Breaking SHA1-HMAC

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Satish and I are working together on a school project - I have a quick question what if it is a truncated hash. Instead of having the full hash we know the message and the truncated hash - say we know abcd as the message and lets say we are limited in the hash length so only 8717 is available as the hash value. Would that improve the performance of hashcat in possibly finding collisions and keys that would provide the same resultant hash?