Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

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6

This precise issue recently arose in light of suspicious patterns in the S-box of a Russian cipher Kuznyechik. See: Xavier Bonnetain and Léo Perrin and Shizhu Tian: Anomalies and Vector Space Search: Tools for S-Box Analysis, Asiacrypt 2019 One way the authors chose to quantify how unlikely such a permutation could have occurred by chance is to find the ...

26

There are at most $n \cdot (n - 1)$ permutations of $\mathbb Z/n\mathbb Z$ of the form $x \mapsto ax + b$: if $n$ is prime, there are $n - 1$ choices for $a$ and $n$ choices for $b$ under which this is a permutation. There are $n!$ permutations of $\mathbb Z/n\mathbb Z$ altogether. So the probability that a uniform random permutation has this form is ...

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Pseudorandom permutation Confusingly, nothing really gets permuted here in the classic definition of a permutation. It's more of a cryptographic twist on the common notion of permutation. The actual input/output behaviour is like:- And each input is mapped to exactly one output value. The above diagram is simplistic in that the size of the inputs and ...

1

You're close. As Mikero noted in the comments, this scheme is CCA-secure as proven in his book. The proof strategy that seems easiest here is to do game-hops and with the IND$-CPA definition: Start with the real case where$c=F_K(r\mathbin\|m)$is returned Swap out$F_K(\cdot)$for a random permutation$\pi$, so$c=\pi(r\mathbin\|m)$is returned, you "lose"... 3 All three are families of functions. For example,$f_k(x) = k \oplus x$, where$\oplus$is xor and$k$and$x$are 256-bit strings, is a family of functions; for any 256-bit string$k$, there is a function$f_k$which given another 256-bit string$x$returns the xor of$k$and$x\$. The input and output spaces need not be the same; we could imagine a family ...

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