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Under an ideal cipher model, every key implements a random permutation. A random wrong key that maps $x_1$ to $y_1$ thus maps $x_2\ne x_1$ to a random ciphertext $y_2'$ other than $y_1$. For a $b$-bit block cipher, there are $2^b-1$ such ciphertexts, thus the probability that $y_2'=y_2$ is $1/(2^b-1)$. The probability that an incorrect key survives two tests ...

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From probability: Let X be an experiment with possible different outcomes $x_1 ,...,x_n$ with respective probabilities $P(x_1)=p_1,...P(x_n)=p_n$ . Let A be the subset of sample space ${ x_1..,x_n}$ with probability P(A)=p. Let K <= N integers with N >0 and K>=0, $$\begin{pmatrix}N \\k \\ \end{pmatrix} p^k (1-p) ^{ (N-k)} \tag{1}$$ that A ...

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It is correct that The literature is rich supporting the statement that a random Sbox can make any cryptographic scheme weaker But in general such statements apply to fixed public S-boxes (and as an aside, typically not to sizable ones, especially when they are permutations). But the question is about a secret key-dependent S-box (and a permutation on top ...

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Are such competitions held, and is there a recognized progress meter that is kept? No. It is generally believed that $2^{128}$ AES keyschedule and encryption operations are out of reach for just about anyone. If and when that changes and $2^{128}$ draws in to be a more realistic number perhaps people will do that. However, I have been unable to find any ...

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I presume when you say you can "recover" 16 bit keys you mean by brute forcing. That isn't really recovering a key in the sense of a cryptographic break. Obviously all keys can be recovered that way, just in an insurmountable time. The longest key that can be recovered is the longest possible key (256 bit), which can be recovered quicker than ...

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I have an Intel(R) Core(TM) i7-7700HQ CPU @ 2.80GHz. Intel I7 has around 10 generations to speak of. The result cannot be accurate without providing the actual referenced Intel I7. Here is the method; Run openssl speed -evp aes-128-cbc command. That will give you the metric. My CPUs output: aes-128-cbc for 3s on 16 size blocks: 144516288 aes-128-cbc's in 3....

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Mining ASIC's is not suitable for SHA256 brute-force/rainbow tables, they fixed by initial silicon design only for bitcoin double-sha256 mining. They drop 10^9 non-suitable hashes internally (even dropping not finished rounds), just to provide 1 per fix matching criteria hash should start from 0x0000000000xxx the only suitable solution for final block ...

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Preliminary: the present answer assumes an Elliptic Curve group of order $n$ built on a prime field of order $p$, with one of $p$ or $n$ a 160-bit prime of the form in the question (rather $p$, which will give the most computational benefit, and is close to common practice). Choosing "public key $P$ as $p*G$ where $p$ is an Optimal prime" is not ...

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