Score:2

Security of Even-Mansour based Merkle-Damgård

cn flag

Assuming I have single-key Even-Mansour with single $2n$-bit permutation in wide-pipe Merkle-Damgård specifically with Matyas-Meyer-Oseas mode outputting $n$-bit hash.

What security can I expect against collisions and preimages?

Am I wrong to expect $2^\frac{n}{2}$ for both?

fgrieu avatar
ng flag
Does this mean the recurrence is $H_{i+1}:=E(M_i\oplus H_i)\oplus M_i\oplus H_i$ with each quantity $2n$-bit, where $M_i$ is one of $k$ padded message block(s), $H_0$ an arbitrary constant, and a certain half of $H_k$ is the final $n$-bit hash?
cn flag
@fgrieu-onstrike Yes.
fgrieu avatar
ng flag
I don't immediately see a preimage attack with cost $\mathcal O(2^{n/2})$. Do you?
cn flag
I expected this due to Even-Mansour, but it may not be the case due to wide-pipe.
pe flag
See §3 of [Luo-Lai](https://eprint.iacr.org/2013/233)
cn flag
@SamuelNeves So construction in paper gets about 2^(n/4) collision resistance and 2^(n/2) preimage resistance. However, there are two additional transformations there, which makes me think without them it would not be secure at all.
pe flag
In §2.3, [Knudsen](http://www2.mat.dtu.dk/people/Lars.R.Knudsen/smash/smash-proc.pdf) points out the issue when both $L_1$ and $L_2$ are the identity. That is, if $h_i \oplus m_i = h_i' \oplus m_i'$ you get a collision.
cn flag
@SamuelNeves So no resistance to collisions. I don't know how I missed that.
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