In response to the question about digital signatures, I will give a brief summary of one form.
To understand digital signatures, it is important to understand what a hash function is. A hash takes data in, and give you something else out. In the case of a digital signature, the output is best described as garbage, but USEFUL garbage.
Public key encryption uses 2 keys (in most cases). The idea is that you have 1 public key, that you give everyone, so that they can encrypt files that they send to you. This can be posted on the internet, as it does not pose a security risk, since it is what one would term a "hard problem" to figure out what the other key, the private key, is by using it.
A in laymen's terms, a "hard problem" is one that it would take an extremely long time for a computer to solve. The hard problem with public key encryption is factoring a number that is the product of 2 large prime numbers. At relatively short key lengths, this can take more computing power and time than you will ever have to spend on it.
On to what the signature is. With the signature, you run your hash on data that you transmit. For instance, if you are sending an email, the hash is typically the body of the email in a digested form, which is another kind of hash, or a line of text. It comes out as garbage. On the other end, a hash is run on it. If they can reconstitute it using your public key, you have a legally binding digital signature in Ireland.

