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Daniel Bleichenbacher has described such kind of attacks in his article Generating ElGamal signatures without knowing the secret key. He noticed that if verifier would accept signatures where $r$ is larger than $p$ then any signature $(r,s)$ on $H(M)$ could be used to generate a signature $(r2, s2)$ on arbitrary hash value $H(M2)$. For that attacker should ...


One property that this unpadded system is that it is homomorphic; if $A^d = X$ and $B^d = Y$, then we know that $(AB)^d = XY$, and it doesn't matter if we don't know what $d$ is. More generally, if we have a collection of $H_1, H_2, H_3, ... H_n$, and a collection of signatures $S_1, S_2, S_3, ..., S_n$, then for any set of integers $e_1, e_2, e_3, ..., ...

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