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Given 2 messages $m_1$ and $m_2$, in a chosen prefix attack, we want to find $s_1$ and $s_2$ such that:

$\text{MD5}(m_1 || s_1) = \text{MD5}(m_2 || s_2)$

Are $s_1$ and $s_2$ found by brute force or are there some rule(s) to construct $s_1$ and $s_2$ based on $m_1$ and $m_2$?

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  • $\begingroup$ Generally for these kind of attacks the $m$ and $s$ input consist of one or more blocks. The size of these blocks is determined by the internal block size of the cipher, which, for MD5, is 512 bit. Brute forcing a 512 bit block would take $2^{512} / 2 = 2^{511}$ tries on average. That's a calculation that will never finish (even if we take into account that it takes a very long time for black holes to vaporize due to Hawking radiation :P ) $\endgroup$ – Maarten Bodewes Oct 3 '18 at 1:56
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The answer is due to the Stevens et. al's work.

They showed that, with an approximately $2^{39}$ calls to the MD5 compression function, it is possible, for any chosen $m_1$ and $m_2$, to construct $s_1$ and $s_2$ such that $\text{MD5} (m_1||s_1) = \text{MD5} (m_2||s_2)$.

They also gave examples for colliding documents, software integrity checking, etc ...

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