In the group G = , when the order of an element is the same as order of the group (i.e. f(n)), that element is called the Non - primitive root of the group.

Some number theory concepts used in cryptography are: Modular arithmetic: A system of arithmetic for integers where numbers "wrap around" when they reach a certain value. It's a key ingredient in many public key cryptosystems. Prime numbers: Form the basis for creating secure cryptographic systems. The Chinese remainder theorem: A key concept from number theory used in cryptography. Euler's totient function: A concept from number theory employed in various encryption algorithms.  Number theory also helps in analyzing the security of cryptographic algorithms and detecting potential... Show more

Some number theory concepts used in cryptography are:
Modular arithmetic: A system of arithmetic for integers where numbers "wrap around" when they reach a certain value. It's a key ingredient in many public key cryptosystems.
Prime numbers: Form the basis for creating secure cryptographic systems.
The Chinese remainder theorem: A key concept from number theory used in cryptography.
Euler's totient function: A concept from number theory employed in various encryption algorithms. 

Number theory also helps in analyzing the security of cryptographic algorithms and detecting potential vulnerabilities. 
 

Related Test: Cryptography Practice Test: Basic Concepts in Number Theory and Finite Fields

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