# AES vs Blowfish taking key-length into account

I understand that Blowfish is getting old, but is still a secure algorithm, and that AES is very popular, and is recommended by most people. My question is, how do the two compare when a 256-bit key is used for AES, and a 448-bit key (the maximum according to the standard) is used for Blowfish? Would Blowfish with a 448-bit key be more resistant to brute-force attacks? Are there any other considerations? (let's assume that we already agree that 256-bit keys are sufficiently resistent to brute-forcing).

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## 1 Answer

Blowfish has a 64-bit block size whereas AES has a 128-bit block size, so you are sort of comparing apples and oranges (there are some things you can do in AES which would be unwise in Blowfish, in particular Blowfish in CTR mode can be distinguished from a random stream after only a few dozen gigabytes of output - see fgrieu's answer here, replacing 128 by 64 in the calculations).

As for strict brute force complexity, I think you've pretty much answered your own question, if we assume that 256-bit keys are sufficiently resistant to brute-forcing then using a longer key makes no sense. It's like trying to decide what's best between "infeasible" and "infeasible". But theoretically speaking, Blowfish uses all 448 bits of the key, so a brute-force attack would take on average $2^{447}$ guesses at the key, whereas AES would take $2^{255}$ guesses on average (AES-256, that is).

Now if you want to take cryptanalytic advances into account, AES-256 has a much lower margin of security (break complexity / brute-force complexity) than Blowfish, though both remain secure today. That said, it should be kept in mind that since AES is the Advanced Encryption Standard, it has received considerably more attention from cryptographers than Blowfish!

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When considering the margin of security one should not forget that AES is THE target for more than 10 years now while the cryptanalitic effort on blowfish is not as strong nowadays – Alexandre Yamajako Dec 19 '12 at 12:11
@AlexandreYamajako That is quite true and a fair point that I hesitated to put in my answer, Blowfish has not received nearly the same amount of cryptanalytic attention as AES. I will add it now. – Thomas Dec 19 '12 at 12:15
@AlexandreYamajako: a fair point, but let's not forget that AES was only adopted by NIST in 2001 (which is when it really became the subject of much scrutiny), whereas Blowfish was published in 1993, and as of today there has still been no effective cryptanalysis of it. I'm sure that NIST chose Rijndael/AES for a very good reason, but Blowfish still has its merits (despite not having the 'celebrity' status of AES). – hunter Dec 19 '12 at 15:29
@Thomas: thanks for the heads-up regarding CTR mode - I didn't know that. Regarding block-size, does a larger block size equate to higher security? I take your point about 256-bit being 'infeasible' to crack, but I'm really just interested in this from theoretical viewpoint, not a practical one. My client requires strong encryption (nothing is unbreakable) well into the foreseeable future, and with quantum computing making leaps and bounds, I'm just trying to get a better grasp on the subject. – hunter Dec 19 '12 at 15:38