I have a PDF document that is 128bit encrypted.
The user insists on a four character password which is all numeric e.g. 1558 or 6977 or 4793.
128bit encryption is strong – is this strength negated by the password weakness?
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The strength of the encryption is different to the strength of key generation. One could implement a secure, modern key generation mechanism such as PBKDF2 as Slabks says, but use a relatively weak encryption cipher (like 128-bit RC4) compared to a stronger cipher (like 128-bit AES).
However, as Christian says, a single 4 digit PIN has a maximum of 10000 passwords which is not a lot of entropy to generate a key from. If there is some form of hash or other tamper detection, it would be relatively easy to brute force the encryption document with a dedicated, modern system. As you say, yes, the encryption strength is reduced by the password weakness.
To add to Christian’s comment above, you see PINs now on some phone and tablet apps like DropBox because, as Christian says, they are being authenticated by the server and lock you out when too many incorrect PINs are entered. It is acceptable for ATM cards and these apps due to the limited input capabilities of ATMs, phones and tablets but is not an acceptable excuse for a system with a full keyboard.