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The keys used in an One Time Pad are required to be randomly generated from a keyspace $\mathcal{K}$, we require 256 bit random keys, i.e. $\mathcal{K}=\{0,1\}^{256}.$ Suppose we randomly select an integer $i \in I$ and compute its 256 bit message digest ($d$) through the $\operatorname{SHA-256}$ hash function. Now, can the digest $d$ be considered as a randomly generated key for the OTP scheme?

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    $\begingroup$ This way you're running SHA-256 in CTR-Mode, which is inefficient (because SHA-256 is slow compared to AES) but is secure. And BTW: This isn't called "OTP", but "stream cipher" because your key isn't perfectly random. $\endgroup$
    – SEJPM
    May 14 '16 at 14:08
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Your first sentence is entirely wrong. A OTP is a theoretical construct that requires a fully random key (at least) the size of the plaintext. Limiting the amount of random bits to 256 will by definition not be an OTP - at least not for constructions that accept a plaintext larger than 256 bits.

The same idea is that if you use a key called $i$ which is smaller than 256 for an OTP of 256 bit. The best you can hope for is to create a stream cipher, e.g. using CTR mode as SEJPM suggests. Stream ciphers are however not perfectly secure; the key may be brute forced and the plaintext exposed.

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