# Cracking 2-Key Triple DES

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.

• Very similar question. If in addition the attack must be practical, there is this older question.
– fgrieu
Commented Mar 8, 2023 at 14:34
• @fgrieu thank you, I had a look at both and used the first question you linked as the second seemed a bit out of my depth of understanding however I understand the other a lot better as very similar as you said. I am still however a little confused, it seems like a sophisticated attack would yield 2$^{80}$ by RGS and Mitchell's conclusion however my answer is required to the nearest year and such a decryption would take just above a second so I don't think this could possibly be correct. I will hence assume that the attack isn't that sophisticated and is simply using brute force (2nd attempt). Commented Mar 8, 2023 at 15:31
• The one important thing about the attacks on 2-key triple DES that require $2^{~80}$ DES is: these $2^{~80}$ DES are NOT the actual bottleneck; memory accesses are. Thus I do agree this likely is not what's asked is your context. Beware that the time you computed in the second option is maximum rather than expected; and (independently) is disregarding a simple optimization that is possible with a little chosen plaintext (like 48 bytes). Also, "encryptions per second" is likely counting single-DES encryptions, and for maximum points you should discuss if it matters that triple DES uses 3 DES.
– fgrieu
Commented Mar 8, 2023 at 17:22
• Why 2^40 ? does meet-in-the-middle even work like this for 2-key TDES? Commented Mar 9, 2023 at 13:07