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Does checking sig with DSA implies both that the sender is verified , and the msg is original without change of any bit? (case i dont have a reference HASH for that file, only public key)

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    $\begingroup$ As of 2019, the DSA algorithm as specified in initial versions of NIST FIPS 186 had so many mis-implementations that it's being deprecated by TLS1.3 and SSH, and also in the next revision of FIPS 186. $\endgroup$ – DannyNiu Dec 26 '19 at 11:10
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If you know the sender's verification key previously: Yes, it does prove the authenticity and integrity of that message. No one else could have created a matching signature - for any message under that public key.

As a side note: hashes of files are in theory a good idea to check that it was not changed. But when you get the hash from the same source as the file itself (e.g. the webserver offering a file for download), then that's utterly worthless. Anyone able to manipulate the file can also just replace the hash (doesn't matter if he has access to the file server or if it's a man-in-the-middle attack).

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