? Could someone make an asset that has 1 coin but 1.910980182309824791827981240912094109249129837 in total token supply ?
Yes?
Not using 64 bit Integers such as Bitcoin uses.
Even using unsigned 64 bit Integers the largest number that can be stored precisely is 2^64 or roughly 10^19. OP's example of 1.910980182309824791827981240912094109249129837 being in the range of 10^45, would require 256 bit Integers (ie. 2^256 or roughly 10^77) as even 128 bit integers (~ 10^38) would lack precision. Note that in common programming languages 64 bit integers is all you get (if even that), 128 bit if you have long doubles at your disposal. Everything beyond that requires a custom implementation.
Side note on precision, for those unfamiliar with software development: Storing a number beyond the precision level of a numeric data-type leads to one of the following outcomes: For (a) integers, the number wraps around, like it would with the odomoter of a car (ie. starting from zero, if the integer is unsigned or starting from the lowest negative number, if the integer is signed), for (b) floating point numbers (ie. if the the position of the decimal point is stored as well), it essentially starts truncating the last few digits. Neither which is desirable for monetary transactions.
Not as part of token supply calculations. This paper is suggesting an alternative to RSA's asymmetric encryption scheme and is unlikely to make any sense as far as storing transaction amounts is concerned.