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The question asks how to systematically pick the public exponent $e$ in RSA. I'll stick to public modulus $N$ that is the product of exactly two distinct odd primes $p$ and $q$, but the choice of $e$ is not fundamentally different in multiprime RSA. What's an acceptable public exponent $e$? The public exponent in RSA should be an integer $e>1$ with ...


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@CodesInChaos is right, here is an example of his method on your data : $40 = 2^3 5$ so I pick, say $e=3$, which is for sure coprime with $40$. Actually $e=3$ is a common value in some implementations of RSA (see @fgrieu giant response about that) By chance (or did you teacher foresaw it ?) Extended Euclidian Algo is pretty fast here : $40 = 13 \times 3 ...


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1) Yes. This is the common modulus attack and has actually been answered many times on this forum. 2) Assuming $r$ is prime, yes. $\phi(n)$, (the totient of $n$) can be computed by subtracting 1 from each of $n$'s prime factors and multiplying them together.


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It is extremely likely to be either RSA with PSS padding or RSA with PKCS#1 v1.5 padding, the latter being the most likely. If you sign two times and the output is twice the same then it is not PSS and PKCS#1 v1.5 would be the prime suspect (that was my brain making fun of me, pun not intended). RSASSA-PSS is different from other RSA-based signature ...


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The "normal", unmodified RSA (called textbook RSA) is susceptible to some attacks. We need to change it slightly to avoid this problems. The question Definition of Textbook RSA and the Wikipedia lists some possible attacks. In practice a special padding algorithm is used, like the Optimal asymmetric encryption padding (OAEP). The documentation of the ...



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