10.17 Here is an improved version of the scheme given in the previous problem. As before, 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: . Bob picks a value k. . Bob sends Alice C1 = kG. . Alice sends Bob M and the signature S = M - XAC1. . 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 forging a message in this scheme is as hard as breaking (Elgamal) elliptic curve cryptography. (Or find an easier way to forge a message?) c. This scheme has an extra "pass" compared to other cryptosystems and signature schemes we have looked at. What are some drawbacks to this? | |
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