It is tempting to try to develop a variation on Diffie-Hellman that could be used as a digital signature. Here is one that is simpler than DSA and that does not require a secret random number in addition to the private key.
q prime number
a a < q and a is a primitive root of q
X X < q
Y = a
X mod q
To sign a message M, compute h = H(M), the hash code of the message. We require that gcd(h, q 1) = 1. If not, append the hash to the message and calculate a new hash. Continue this process until a hash code is produced that is relatively prime to (q 1). Then calculateZ to satisfy Z x h X(mod q 1). The signature of the message is a Z. To verify the signature, a user verifies thaYt = (aZ)h= aX mod q.
a. Show that this scheme works. That is, show that the verification process produces an equality if
the signature is valid.
[url removed, login to view] that the scheme is unacceptable by describing a simple technique for forging a user's
signature on an arbitrary message.
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