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Secure embedded TRNGs are difficult
In an embedded system where the adversary is assumed to control the environment of the Target of Evaluation¹, like a Smart Card, making a TRNG is notoriously tricky. It's hard to ensure the output is truly unpredicatable.
When there is a hardware source, one line of attack freezes it, either literally (thru evaporation of ...
2
Yes. All $4\times4$ bit S-boxes have been classified. It is possible to reach a maximum differential of 4 as well as optimum nonlinearity.
SERPENT used optimal $4\times 4$ S-boxes with respect to differential cryptanalysis. So does PRESENT, to the best of my knowledge.
Some links
2011 - Markku-Juhani O. Saarinen, Cryptographic Analysis of All 4 × 4-Bit S-...
2
CAUTION: The following matches the requirement "no short-cut in computing $m_i$ is allowed. It always either require the knowledge of $m_{i-1}$ or $m_{i+1}$. Given two messages $m_i$, $m_j$ there should be no easy way to compute the difference $|i-j|$" only with respect to an adversary not knowing the key. That goes straight against the added ...
2
The C#/.NET GetHashCode() is not a cryptographic hash function. As a non-cryptographic hash function I think what you've written is reasonable assuming that X and Y are the only "public" properties that make up the object.
Having said that, cryptographic hash functions are very different both in implementation and purpose than C#/.NET/Java hash ...
1
I'll leave Q1 and Q2 for others, here's an 128-bit transformation based on ChaCha20 and Gimli's round constant.
First 4 32-bit words are mixed together using the ChaCha quarter-round function (in [1] and [2]). For completeness, it will be repeated here:
a += b; d ^= a; d <<<= 16;
c += d; b ^= c; b <<<= 12;
a += b; d ^= a; d <<<= 8;
...
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