What are the underlying assumptions, especially with regards to the cost to potential attackers, (threat model) of the NIST minimum 112 bits recommendation for US government in 800-63B?

Question

What are the underlying assumptions, especially with regards to the cost to potential attackers, (threat model) of the NIST minimum 112 bits recommendation for US government in 800-63B?

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Answer 1

800-63B is a document written by NIST (National Institute of Standards and Technology) that sets the standard for all government computer systems other than national security services (CIA, FBI etc) The standards are for the cost effective implementation policies for users to access secured systems. They recommend a secret key of 112 bits. 112 bits is the length of the secret key to gain access to the system. The size of a a decimal number able to be stored in 112 bits is :

5,192,296,858,534,827,628,530,496,329,220,096

That number is so large that if someone were to try and brute force (try each unique key one at a time) calculate the secret key it would take so much computer power and time that it would be cost prohibitive for most attackers to attempt.