Roots of Unity in ℤ/mℤ
In this chapter we develop the information needed to prove Rabin’s theorem. We first count the number of nth roots of 1 or of −1 modulo m for any n and m. This allows us to count, for any odd composite number m, the number of false witnesses for m—that is, the number of numbers a modulo m such that m is a strong a-pseudoprime. These techniques yield a proof of Rabin’s theorem. We conclude the chapter with some observations about designing RSA codes related to strong a-pseudoprime testing.
KeywordsPrime Divisor Primitive Element Great Common Divisor Primitive Root Chinese Remainder Theorem
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