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Well, all representations of the field $GF(2^8)$ are isomorphic. What that means is that there is a mapping between one representation of that field to another, where that mapping preserves all field properties. That is, if we had two representations $A$ and $B$, there exists a mapping $M$ from elements of $A$ to elements of $B$ such that, for any two ...


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I have successfully made the abstraction that you want. You should not abstract on internal implementation details but rather the interfaces. The internal implementation can be resued in several ways, but is not the point of abstract. I have included some excerpts that shows how this works. Here is a (slightly edited) portion of a header file that shows the ...


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You'll find the test vector in a draft "Test Vectors for the Stream Cipher ChaCha draft-strombergson-chacha-test-vectors-00" available at the following link: http://tools.ietf.org/html/draft-strombergson-chacha-test-vectors-00 The document links a github repo where you can find all the vectors https://github.com/secworks/chacha_testvectors/ Another ...


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There are in the RFC : http://tools.ietf.org/html/draft-agl-tls-chacha20poly1305-04#section-7 The following blocks contain test vectors for ChaCha20. The first line contains the 256-bit key, the second the 64-bit nonce and the last line contains a prefix of the resulting ChaCha20 key-stream. KEY: ...


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If the permutation will fit in memory then the previous answer is the best approach. If it won't work then you might consider a linear congruential generator (LCG) of the form y = A * x + C. There is a lot of theory there (Knuth is always a good place to start for this). If you want N elements then you need to design a and b relative to N to get the full ...


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GF$(2^8)$ or $\mathbb F_{2^8}$ can also be viewed as the vector space $\mathbb F_2^8$ of $8$-bit vectors (or bytes) over GF$(2)$ or $\mathbb F_2$. Suppose $\{\beta_0, \beta_1, \cdots, \beta_7\}$ is a basis of $\mathbb F_2^8$ over $\mathbb F_2$, that is, the sum $$a_0\beta_0 \oplus a_1\beta_1 \oplus \cdots \oplus a_7\beta_7, ~ a_i \in \mathbb F_2$$ equals ...


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You can begin by enumerating all the irreducible polynomials of degree 8. This gives you all the possible fields representations. If I remember Eisenstein criterium is one of the algorithm for testing irreducibility of polynomials All these field are isomorphic to each other.


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Your scheme is indeed an instance of output feedback mode (OFB), using $$(\mathit{key},\mathit{pad}) \mapsto H(\mathit{key}\oplus\mathit{pad})\text,$$ where $\mathit{key}$ corresponds to keyhash and $\mathit{pad}$ to hash, as the "block cipher". (It is very likely not really a block cipher due to lack of bijectivity, but that's not needed for output feedback ...


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You are creating a bitstream and XORing it with your plaintext so yes, it is. More precisely, it's a block cipher. Have a look at a previous discussion.



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