How to find the radix?

In the realm of cryptography and especially in the context of cryptography related to cryptocurrencies, the radix serves as a fundamental building block. Could you elaborate on how one might find the radix in a given scenario? I understand that it typically refers to the base or number system being used, but how does one determine this for a specific cryptographic algorithm or function? Is there a universal approach or does it vary depending on the specific application? And finally, what implications does the choice of radix have on the security and efficiency of the cryptographic system?