# Security implications of using a high entropy password with a low iteration count for a key derivation function

This question is related to my other question, but also this entropy calculation question as well as this article about PBKDF2. It may also be considered as a duplicate of this question, although in our current case the password's entropy isn't as high.

If a low iteration count is used, it can allow for fast brute-forcing, but what if the entropy of the password is high enough (50 bits? 100bits? more?)? Would it still matter this much?

Would there even be a way of determining a minimum entropy?
A limited charset like "0123456789ABCD" would surely hinder reaching high levels of entropy, but given a long enough length, it's rather hard for me to guess if it could still be considered safe or not.

• Entropy is not a measure of your character set, it is a measure of the number of possibilities and their probabilities. A long string does not guarantee high entropy. The character set and the length of the string don't matter much - that just addresses the encoding, at most they are an upper limit of entropy. – tylo Sep 10 at 6:43
• if you use a high enough entropy password, such as 36 random digits, even a single iteration of a hash is enough (we use 24 digits for 80-bit password security at work) – Richie Frame Sep 11 at 0:17

From a 14-character alphabet like that, if you choose each character independently and uniformly at random, to attain 128 bits of entropy it suffices to use $$\lceil\log_{14} 2^{128}\rceil = \lceil128\log 2/\!\log 14\rceil = 34$$ characters. (For 256 bits of entropy, 68 characters.)