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RSA-Based Signature Algorithms

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RSA-Based Signature Algorithms

From Beginning Cryptography with Java - chapter 4, digital signatures:

Signatures are created using the RSA algorithm by applying the RSA algorithm using the private key and then distributing the result as the signature. Because of the way the RSA algorithm works, this means the signature can be decrypted using the public key, giving you the process you see in Figure 4-5. The reason it works so well is that if a signature decrypts successfully with a given public key, then it must have been created with the corresponding private key.

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"the signature can be decrypted using the public key"? I thought decryption is done by the private key...?