I've been given that an attacker has a 2-Key Triple DES Cracker that is capable of performing 10$^{24}$ encryptions per second and have subsequently been asked how long it must take before the attacker successfully finds the correct key.
This doesn't seem too hard however I'm caught between two different answers, here's what I've done:
My first attempt assumed that this would be a meet-in-the-middle attack, which I understand would require 2$^{80}$ operations for 2$^{40}$ known plaintext/ciphertext pairs, which would yield 2$^{80}$ /10$^{24}$= 1.21 seconds (to 2 d.p.) however I decided that this wasn't feasible as I thought that Triple-DES was more secure against this kind of attack, although I know it to be possible.
My second attack assumed that this would be an exhaustive key search attack which seemed more feasible as that's what the cracker seemed to operate to do. To my understanding this would yield 2$^{112}$ /10$^{24}$= 165 years as 3-Key Triple-DES provides 112 bits of security.
I feel like my second attempt is what the question is requiring me to do however I'm still unsure if what I've done is correct, assuming that my second answer is on the right track would we still only require to find the outer cipher which would yield only 2$^{111}$ encryptions on average.
My apologies if my working seems inadequate, this is the first time I've done cryptography before and as a pure maths student it's quite different to everything I've done over the past few years.
