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USDamon
 

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    1. PODeriving axis/angle rotation from two pairs of three points (or, two pairs of two vectors)
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    1. CO... and decrypted random data is "random garbage" too, which makes it harder to tell that you've found the key than if the data was some actual known plaintext or plaintext of some known structure. So, an attacker would need 2 decryption steps instead of 1, effectively adding 1 bit of key lenght. But the problem is that a lot of users will just give you their password if you tell them that there has been an incident of "newtonian bit collapse" in the system, so you must verify that their password still works correctly and their data is still valid. Even a 16384 bit key won't prevent that.
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    2. CO@Charles: Correct. That is why many people use a cryptographic hash (e.g. SHA-256) to generate the actual key from a passphrase. That would turn the 40-50 characters into 32 characters. The problem is that you're already lucky if someone uses 10 characters. A 256 bit hash that was generated from a data that has only 30-35 bits of entropy still only has 30-35 bits of entropy. You can make an attacker's life a tiny bit harder e.g. by securing a cryptographically secure random number with this key. That makes an attack slighly harder insofar as encrypted random data is "random garbage" and ...
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    3. CO@GregS: I remember NIST claiming that their Electronic Authentication Guidelines ensure that 8-character passwords have at least 30 bits, that would be 2,13 bits per character. Wikipedia claims 50 characters for case-insensitive alphanumeric, and 43 for case-sensitive alphanumeric for 256 bits of entropy, which is not very far off my figures.
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