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There's not really a good way to answer your question other than to explain the concepts involved. The answer can be any one of "yes", "no", or "it depends". Asymmetric encryption algorithms use public keys that have some structure. For instance, RSA public keys areĀ a tuple of $(n,e)$, where $e$ is the exponent, and $n=pq$ for some primes $p$, $q$ unknown ...


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The fastest way to solve your problem instance is as outlined in the above comments. First choose yourself a random message $m$ with $1<m<n$. Now compute $c\equiv m^d \pmod n$. Try if any of the following equations holds, if an equation does hold you've found the public exponent $e$. $m \equiv c^3 \pmod n$ $m \equiv c^{17} \pmod n$ $m \equiv ...


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The first (and hardest) step is to factor $n$; the easiest way to do this (given $e$ and $d$) is with this randomized procedure: Select a random value $z$ from the range $(2, n-2)$ Compute the value $\lambda = (ed-1)/2^k$, where $k$ is that integer that makes $\lambda$ an odd integer. Compute $t = z^\lambda \bmod n$. If $t = 1$ or $t = n-1$, we fail on ...


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For a pre-shared secret, you just use a secure MAC to authenticate the key exchange, e.g. for the exchanged public ephemeral keys $A$, $B$ and the resultant shared secret $S$, one side could send $HMAC(PSK, S, A, B)$ and the other $HMAC(PSK, S, B, A)$. Each side can easily verify that the other is using the same exchanged values and shared secret, and that ...



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