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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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So far as I know, Windows does not (but you never know, it has an endless series of APIs so anything is possible). However, Intel hardware does. The Microsoft C/C++ compiler (and the Intel compiler) has intrinsics for obtaining a hardware generated random value. That value is obtained by running two circuits backwards so that are unstable. They generate a ...


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My algorithm so far is entirely built on bases. The point here is NOT get the minimal complexity, but rather a random complexity - preferrably highly non-affine. Here is a rough sketch of the algorithm so far. Does this look like it would to the trick? So far as I can see, everything is covered that defines a finite field. In order to construct a random ...


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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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No, of course this is not a good idea. CLCG's were not designed for cryptographic purposes, and there's no reason to expect them to provide cryptographic security. Why would you do that, when there are perfectly good cryptographic-strength PRNGs available? As one simple example, if you use a CLCG built out of two linear congruential generators with the ...


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Assuming that nobody's screwed up the implementation, it should not matter what kind of RNG you get. This is because all java.security.SecureRandom implementations are supposed to be cryptographically strong, as defined in RFC 1750 ยง6.3 (emphasis mine): 6.3 Cryptographically Strong Sequences In cases where a series of random quantities must be ...


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The key thing here is that even in the case that the final algorithm used is "SHA1PRNG", some entropy will be collected somehow for generating the seed that initializes the PRNG. So, it all depends on the seed. In this case, you can see in the code of sun.security.provider.SecureRandom that the seed is generated by the class ...



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