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When using secure hash functions in an RSA signature, why do we sign the hash Sign...

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Advance Math

When using secure hash functions in an RSA signature, why do wesign the hash Sign (H (m)) instead of taking the take the hash H(Sign (m)) ?

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If you have a message mN with N being the RSA modulus then you have to perform at least 2 RSA signatures as m does not longer fit into ZN Let us assume that it requires k such signatures and write the message mm1 mk and the overall signature will be 1 k ie k RSA signatures Now without any additional measures anyone getting to hold m can manipulate the message and adopt the signature    See Answer
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