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Erschienen in:
2019 | OriginalPaper | Buchkapitel
12. Homomorphisms and Euler’s Phi Function
verfasst von : Lindsay N. Childs
Erschienen in: Cryptology and Error Correction
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Abstract
This chapter introduces some more ideas of abstract algebra: ring homomorphisms, group homomorphisms, the Fundamental Homomorphism Theorem, the direct product of rings or of groups. These concepts provide a suitable setting for proofs of the Chinese Remainder Theorem and for the formula satisfied by Euler’s phi function, which counts the number of units of the ring \(\mathbb {Z}_{m}\) in terms of the factorization of m. Ideas in this chapter will also be used in some of the analyses in Chaps. 14 and 16.