A cyclic subgroup is a subset of a group that can be generated by a single element, where every element in the subgroup can be expressed as powers of that element. This concept is foundational in group theory and has significant applications in various fields, particularly in elliptic curve cryptography, where cyclic subgroups play a critical role in constructing secure cryptographic protocols. The structure and properties of cyclic subgroups aid in understanding the larger group and facilitate operations such as encryption and digital signatures.
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