4 ms·
aⁿ grows (a/b)ⁿ as quickly as bⁿ. The multiplicative difference still grows exponentially in n.
by pxx 2y ago
aⁿ grows (a/b)ⁿ as quickly as bⁿ. The multiplicative difference still grows exponentially in n.
- afiori 2y agoa^n is polynomial in a and exponential in n. This is why longer password are more efficient than complex passwords: to gain the same security effect of doubling the password length you would need to square the alphabet
- pxx 2y agoYou've the proper definitions but are missing the context. An exponential with larger base still has an exponential multiplicative difference compared to an exponential with a smaller base. We're comparing the growth rate of of two exponentials representing variable-length identifiers. We're not looking at a constant-length identifier (which is what you're doing with only looking at a^n). Notice the context of where exponential is used in the article: we are changing n from 5 to 8.