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it's the doubts lie in the very core concept, but I wanna know how the nodes know that the private+public key is right.

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Blockchains use elliptic curve cryptography which is a type of public key cryptography.

In a public key cryptosystem the private key is used to sign a message, and the public key is used to verify a message.

Blockchains don't need the private key to verify a transaction.

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