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2 is also prime with roughly the same probability if

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Unformatted text preview: / 2 is also prime with roughly the same probability. If we believe this conjecture, then a reasonable way to generate strong primes is the same “generate and test” procedure we used above; namely, generate a random k-bit number p , and test if both p and q = ( p- 1) / 2 are prime; if so, output p ; otherwise, repeat. 11.4 Deterministic Primality Tests In a very recent breakthrough, Agrawal, Kayal, and Saxena have shown how to test for primality in deterministic polynomial time (see http://www.cse.iitk.ac.in/primality.pdf ). Prior to this result, no such deterministic, polynomial-time test was known to exist, despite many years of extensive research in this area. It is not yet clear if this new algorithm will have much impact on practice. We do not discuss this algorithm any further here. 69...
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