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(Multi-User) Security Key-prefixed Schnorr Signature

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Bernstein proofs in his paper that single-key security of the classic Schnorr signature system tightly implies the single-key security of the key-prefixed variant of the system. Can this statement be applied also for short schnorr signatures (halved hash output length)? In other words: Does single-key security of short schnorr signature system tightly implies the multi-key security of the key-prefixed variant of the short schnorr system?

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th flag
Are you aware of https://eprint.iacr.org/2019/1105 ?
mangohost

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