Hi,
Assumption 1 : a privacy key can become uncrackable. Assumption 2 : an individual signature can become immune to fraud. Posit : fuse the two together so that pseudonyms/aliases/online names ensure complete privacy, but ensure that you talk to the same person everytime. Probably proposed already.
Unforutnately both of your assumptions are wrong. A key cannot be 100% uncrackable, and a signature cannot be 100% immune to fraud. With electronic security, there is always a chance that a key can be cracked or a signature forged. The question is how hard is it to crack the key or forge the signature? You need to balance the security with the price.
Derek is correct in that your use of the words "uncrackable" and "immune to fraud" were a bit over the top (in recent years everyone in the security and crypto community has become very nervous whenever anyone says things like this; they are usually trying to sell you something which is neither.) OTOH, he might want to temper his statement with a reference to fail-stop signatures... Just because someone with a lot of computational resources can produce a private key which matches your public key does not necessarily mean that they are the same ones that you generated, only that they found a set which work for the particular modulus which was chosen... In the "real world" there is nothing to prevent someone from forging your real signature on a check or document or from disguising themselves as you and taking your place at an important business meeting. The digital equivalents can be slightly more secure, but nothing is ever perfect. jim