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 U p of units of ℤ/pℤ is a cyclic group. Then we determine all numbers m for which U m is a cyclic group, and conclude with a look at discrete logarithm cryptography.
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© 2009 Springer-Verlag Berlin Heidelberg
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(2009). Cyclic Groups and Cryptography. In: Childs, L.N. (eds) A Concrete Introduction to Higher Algebra. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-74725-5_19
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DOI: https://doi.org/10.1007/978-0-387-74725-5_19
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