Abstract. The reflection attack is a recently discovered self similarity analysis which is usually mounted on ciphers with many fixed points. In this paper, we describe two reflection attacks on r-round Blowfish which is a fast, software oriented encryption algorithm with a variable key length k. The attacks work successfully on approximately 2 k+32−16r number of keys which we call reflectively weak keys. We give an almost precise characterization of these keys. One interesting result is that 2 34 known plaintexts are enough to determine if the unknown key is a reflectively weak key, for any key length and any number of rounds. Once a reflectively weak key is identified, a large amount of subkey information is revealed with no cost. Then, we recover the key in roughly r · 2 16r+22 steps. Furthermore, it is possible to improve the attack for some key lengths by using memory to store all reflectively weak keys in a table in advance. The pre-computation phase costs roughly r · 2 k−11 steps. Then the unknown key can be recovered in 2 (k+32−16r)/64 steps. As an independent result, we improve Vaudenay's analysis on Blowfish for reflectively weak keys. Moreover, we propose a new success criterion for an attack working on some subset of the key space when the key generator is random.
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