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How many bits long should the prime modulus $M$ be in order to be secure? The modulus $M$ should be long enough to prevent discrete logarithms from being computable. As of 2015 this means 2048 bits length is fine, but for other (official) recommendations you should consult keylength.com Should the $M$ be secret? You can make $M$ secret but ...


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There are many "cryptographically strong pseudorandom generators" and we know how to construct them well. If you have a strong 128-bit (or more) key $k$, then you can just use AES-CTR to get as much randomness as you need: $AES_k(0)||AES_k(1)||AES_k(2)||\cdots$. You can also do a similar thing with SHA256. The real problem that arises is where to get the key ...


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No, we do not know an algorithm running in linear time (or even polynomial time, relative to the number of digits in $n$) that outputs 'true' if $n$ is the product of exactly two prime numbers, and 'false' otherwise. If such an algorithm existed, I do not see that it would imply possibility to factor $n$, or otherwise break RSA. For sure, it would not be a ...


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In ssh-keygen.c of the OpenSSH source code, there is the following call: if (prime_test(in, out, rounds == 0 ? 100 : rounds, generator_wanted, checkpoint, start_lineno, lines_to_process) != 0) ...and a comment for the function prime_test says: * perform a Miller-Rabin primality test Therefore, it does indeed use a ...



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