If blinding is applied to the formatted message but the random value does not honor Jacobi requirements on p and q, then it could lead to private key recovery.
In a blind signature protocol, the signer digitally signs a message without being able to learn its content.
The one-time pad (OTP) is an application of blinding to the secure communication problem, by its very nature.
Therefore, Alice sends the message after blinding it with a secret key or OTP that she shares with Bob.
Side-channel attacks allow an adversary to recover information about the input to a cryptographic operation, by measuring something other than the algorithm's result, e.g., power consumption, computation time, or radio-frequency emanations by a device.