The following is a first attempt at an elliptic curve signature scheme. We have a global elliptic curve, prime p, and generator G. Alice picks a private signing key XA and forms the public verifying key YA = XAG. To sign a message M: Alice picks a value k.

Alice sends Bob M, k and the signature S = M - kXAG. Bob verifies that M = S + kYA. a. Show that this scheme works. That is, show that the verification process produces an equality if the signature is valid. b. Show that the scheme is unacceptable by describing a simple technique for forging a users signature on an arbitrary message.