Cyclic Groups and Cryptography

Part of the Undergraduate Texts in Mathematics book series (UTM)

In this chapter we prove the Primitive Root Theorem, which says that if p is prime, there is a unit b of order p − 1 modulo p. This is equivalent to the statement that the group Up of units of ℤ/pℤ is a cyclic group. Then we determine all numbers m for which Um is a cyclic group, and conclude with a look at discrete logarithm cryptography.


Abelian Group Cyclic Group Cyclic Subgroup Pseudorandom Number Discrete Logarithm 
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© Springer-Verlag Berlin Heidelberg 2009

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