1. Trust.

We trust what we know and who we know. Most of us trust ourselves allright. Most of us also trust our own purse reasonably well.
Keeping money in the bank requires trust in the banking company, in the bank manager and in the bank employees - a kind of wide-encompassing trust that does not come easily to many of us. So, what do the banks do to create that trust? They give us some minimal control over what they do with our money by letting us verify how much money we have in the bank, how much interest our money gathers over time (if any), etc..
Clearly, we also trust what we control, just as we trust the car we drive.
So let's go all the way into that direction and let's give ourselves complete control over our own money: we'll be able to trust our money if we feel we control it even better than our own wallet. Hence, if the money is virtual (i.e.: computer bits, not paper bits) the computer should be our wallet, or rather should replace our purse. This requires a distributed system with each person in complete control over her/his/its part of the system.

2. Security.

In this context, security is the set of methods and rules we use to make sure our transactions are secure, i.e.:

2.1. Security of transaction

We want to make sure nobody interferes with our transactions nor intercepts them while they happen.
Problem solved using secure public key encryption systems during all transactions.

2.2. Correctness of transaction

We want to make sure the transaction we made has been done the way we wanted (same amount, same person).
Problem solved using direct wallet-to-wallet transactions signed using a secure public key signature system, with the wallet keeping a permanent record of these transactions (amount, from whom, to whom, for what reason), record that we may then consult.

2.3. Control of identity

We want to make sure the person with which we transact is really who she/he/it claims to be and is really authorized to make such a transaction.
Problem solved if (a) we use only wallet-to-wallet transactions, (b) the wallet can easily read the fingerprints of its user and check if they are the same as those of its owner, and (c) each wallet clearly identifies itself (or better: its owner) to the other wallet during all transactions.

3. Safety.

In this context, safety is the set of methods and rules we use to make sure our money is safe, i.e.:

3.1. Safety of storage

We want to be able to recover from the loss of our wallet without any monetary loss (i.e.: we don't loose our money).
This requires some means to make regular backups of the content of our wallet, so a new wallet can be issued with a copy of the contents of the original wallet in case the original wallet is lost or destroyed. Centralizing the creation and storage of these backups would protect everyone against her/his/its own negligence but would require ways to ensure the safety of these backups and to ensure that these backups can't be restored to someone else's wallet. Assuming that such "safety of backup" can be provided by some kind of virtual banking cooperative, for instance, it becomes easy to envision a system whereby all our recent transactions are encrypted and transmitted to the backup facility whenever we connect our wallet to the virtual banking cooperative (be it through the internet or through some banking terminal). With such a mechanism in place, implementing "proposed transactions" becomes easy: some entities (our employer, the government, some regular customers or suppliers) would at times send "proposed transactions" (weekly salary from our employer, payments from our regular customers, payments to the phone company and other regular suppliers, tax payment to the government, etc.) to the virtual banking cooperative, so that this one would transmit these proposed transactione one at a time to our wallet where we can either acknowledge them ou refuse them, the status (acknowledged or refused) beeing then transmitted to the entity proposing the transaction. In case of loss of wallet, we simply go to the local office of the virtual banking cooperative, let them download the latest backup into a fresh virgin wallet, establish our identity by activating the wallet (requires verification of fingerprints and entering a reasonably secure passphrase) and contacting a number of witnesses identified as such in the wallet, then they give us the new wallet and completely deactivate the old one.

3.2. Safety of backup

We want to be able to make sure that the backups can't be altered while in centralized storage and that these backups can't be restored to someone else's wallet. The first requirement is easily met by encrypting the backups using some kind of secure public-key encryption system, while the second is met by ensuring that the download can only be done (a) after the loss or theft of the original wallet has been declared, and (b) on a virgin wallet that has recorded matching fingerprints and a matching passphrase.

3.3. Safety of transaction

We want to make sure no transaction is ever done without our personal authorization (i.e.: nobody steals our money).
Easy enough: (a) no transactions can be done on the backups, and (b) every transaction and proposed transaction requires conscious acknowledgment with fingerprints and some kind of protocol (password or id number exchange).

Finally, is there a further need for confidentiality?
Securely encrypting transactions and backups would provide much better confidentiality than we have right now.

Conclusion

There are no technical problems here, only political and organizational ones. All required technologies are actually available, so a definite proposal for such a system could be made right now. The PIP or Personal Information Processor is precisely a proposal for a new tool that would be easy to use (and put in service) to make different kinds of new monetary systems trustworthy, secure and safe (like LET's, barter clubs or the ecosocietal system, for instance).