Randomizing Your Signatures

Wouldn’t it be great if you could randomize your wet signature, so that every time you signed, or whenever anyone looked at your signature, it would change? Well, let’s implement a method that allows us to do this.

Let’s say that I sign a message that you receive. You check the signature of the message and store it, and the signature. But, I want to preserve your privacy by storing the signature, so that no-one can trace it back to the original message? Well for this we can used a randomized method of creating signatures.

One of the best methods around is the PS (Pointcheval Sanders) Short Randomizable Signature and was defined in [1][here]:

It uses crypto pairs to produce a signature which can be randomized. Initially we have two pairing points (g1 on the G1 curve, and g2 on the G2 curve. The private key is created with two random numbers (x and y):

sk=(x ,y)

and a public key with:

pk=(g2,x g2,y g2)=(g2,X,Y)

To create the signature we take a message (m) and create a random value for the signature (h) and then determine two signature elements: