Blind Signature

Blind signature is a technique which is used to obtain digital signature on some value without exposing that. The scenario is like this, consider a person A who wants a digital signature of B on some message m, but at the same time A did not want to disclose the message even to B. How to do it?

The question seems complex! if B does not know the massage then how could he sign on it? D. Chaum had proposed a solution for this problem in his paper "blind signature for untraceable cash". The proposal is as follows.

1. Let public key of B is (n,e)
2. A generates a random number r
3. Then A calculates c=m*(r^e) and sends to B for digital signature
4. B now did not know about m, because he got m*(r^e) and since r is not disclosed to B he has no idea about m. B does digital signature on the value m*(r^e) using his private key (n,d).
5. Signature scheme being RSA the output is actually (m*(r^e))^d. which is (m^d)*(r^ed). which in turn is ( (m^d) * r )
6. This value is send back to A
7. Since A knows r he calculates inverse of r say r'. such that r*r' = 1 mod n. And then finds s=( (m^d) * r ) * r'.
8. Value of s is m^d which is the digital signature on m by B.

The digital signature of m is been obtained by A without even exposing the value of m to B.