Signing For A Gabled Message — The Blinding attack

So can Eve get Bob to sign for something that actually gives away his private? This is known as the blinding attack, and where we get Bob to sign for a message that is garbled.

Eve starts by creating a message (M — “Pay Eve $1 million”) and then creates another message:

M′=rᵉ M (mod N)

where e is Bob’s encryption key exponent and r is a random number. Eve then gets Bob to sign for this. The signature is then:

S′=(M′)ᵈ (mod N)

Bob gives S’ to Eve, and she just divides by r to get the signature for the original message:

So Eve takes Bob signature and adds it to the original message that Bob wouldn’t sign, and she can prove that Bob signed it. If she is sending to Alice the Banker, she would take the message:

"Pay Eve $1 million"

and add Bob signature for the message (S′/r), and then encrypt everything with Alice the Banker’s public key. Alice will get the encrypted message and decrypts with her private key, and reads the message:

"Pay Eve $1 million"

and she then looks at the signature, and gets Bob’s public key and checks the signature. It will match, so she will pays Eve one million dollars from Bob’s account. So here are the basic…