Answer by fgrieu for Is it reasonable to assure that p-1 and q-1 aren't smooth?
About difficulty of insuring that $p-1$ is not smooth: it is easy to generate $p$ with assurance that $p-1$ is not smooth. The idea is to first choose a big random prime $p_1$ still much smaller than...
View ArticleAnswer by Thomas Pornin for Is it reasonable to assure that p-1 and q-1...
Checking for smoothness can be computationally expensive, depending on the size of the "small" primes (there is no "natural" definition of "small", one has to define an arbitrary limit). Also, it is...
View ArticleAnswer by Henno Brandsma for Is it reasonable to assure that p-1 and q-1...
I'll leave the probability to someone else, but to ensure the non-smoothness of $p-1$ most libraries (including OpenSSL) will generate a prime $p'$ such that $2p' + 1$ is also prime, and then use $p =...
View ArticleIs it reasonable to assure that p-1 and q-1 aren't smooth?
I came across the requirement that, in RSA, $p-1$ and $q-1$ shouldn't be smooth, shouldn't consist of lots of small factors. Therefore my question:How complicated is it to check whether $p-1$ is...
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