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.Public elements: q prime number a a < q and a is a primitive root of qPrivate key: X X < qPublic key: Y = aX mod qTo 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). View complete question »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.Public elements: q prime number a a < q and a is a primitive root of qPrivate key: X X < qPublic key: Y = aX mod qTo 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 calculate Z to satisfy Z x h= X(mod q 1). The signature of the message is aZ. To verify the signature, a user verifies that Y = (aZ)h = aX mod q.Show that this scheme works. That is, show that the verification process produces an equality if the signature is valid. View less »

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