Questions tagged [miller]
4 questions
4
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Enhanced Miller Rabin outcome for composite numbers
I'm going through the Enhanced MR test cited in FIPS 186-5, in which it is mentioned that a composite number can be COMPOSITE WITH FACTOR or COMPOSITE AND NOT A POWER OF A PRIME.
When I tested this on the same modulus for longer number(approx…
sg777
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Generating Carmichael numbers in polynomial time
I'm generating RSA 2048-bit keys with $p$ and $q$ of 1024-bit primes. For primality, I'm using the Miller-Rabin test. As Carmichael numbers pass the MR test, I tried to compute how many such numbers exist.
From wiki, the number of Carmichaels…
sg777
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2
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Probability of Enhanced MR test outcome for NOT A POWER OF PRIME
I come up with an approach to find the probability of the outcome "PROVABLY COMPOSITE AND NOT A POWER OF A PRIME" of enhanced MR test.
In context of this question, the probability/error probability which I'm trying to compute is the probability at…
sg777
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1
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1 answer
Enhanced MR test understanding the steps in detail
I'm going through the Enhanced MR test cited in FIPS 186-5, I have couple of questions regarding the following steps
4.5 $z = b^m \pmod w.$
4.6 $\textrm{If }((z = 1)\textrm{ or }(z = w – 1)), \textrm{then go to step }4.15.$
Q.1 Since $b$ is coprime…
sg777
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