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6

Rick Demer already wrote the answer in the very first comment, but without explanation: Hybrid encryption. But since you asked for a real practical example to encrypt your word document, this is how: Your file is on your disc, and it is 100,000 byte large. You can then do: First, you start up a random number generator. Preferably you should either have ...

2

Yes, absolutely. Here is the standard construction to address this problem. Let $pk_1,\dots,pk_n$ be the public keys of the $n$ recipients. We pick a random symmetric key $k$, encrypt the message $m$ (using authenticated encryption) under key $k$ to get $c=AE_k(m)$, and then encrypt $k$ under each of the public keys. Finally, we form the whole ciphertext ...

1

Well, exponentiating a word document is rather easy. As you've said, it's $100,000$ bytes, or $800,000$ bits. This word document can thus be interpreted as a number between $0$ and $2^{800,000}$. Sure this number may be large, but it can be exponentiated. However, more commonly symmetric encryption is used with a $128$ or $256$ bit key to encrypt the word ...

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