It is very difficult to know the exact origins of mathematics. I would like to know about new number systems which are under research. New number systems can be used for cryptography.
I don't understand what you mean by "dimension zero" of a number system.
If you are looking for a "new number system" you may want to see the paper Z₂-graded Number Theory" (By Regev, Henke and myself)
https://www.researchgate.net/publication/233038548_2-Graded_Number_Theory?ev=prf_pub
where we investigate the arithmetic/algebraic properties of a number system that extends the integers (that I prefer to call the "superintegers"). I don't know if it can be any use in cryptography. The main motivation to study their arithmetic properties is that they are convenient as index sets for grading superalgebras, and for indexing characters of the symmetric group, as their arithmetic operations are related to "hook numbers" of young diagrams related to characters, so they do encode some not entirely trivial combinatorics in their arithmetics.
Article ℤ2-Graded Number Theory
Zero in Four Dimensions
http://www.pantaneto.co.uk/issue5/arsham.htm
If dimension is meant by the minimal number of nonzero vectors required to span a vector space then the only number system with a zero dimension is the trivial vector space {0}. Nonetheless this is a strange question
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