What difference does key length make when signing a file?

I've never taken any classes on encryption or security and I'm trying to teach myself some basics, so forgive me if this is a silly question (don't worry, I'm not working on anything sensitive)

So, I'm playing around with Crypto++ so that I can make a signature of a file to see if the file has been edited by someone other than me. The test application that comes with the library looks like it has options (rs and rv) that do exactly what I want to do in my own program (verify the integrity of the signature of a file). Of course, before doing that I need to generate a public and private key. When doing 开发者_运维问答so with the test application's g option it asks me to specify the key length in bits. What difference does the key length make?

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The key length determines how hard it is for someone to break your cryptography. For digital signatures, that means how hard is it for someone to generate a fake signature.

For RSA a key length of 1024 bits is sufficient for non-sensitive information, but it should only be used for a few years and then replaced with a new key. 2048 bits is stronger and 4096 is stronger still.

For a naive brute-force attacker, adding a single bit to the key length doubles the amount of work they need to do to compromise your key. However, algorithms like RSA do not scale in this way: a 2048-bit RSA key is not 2^1024 times as hard to break as a 1024-bit key (unless the attacker is really stupid).

Generally public key algorithms (e.g. RSA) need much larger keys than symmetric key algorithms (e.g. AES) because they rely on different mathematical properties.

For a good primer on cryptography you should check out Peter Gutmann's godzilla crypto tutorial. It's pretty readable and gives you a good overview of how crypto works in its various forms.