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Given a “safe” (meaning: brute-force is your only shot) cryptographically strong PRNG, wouldn't it be safe to encrypt data using the CSPRNG to create a key as long as the data and then encrypt the data by XORing it with the key?

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    $\begingroup$ We call that a (synchronous) stream cipher. $\endgroup$ – CodesInChaos Nov 18 '17 at 10:02
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Yes it would.

As CodesinChaos reminded us in his comment:

We call that a (synchronous) stream cipher.

Look up RC4 and A5/1, two of the most statistically popular ciphers in the universe. Also compare to a correctly generated one time pad. Not a lot else to say at this point.

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The only secure-proven encryption scheme is the one-time-pad. That uses a key of plaintext-length for XOR-encryption once, else it is broken. If your CS-PRNG is not breakable, in sence of any attacker is able to win the predictable game, it is close to being a OTP.

Now think about you would like to encrypt a branch of Wikipedia. How would you like to (1) store and (2) transport the key secure? How would you make sure that no key is used twice?

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