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I wanted to better understand how public-key cryptography avoids 51% attacks and mining attacks, also if this question is wrong please correct so that i can improve my research and provide me with right resources

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Public key cryptography has nothing to do with 51% attacks. The only thing a miner can do with >50% hash power is double spend bitcoins for which he controls the private key or censor transactions by not including them in the blocks he creates. He cannot spend bitcoins for which he doesn't control the private keys.

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