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My question refers to the paper "Multi-user Schnorr security, revisited" by Bernstein. Does the implication shown in the paper

security of classic Schnorr $\implies $ multi-key security of key-prefixed Schnorr

apply to short Schnorr signatures?

By short Schnorr signatures I mean those of size $3k$-bit that you get by truncating the hash output bits by $k$.

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